Diff for /imach/src/imach.c between versions 1.48 and 1.140

version 1.48, 2002/06/10 13:12:49 version 1.140, 2011/09/02 10:37:54
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.140  2011/09/02 10:37:54  brouard
      Summary: times.h is ok with mingw32 now.
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    Revision 1.139  2010/06/14 07:50:17  brouard
   first survey ("cross") where individuals from different ages are    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   interviewed on their health status or degree of disability (in the    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.138  2010/04/30 18:19:40  brouard
   (if any) in individual health status.  Health expectancies are    *** empty log message ***
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.137  2010/04/29 18:11:38  brouard
   Maximum Likelihood of the parameters involved in the model.  The    (Module): Checking covariates for more complex models
   simplest model is the multinomial logistic model where pij is the    than V1+V2. A lot of change to be done. Unstable.
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.136  2010/04/26 20:30:53  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    (Module): merging some libgsl code. Fixing computation
   'age' is age and 'sex' is a covariate. If you want to have a more    of likelione (using inter/intrapolation if mle = 0) in order to
   complex model than "constant and age", you should modify the program    get same likelihood as if mle=1.
   where the markup *Covariates have to be included here again* invites    Some cleaning of code and comments added.
   you to do it.  More covariates you add, slower the  
   convergence.    Revision 1.135  2009/10/29 15:33:14  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 1.134  2009/10/29 13:18:53  brouard
   identical for each individual. Also, if a individual missed an    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.133  2009/07/06 10:21:25  brouard
     just nforces
   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 1.132  2009/07/06 08:22:05  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    Many tings
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.131  2009/06/20 16:22:47  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    Some dimensions resccaled
   and the contribution of each individual to the likelihood is simply  
   hPijx.    Revision 1.130  2009/05/26 06:44:34  brouard
     (Module): Max Covariate is now set to 20 instead of 8. A
   Also this programme outputs the covariance matrix of the parameters but also    lot of cleaning with variables initialized to 0. Trying to make
   of the life expectancies. It also computes the prevalence limits.    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.129  2007/08/31 13:49:27  lievre
            Institut national d'études démographiques, Paris.    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.128  2006/06/30 13:02:05  brouard
   It is copyrighted identically to a GNU software product, ie programme and    (Module): Clarifications on computing e.j
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.127  2006/04/28 18:11:50  brouard
   **********************************************************************/    (Module): Yes the sum of survivors was wrong since
      imach-114 because nhstepm was no more computed in the age
 #include <math.h>    loop. Now we define nhstepma in the age loop.
 #include <stdio.h>    (Module): In order to speed up (in case of numerous covariates) we
 #include <stdlib.h>    compute health expectancies (without variances) in a first step
 #include <unistd.h>    and then all the health expectancies with variances or standard
     deviation (needs data from the Hessian matrices) which slows the
 #define MAXLINE 256    computation.
 #define GNUPLOTPROGRAM "gnuplot"    In the future we should be able to stop the program is only health
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    expectancies and graph are needed without standard deviations.
 #define FILENAMELENGTH 80  
 /*#define DEBUG*/    Revision 1.126  2006/04/28 17:23:28  brouard
 #define windows    (Module): Yes the sum of survivors was wrong since
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    imach-114 because nhstepm was no more computed in the age
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    loop. Now we define nhstepma in the age loop.
     Version 0.98h
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 #define NINTERVMAX 8    Forecasting file added.
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.124  2006/03/22 17:13:53  lievre
 #define NCOVMAX 8 /* Maximum number of covariates */    Parameters are printed with %lf instead of %f (more numbers after the comma).
 #define MAXN 20000    The log-likelihood is printed in the log file
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.123  2006/03/20 10:52:43  brouard
 #define AGEBASE 40    * imach.c (Module): <title> changed, corresponds to .htm file
 #ifdef windows    name. <head> headers where missing.
 #define DIRSEPARATOR '\\'  
 #else    * imach.c (Module): Weights can have a decimal point as for
 #define DIRSEPARATOR '/'    English (a comma might work with a correct LC_NUMERIC environment,
 #endif    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    1.
 int erreur; /* Error number */    Version 0.98g
 int nvar;  
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Revision 1.122  2006/03/20 09:45:41  brouard
 int npar=NPARMAX;    (Module): Weights can have a decimal point as for
 int nlstate=2; /* Number of live states */    English (a comma might work with a correct LC_NUMERIC environment,
 int ndeath=1; /* Number of dead states */    otherwise the weight is truncated).
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Modification of warning when the covariates values are not 0 or
 int popbased=0;    1.
     Version 0.98g
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.121  2006/03/16 17:45:01  lievre
 int jmin, jmax; /* min, max spacing between 2 waves */    * imach.c (Module): Comments concerning covariates added
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    * imach.c (Module): refinements in the computation of lli if
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    status=-2 in order to have more reliable computation if stepm is
 double jmean; /* Mean space between 2 waves */    not 1 month. Version 0.98f
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Revision 1.120  2006/03/16 15:10:38  lievre
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    (Module): refinements in the computation of lli if
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    status=-2 in order to have more reliable computation if stepm is
 FILE *fichtm; /* Html File */    not 1 month. Version 0.98f
 FILE *ficreseij;  
 char filerese[FILENAMELENGTH];    Revision 1.119  2006/03/15 17:42:26  brouard
 FILE  *ficresvij;    (Module): Bug if status = -2, the loglikelihood was
 char fileresv[FILENAMELENGTH];    computed as likelihood omitting the logarithm. Version O.98e
 FILE  *ficresvpl;  
 char fileresvpl[FILENAMELENGTH];    Revision 1.118  2006/03/14 18:20:07  brouard
 char title[MAXLINE];    (Module): varevsij Comments added explaining the second
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    table of variances if popbased=1 .
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    (Module): Version 0.98d
   
 char filerest[FILENAMELENGTH];    Revision 1.117  2006/03/14 17:16:22  brouard
 char fileregp[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
 char popfile[FILENAMELENGTH];    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    (Module): Function pstamp added
     (Module): Version 0.98d
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.116  2006/03/06 10:29:27  brouard
 #define FTOL 1.0e-10    (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 #define NRANSI  
 #define ITMAX 200    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
 #define TOL 2.0e-4  
     Revision 1.114  2006/02/26 12:57:58  brouard
 #define CGOLD 0.3819660    (Module): Some improvements in processing parameter
 #define ZEPS 1.0e-10    filename with strsep.
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     Revision 1.113  2006/02/24 14:20:24  brouard
 #define GOLD 1.618034    (Module): Memory leaks checks with valgrind and:
 #define GLIMIT 100.0    datafile was not closed, some imatrix were not freed and on matrix
 #define TINY 1.0e-20    allocation too.
   
 static double maxarg1,maxarg2;    Revision 1.112  2006/01/30 09:55:26  brouard
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.111  2006/01/25 20:38:18  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): Lots of cleaning and bugs added (Gompertz)
 #define rint(a) floor(a+0.5)    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.110  2006/01/25 00:51:50  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): Lots of cleaning and bugs added (Gompertz)
   
 int imx;    Revision 1.109  2006/01/24 19:37:15  brouard
 int stepm;    (Module): Comments (lines starting with a #) are allowed in data.
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.108  2006/01/19 18:05:42  lievre
 int estepm;    Gnuplot problem appeared...
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    To be fixed
   
 int m,nb;    Revision 1.107  2006/01/19 16:20:37  brouard
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Test existence of gnuplot in imach path
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.106  2006/01/19 13:24:36  brouard
 double dateintmean=0;    Some cleaning and links added in html output
   
 double *weight;    Revision 1.105  2006/01/05 20:23:19  lievre
 int **s; /* Status */    *** empty log message ***
 double *agedc, **covar, idx;  
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    (Module): If the status is missing at the last wave but we know
 double ftolhess; /* Tolerance for computing hessian */    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 /**************** split *************************/    contributions to the likelihood is 1 - Prob of dying from last
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 {    the healthy state at last known wave). Version is 0.98
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */    Revision 1.103  2005/09/30 15:54:49  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.102  2004/09/15 17:31:30  brouard
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */    Add the possibility to read data file including tab characters.
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.101  2004/09/15 10:38:38  brouard
       extern char       *getwd( );    Fix on curr_time
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.100  2004/07/12 18:29:06  brouard
 #else    Add version for Mac OS X. Just define UNIX in Makefile
       extern char       *getcwd( );  
     Revision 1.99  2004/06/05 08:57:40  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    *** empty log message ***
 #endif  
          return( GLOCK_ERROR_GETCWD );    Revision 1.98  2004/05/16 15:05:56  brouard
       }    New version 0.97 . First attempt to estimate force of mortality
       strcpy( name, path );             /* we've got it */    directly from the data i.e. without the need of knowing the health
    } else {                             /* strip direcotry from path */    state at each age, but using a Gompertz model: log u =a + b*age .
       s++;                              /* after this, the filename */    This is the basic analysis of mortality and should be done before any
       l2 = strlen( s );                 /* length of filename */    other analysis, in order to test if the mortality estimated from the
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    cross-longitudinal survey is different from the mortality estimated
       strcpy( name, s );                /* save file name */    from other sources like vital statistic data.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */  
       dirc[l1-l2] = 0;                  /* add zero */    The same imach parameter file can be used but the option for mle should be -3.
    }  
    l1 = strlen( dirc );                 /* length of directory */    Agnès, who wrote this part of the code, tried to keep most of the
 #ifdef windows    former routines in order to include the new code within the former code.
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    The output is very simple: only an estimate of the intercept and of
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    the slope with 95% confident intervals.
 #endif  
    s = strrchr( name, '.' );            /* find last / */    Current limitations:
    s++;    A) Even if you enter covariates, i.e. with the
    strcpy(ext,s);                       /* save extension */    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
    l1= strlen( name);    B) There is no computation of Life Expectancy nor Life Table.
    l2= strlen( s)+1;  
    strncpy( finame, name, l1-l2);    Revision 1.97  2004/02/20 13:25:42  lievre
    finame[l1-l2]= 0;    Version 0.96d. Population forecasting command line is (temporarily)
    return( 0 );                         /* we're done */    suppressed.
 }  
     Revision 1.96  2003/07/15 15:38:55  brouard
     * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 /******************************************/    rewritten within the same printf. Workaround: many printfs.
   
 void replace(char *s, char*t)    Revision 1.95  2003/07/08 07:54:34  brouard
 {    * imach.c (Repository):
   int i;    (Repository): Using imachwizard code to output a more meaningful covariance
   int lg=20;    matrix (cov(a12,c31) instead of numbers.
   i=0;  
   lg=strlen(t);    Revision 1.94  2003/06/27 13:00:02  brouard
   for(i=0; i<= lg; i++) {    Just cleaning
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.93  2003/06/25 16:33:55  brouard
   }    (Module): On windows (cygwin) function asctime_r doesn't
 }    exist so I changed back to asctime which exists.
     (Module): Version 0.96b
 int nbocc(char *s, char occ)  
 {    Revision 1.92  2003/06/25 16:30:45  brouard
   int i,j=0;    (Module): On windows (cygwin) function asctime_r doesn't
   int lg=20;    exist so I changed back to asctime which exists.
   i=0;  
   lg=strlen(s);    Revision 1.91  2003/06/25 15:30:29  brouard
   for(i=0; i<= lg; i++) {    * imach.c (Repository): Duplicated warning errors corrected.
   if  (s[i] == occ ) j++;    (Repository): Elapsed time after each iteration is now output. It
   }    helps to forecast when convergence will be reached. Elapsed time
   return j;    is stamped in powell.  We created a new html file for the graphs
 }    concerning matrix of covariance. It has extension -cov.htm.
   
 void cutv(char *u,char *v, char*t, char occ)    Revision 1.90  2003/06/24 12:34:15  brouard
 {    (Module): Some bugs corrected for windows. Also, when
   int i,lg,j,p=0;    mle=-1 a template is output in file "or"mypar.txt with the design
   i=0;    of the covariance matrix to be input.
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    Revision 1.89  2003/06/24 12:30:52  brouard
   }    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
   lg=strlen(t);    of the covariance matrix to be input.
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);    Revision 1.88  2003/06/23 17:54:56  brouard
   }    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
      u[p]='\0';  
     Revision 1.87  2003/06/18 12:26:01  brouard
    for(j=0; j<= lg; j++) {    Version 0.96
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }    Revision 1.86  2003/06/17 20:04:08  brouard
 }    (Module): Change position of html and gnuplot routines and added
     routine fileappend.
 /********************** nrerror ********************/  
     Revision 1.85  2003/06/17 13:12:43  brouard
 void nrerror(char error_text[])    * imach.c (Repository): Check when date of death was earlier that
 {    current date of interview. It may happen when the death was just
   fprintf(stderr,"ERREUR ...\n");    prior to the death. In this case, dh was negative and likelihood
   fprintf(stderr,"%s\n",error_text);    was wrong (infinity). We still send an "Error" but patch by
   exit(1);    assuming that the date of death was just one stepm after the
 }    interview.
 /*********************** vector *******************/    (Repository): Because some people have very long ID (first column)
 double *vector(int nl, int nh)    we changed int to long in num[] and we added a new lvector for
 {    memory allocation. But we also truncated to 8 characters (left
   double *v;    truncation)
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Repository): No more line truncation errors.
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;    Revision 1.84  2003/06/13 21:44:43  brouard
 }    * imach.c (Repository): Replace "freqsummary" at a correct
     place. It differs from routine "prevalence" which may be called
 /************************ free vector ******************/    many times. Probs is memory consuming and must be used with
 void free_vector(double*v, int nl, int nh)    parcimony.
 {    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Revision 1.82  2003/06/05 15:57:20  brouard
 {    Add log in  imach.c and  fullversion number is now printed.
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  */
   if (!v) nrerror("allocation failure in ivector");  /*
   return v-nl+NR_END;     Interpolated Markov Chain
 }  
     Short summary of the programme:
 /******************free ivector **************************/    
 void free_ivector(int *v, long nl, long nh)    This program computes Healthy Life Expectancies from
 {    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   free((FREE_ARG)(v+nl-NR_END));    first survey ("cross") where individuals from different ages are
 }    interviewed on their health status or degree of disability (in the
     case of a health survey which is our main interest) -2- at least a
 /******************* imatrix *******************************/    second wave of interviews ("longitudinal") which measure each change
 int **imatrix(long nrl, long nrh, long ncl, long nch)    (if any) in individual health status.  Health expectancies are
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    computed from the time spent in each health state according to a
 {    model. More health states you consider, more time is necessary to reach the
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Maximum Likelihood of the parameters involved in the model.  The
   int **m;    simplest model is the multinomial logistic model where pij is the
      probability to be observed in state j at the second wave
   /* allocate pointers to rows */    conditional to be observed in state i at the first wave. Therefore
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   if (!m) nrerror("allocation failure 1 in matrix()");    'age' is age and 'sex' is a covariate. If you want to have a more
   m += NR_END;    complex model than "constant and age", you should modify the program
   m -= nrl;    where the markup *Covariates have to be included here again* invites
      you to do it.  More covariates you add, slower the
      convergence.
   /* allocate rows and set pointers to them */  
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    The advantage of this computer programme, compared to a simple
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    multinomial logistic model, is clear when the delay between waves is not
   m[nrl] += NR_END;    identical for each individual. Also, if a individual missed an
   m[nrl] -= ncl;    intermediate interview, the information is lost, but taken into
      account using an interpolation or extrapolation.  
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
      hPijx is the probability to be observed in state i at age x+h
   /* return pointer to array of pointers to rows */    conditional to the observed state i at age x. The delay 'h' can be
   return m;    split into an exact number (nh*stepm) of unobserved intermediate
 }    states. This elementary transition (by month, quarter,
     semester or year) is modelled as a multinomial logistic.  The hPx
 /****************** free_imatrix *************************/    matrix is simply the matrix product of nh*stepm elementary matrices
 void free_imatrix(m,nrl,nrh,ncl,nch)    and the contribution of each individual to the likelihood is simply
       int **m;    hPijx.
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */    Also this programme outputs the covariance matrix of the parameters but also
 {    of the life expectancies. It also computes the period (stable) prevalence. 
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    
   free((FREE_ARG) (m+nrl-NR_END));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 }             Institut national d'études démographiques, Paris.
     This software have been partly granted by Euro-REVES, a concerted action
 /******************* matrix *******************************/    from the European Union.
 double **matrix(long nrl, long nrh, long ncl, long nch)    It is copyrighted identically to a GNU software product, ie programme and
 {    software can be distributed freely for non commercial use. Latest version
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    can be accessed at http://euroreves.ined.fr/imach .
   double **m;  
     Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   if (!m) nrerror("allocation failure 1 in matrix()");    
   m += NR_END;    **********************************************************************/
   m -= nrl;  /*
     main
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    read parameterfile
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    read datafile
   m[nrl] += NR_END;    concatwav
   m[nrl] -= ncl;    freqsummary
     if (mle >= 1)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;      mlikeli
   return m;    print results files
 }    if mle==1 
        computes hessian
 /*************************free matrix ************************/    read end of parameter file: agemin, agemax, bage, fage, estepm
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)        begin-prev-date,...
 {    open gnuplot file
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    open html file
   free((FREE_ARG)(m+nrl-NR_END));    period (stable) prevalence
 }     for age prevalim()
     h Pij x
 /******************* ma3x *******************************/    variance of p varprob
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    forecasting if prevfcast==1 prevforecast call prevalence()
 {    health expectancies
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    Variance-covariance of DFLE
   double ***m;    prevalence()
      movingaverage()
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    varevsij() 
   if (!m) nrerror("allocation failure 1 in matrix()");    if popbased==1 varevsij(,popbased)
   m += NR_END;    total life expectancies
   m -= nrl;    Variance of period (stable) prevalence
    end
   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;  
   m[nrl] -= ncl;  
    
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include <math.h>
   #include <stdio.h>
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #include <stdlib.h>
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #include <string.h>
   m[nrl][ncl] += NR_END;  #include <unistd.h>
   m[nrl][ncl] -= nll;  
   for (j=ncl+1; j<=nch; j++)  #include <limits.h>
     m[nrl][j]=m[nrl][j-1]+nlay;  #include <sys/types.h>
    #include <sys/stat.h>
   for (i=nrl+1; i<=nrh; i++) {  #include <errno.h>
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  extern int errno;
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;  #include <sys/time.h>
   }  /*
   return m;  #include <time.h>
 }  #include "timeval.h"
   
 /*************************free ma3x ************************/  #ifdef GSL
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #include <gsl/gsl_errno.h>
 {  #include <gsl/gsl_multimin.h>
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #endif
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  /* #include <libintl.h> */
 }  /* #define _(String) gettext (String) */
   
 /***************** f1dim *************************/  #define MAXLINE 256
 extern int ncom;  
 extern double *pcom,*xicom;  #define GNUPLOTPROGRAM "gnuplot"
 extern double (*nrfunc)(double []);  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
    #define FILENAMELENGTH 132
 double f1dim(double x)  
 {  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   int j;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   double f;  
   double *xt;  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
    #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   xt=vector(1,ncom);  
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define NINTERVMAX 8
   f=(*nrfunc)(xt);  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   free_vector(xt,1,ncom);  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   return f;  #define NCOVMAX 20 /* Maximum number of covariates */
 }  #define MAXN 20000
   #define YEARM 12. /* Number of months per year */
 /*****************brent *************************/  #define AGESUP 130
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #define AGEBASE 40
 {  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   int iter;  #ifdef UNIX
   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;  #else
   double e=0.0;  #define DIRSEPARATOR '\\'
    #define CHARSEPARATOR "\\"
   a=(ax < cx ? ax : cx);  #define ODIRSEPARATOR '/'
   b=(ax > cx ? ax : cx);  #endif
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);  /* $Id$ */
   for (iter=1;iter<=ITMAX;iter++) {  /* $State$ */
     xm=0.5*(a+b);  
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  char fullversion[]="$Revision$ $Date$"; 
     printf(".");fflush(stdout);  char strstart[80];
 #ifdef DEBUG  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     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 erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int nvar=0, nforce=0; /* Number of variables, number of forces */
 #endif  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int npar=NPARMAX;
       *xmin=x;  int nlstate=2; /* Number of live states */
       return fx;  int ndeath=1; /* Number of dead states */
     }  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
     ftemp=fu;  int popbased=0;
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  int *wav; /* Number of waves for this individuual 0 is possible */
       q=(x-v)*(fx-fw);  int maxwav=0; /* Maxim number of waves */
       p=(x-v)*q-(x-w)*r;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       q=2.0*(q-r);  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       if (q > 0.0) p = -p;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       q=fabs(q);                     to the likelihood and the sum of weights (done by funcone)*/
       etemp=e;  int mle=1, weightopt=0;
       e=d;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       else {             * wave mi and wave mi+1 is not an exact multiple of stepm. */
         d=p/q;  double jmean=1; /* Mean space between 2 waves */
         u=x+d;  double **oldm, **newm, **savm; /* Working pointers to matrices */
         if (u-a < tol2 || b-u < tol2)  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
           d=SIGN(tol1,xm-x);  /*FILE *fic ; */ /* Used in readdata only */
       }  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     } else {  FILE *ficlog, *ficrespow;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  int globpr=0; /* Global variable for printing or not */
     }  double fretone; /* Only one call to likelihood */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  long ipmx=0; /* Number of contributions */
     fu=(*f)(u);  double sw; /* Sum of weights */
     if (fu <= fx) {  char filerespow[FILENAMELENGTH];
       if (u >= x) a=x; else b=x;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       SHFT(v,w,x,u)  FILE *ficresilk;
         SHFT(fv,fw,fx,fu)  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
         } else {  FILE *ficresprobmorprev;
           if (u < x) a=u; else b=u;  FILE *fichtm, *fichtmcov; /* Html File */
           if (fu <= fw || w == x) {  FILE *ficreseij;
             v=w;  char filerese[FILENAMELENGTH];
             w=u;  FILE *ficresstdeij;
             fv=fw;  char fileresstde[FILENAMELENGTH];
             fw=fu;  FILE *ficrescveij;
           } else if (fu <= fv || v == x || v == w) {  char filerescve[FILENAMELENGTH];
             v=u;  FILE  *ficresvij;
             fv=fu;  char fileresv[FILENAMELENGTH];
           }  FILE  *ficresvpl;
         }  char fileresvpl[FILENAMELENGTH];
   }  char title[MAXLINE];
   nrerror("Too many iterations in brent");  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   *xmin=x;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   return fx;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
 }  char command[FILENAMELENGTH];
   int  outcmd=0;
 /****************** mnbrak ***********************/  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  char filelog[FILENAMELENGTH]; /* Log file */
 {  char filerest[FILENAMELENGTH];
   double ulim,u,r,q, dum;  char fileregp[FILENAMELENGTH];
   double fu;  char popfile[FILENAMELENGTH];
    
   *fa=(*func)(*ax);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     SHFT(dum,*ax,*bx,dum)  struct timezone tzp;
       SHFT(dum,*fb,*fa,dum)  extern int gettimeofday();
       }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   *cx=(*bx)+GOLD*(*bx-*ax);  long time_value;
   *fc=(*func)(*cx);  extern long time();
   while (*fb > *fc) {  char strcurr[80], strfor[80];
     r=(*bx-*ax)*(*fb-*fc);  
     q=(*bx-*cx)*(*fb-*fa);  char *endptr;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  long lval;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  double dval;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  
     if ((*bx-u)*(u-*cx) > 0.0) {  #define NR_END 1
       fu=(*func)(u);  #define FREE_ARG char*
     } else if ((*cx-u)*(u-ulim) > 0.0) {  #define FTOL 1.0e-10
       fu=(*func)(u);  
       if (fu < *fc) {  #define NRANSI 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define ITMAX 200 
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  #define TOL 2.0e-4 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  #define CGOLD 0.3819660 
       fu=(*func)(u);  #define ZEPS 1.0e-10 
     } else {  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       u=(*cx)+GOLD*(*cx-*bx);  
       fu=(*func)(u);  #define GOLD 1.618034 
     }  #define GLIMIT 100.0 
     SHFT(*ax,*bx,*cx,u)  #define TINY 1.0e-20 
       SHFT(*fa,*fb,*fc,fu)  
       }  static double maxarg1,maxarg2;
 }  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 /*************** linmin ************************/    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 int ncom;  #define rint(a) floor(a+0.5)
 double *pcom,*xicom;  
 double (*nrfunc)(double []);  static double sqrarg;
    #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 {  int agegomp= AGEGOMP;
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  int imx; 
   double f1dim(double x);  int stepm=1;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  /* Stepm, step in month: minimum step interpolation*/
               double *fc, double (*func)(double));  
   int j;  int estepm;
   double xx,xmin,bx,ax;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   double fx,fb,fa;  
    int m,nb;
   ncom=n;  long *num;
   pcom=vector(1,n);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   xicom=vector(1,n);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   nrfunc=func;  double **pmmij, ***probs;
   for (j=1;j<=n;j++) {  double *ageexmed,*agecens;
     pcom[j]=p[j];  double dateintmean=0;
     xicom[j]=xi[j];  
   }  double *weight;
   ax=0.0;  int **s; /* Status */
   xx=1.0;  double *agedc, **covar, idx;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  double *lsurv, *lpop, *tpop;
 #ifdef DEBUG  
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 #endif  double ftolhess; /* Tolerance for computing hessian */
   for (j=1;j<=n;j++) {  
     xi[j] *= xmin;  /**************** split *************************/
     p[j] += xi[j];  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   }  {
   free_vector(xicom,1,n);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   free_vector(pcom,1,n);       the name of the file (name), its extension only (ext) and its first part of the name (finame)
 }    */ 
     char  *ss;                            /* pointer */
 /*************** powell ************************/    int   l1, l2;                         /* length counters */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  
             double (*func)(double []))    l1 = strlen(path );                   /* length of path */
 {    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   void linmin(double p[], double xi[], int n, double *fret,    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
               double (*func)(double []));    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   int i,ibig,j;      strcpy( name, path );               /* we got the fullname name because no directory */
   double del,t,*pt,*ptt,*xit;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   double fp,fptt;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   double *xits;      /* get current working directory */
   pt=vector(1,n);      /*    extern  char* getcwd ( char *buf , int len);*/
   ptt=vector(1,n);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   xit=vector(1,n);        return( GLOCK_ERROR_GETCWD );
   xits=vector(1,n);      }
   *fret=(*func)(p);      /* got dirc from getcwd*/
   for (j=1;j<=n;j++) pt[j]=p[j];      printf(" DIRC = %s \n",dirc);
   for (*iter=1;;++(*iter)) {    } else {                              /* strip direcotry from path */
     fp=(*fret);      ss++;                               /* after this, the filename */
     ibig=0;      l2 = strlen( ss );                  /* length of filename */
     del=0.0;      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      strcpy( name, ss );         /* save file name */
     for (i=1;i<=n;i++)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       printf(" %d %.12f",i, p[i]);      dirc[l1-l2] = 0;                    /* add zero */
     printf("\n");      printf(" DIRC2 = %s \n",dirc);
     for (i=1;i<=n;i++) {    }
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    /* We add a separator at the end of dirc if not exists */
       fptt=(*fret);    l1 = strlen( dirc );                  /* length of directory */
 #ifdef DEBUG    if( dirc[l1-1] != DIRSEPARATOR ){
       printf("fret=%lf \n",*fret);      dirc[l1] =  DIRSEPARATOR;
 #endif      dirc[l1+1] = 0; 
       printf("%d",i);fflush(stdout);      printf(" DIRC3 = %s \n",dirc);
       linmin(p,xit,n,fret,func);    }
       if (fabs(fptt-(*fret)) > del) {    ss = strrchr( name, '.' );            /* find last / */
         del=fabs(fptt-(*fret));    if (ss >0){
         ibig=i;      ss++;
       }      strcpy(ext,ss);                     /* save extension */
 #ifdef DEBUG      l1= strlen( name);
       printf("%d %.12e",i,(*fret));      l2= strlen(ss)+1;
       for (j=1;j<=n;j++) {      strncpy( finame, name, l1-l2);
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);      finame[l1-l2]= 0;
         printf(" x(%d)=%.12e",j,xit[j]);    }
       }  
       for(j=1;j<=n;j++)    return( 0 );                          /* we're done */
         printf(" p=%.12e",p[j]);  }
       printf("\n");  
 #endif  
     }  /******************************************/
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG  void replace_back_to_slash(char *s, char*t)
       int k[2],l;  {
       k[0]=1;    int i;
       k[1]=-1;    int lg=0;
       printf("Max: %.12e",(*func)(p));    i=0;
       for (j=1;j<=n;j++)    lg=strlen(t);
         printf(" %.12e",p[j]);    for(i=0; i<= lg; i++) {
       printf("\n");      (s[i] = t[i]);
       for(l=0;l<=1;l++) {      if (t[i]== '\\') s[i]='/';
         for (j=1;j<=n;j++) {    }
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  }
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  
         }  char *trimbb(char *out, char *in)
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
       }    char *s;
 #endif    s=out;
     while (*in != '\0'){
       while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
       free_vector(xit,1,n);        in++;
       free_vector(xits,1,n);      }
       free_vector(ptt,1,n);      *out++ = *in++;
       free_vector(pt,1,n);    }
       return;    *out='\0';
     }    return s;
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  }
     for (j=1;j<=n;j++) {  
       ptt[j]=2.0*p[j]-pt[j];  char *cutv(char *blocc, char *alocc, char *in, char occ)
       xit[j]=p[j]-pt[j];  {
       pt[j]=p[j];    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
     }       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
     fptt=(*func)(ptt);       gives blocc="abcdef2ghi" and alocc="j".
     if (fptt < fp) {       If occ is not found blocc is null and alocc is equal to in. Returns alocc
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    */
       if (t < 0.0) {    char *s, *t;
         linmin(p,xit,n,fret,func);    t=in;s=in;
         for (j=1;j<=n;j++) {    while (*in != '\0'){
           xi[j][ibig]=xi[j][n];      while( *in == occ){
           xi[j][n]=xit[j];        *blocc++ = *in++;
         }        s=in;
 #ifdef DEBUG      }
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      *blocc++ = *in++;
         for(j=1;j<=n;j++)    }
           printf(" %.12e",xit[j]);    if (s == t) /* occ not found */
         printf("\n");      *(blocc-(in-s))='\0';
 #endif    else
       }      *(blocc-(in-s)-1)='\0';
     }    in=s;
   }    while ( *in != '\0'){
 }      *alocc++ = *in++;
     }
 /**** Prevalence limit ****************/  
     *alocc='\0';
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    return s;
 {  }
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  
      matrix by transitions matrix until convergence is reached */  int nbocc(char *s, char occ)
   {
   int i, ii,j,k;    int i,j=0;
   double min, max, maxmin, maxmax,sumnew=0.;    int lg=20;
   double **matprod2();    i=0;
   double **out, cov[NCOVMAX], **pmij();    lg=strlen(s);
   double **newm;    for(i=0; i<= lg; i++) {
   double agefin, delaymax=50 ; /* Max number of years to converge */    if  (s[i] == occ ) j++;
     }
   for (ii=1;ii<=nlstate+ndeath;ii++)    return j;
     for (j=1;j<=nlstate+ndeath;j++){  }
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  /* void cutv(char *u,char *v, char*t, char occ) */
   /* { */
    cov[1]=1.;  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
    /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  /*      gives u="abcdef2ghi" and v="j" *\/ */
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  /*   int i,lg,j,p=0; */
     newm=savm;  /*   i=0; */
     /* Covariates have to be included here again */  /*   lg=strlen(t); */
      cov[2]=agefin;  /*   for(j=0; j<=lg-1; j++) { */
    /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
       for (k=1; k<=cptcovn;k++) {  /*   } */
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  
         /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/  /*   for(j=0; j<p; j++) { */
       }  /*     (u[j] = t[j]); */
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  /*   } */
       for (k=1; k<=cptcovprod;k++)  /*      u[p]='\0'; */
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  
   /*    for(j=0; j<= lg; j++) { */
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  /*   } */
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  /* } */
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  
   /********************** nrerror ********************/
     savm=oldm;  
     oldm=newm;  void nrerror(char error_text[])
     maxmax=0.;  {
     for(j=1;j<=nlstate;j++){    fprintf(stderr,"ERREUR ...\n");
       min=1.;    fprintf(stderr,"%s\n",error_text);
       max=0.;    exit(EXIT_FAILURE);
       for(i=1; i<=nlstate; i++) {  }
         sumnew=0;  /*********************** vector *******************/
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  double *vector(int nl, int nh)
         prlim[i][j]= newm[i][j]/(1-sumnew);  {
         max=FMAX(max,prlim[i][j]);    double *v;
         min=FMIN(min,prlim[i][j]);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       }    if (!v) nrerror("allocation failure in vector");
       maxmin=max-min;    return v-nl+NR_END;
       maxmax=FMAX(maxmax,maxmin);  }
     }  
     if(maxmax < ftolpl){  /************************ free vector ******************/
       return prlim;  void free_vector(double*v, int nl, int nh)
     }  {
   }    free((FREE_ARG)(v+nl-NR_END));
 }  }
   
 /*************** transition probabilities ***************/  /************************ivector *******************************/
   int *ivector(long nl,long nh)
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  {
 {    int *v;
   double s1, s2;    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   /*double t34;*/    if (!v) nrerror("allocation failure in ivector");
   int i,j,j1, nc, ii, jj;    return v-nl+NR_END;
   }
     for(i=1; i<= nlstate; i++){  
     for(j=1; j<i;j++){  /******************free ivector **************************/
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  void free_ivector(int *v, long nl, long nh)
         /*s2 += param[i][j][nc]*cov[nc];*/  {
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    free((FREE_ARG)(v+nl-NR_END));
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  }
       }  
       ps[i][j]=s2;  /************************lvector *******************************/
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  long *lvector(long nl,long nh)
     }  {
     for(j=i+1; j<=nlstate+ndeath;j++){    long *v;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    if (!v) nrerror("allocation failure in ivector");
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    return v-nl+NR_END;
       }  }
       ps[i][j]=s2;  
     }  /******************free lvector **************************/
   }  void free_lvector(long *v, long nl, long nh)
     /*ps[3][2]=1;*/  {
     free((FREE_ARG)(v+nl-NR_END));
   for(i=1; i<= nlstate; i++){  }
      s1=0;  
     for(j=1; j<i; j++)  /******************* imatrix *******************************/
       s1+=exp(ps[i][j]);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     for(j=i+1; j<=nlstate+ndeath; j++)       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       s1+=exp(ps[i][j]);  { 
     ps[i][i]=1./(s1+1.);    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     for(j=1; j<i; j++)    int **m; 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    
     for(j=i+1; j<=nlstate+ndeath; j++)    /* allocate pointers to rows */ 
       ps[i][j]= exp(ps[i][j])*ps[i][i];    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    if (!m) nrerror("allocation failure 1 in matrix()"); 
   } /* end i */    m += NR_END; 
     m -= nrl; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    
     for(jj=1; jj<= nlstate+ndeath; jj++){    
       ps[ii][jj]=0;    /* allocate rows and set pointers to them */ 
       ps[ii][ii]=1;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   }    m[nrl] += NR_END; 
     m[nrl] -= ncl; 
     
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     for(jj=1; jj<= nlstate+ndeath; jj++){    
      printf("%lf ",ps[ii][jj]);    /* return pointer to array of pointers to rows */ 
    }    return m; 
     printf("\n ");  } 
     }  
     printf("\n ");printf("%lf ",cov[2]);*/  /****************** free_imatrix *************************/
 /*  void free_imatrix(m,nrl,nrh,ncl,nch)
   for(i=1; i<= npar; i++) printf("%f ",x[i]);        int **m;
   goto end;*/        long nch,ncl,nrh,nrl; 
     return ps;       /* free an int matrix allocated by imatrix() */ 
 }  { 
     free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 /**************** Product of 2 matrices ******************/    free((FREE_ARG) (m+nrl-NR_END)); 
   } 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  
 {  /******************* matrix *******************************/
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  double **matrix(long nrl, long nrh, long ncl, long nch)
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  {
   /* in, b, out are matrice of pointers which should have been initialized    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
      before: only the contents of out is modified. The function returns    double **m;
      a pointer to pointers identical to out */  
   long i, j, k;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   for(i=nrl; i<= nrh; i++)    if (!m) nrerror("allocation failure 1 in matrix()");
     for(k=ncolol; k<=ncoloh; k++)    m += NR_END;
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    m -= nrl;
         out[i][k] +=in[i][j]*b[j][k];  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   return out;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 }    m[nrl] += NR_END;
     m[nrl] -= ncl;
   
 /************* Higher Matrix Product ***************/    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     return m;
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
 {     */
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  }
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  /*************************free matrix ************************/
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
      (typically every 2 years instead of every month which is too big).  {
      Model is determined by parameters x and covariates have to be    free((FREE_ARG)(m[nrl]+ncl-NR_END));
      included manually here.    free((FREE_ARG)(m+nrl-NR_END));
   }
      */  
   /******************* ma3x *******************************/
   int i, j, d, h, k;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   double **out, cov[NCOVMAX];  {
   double **newm;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     double ***m;
   /* Hstepm could be zero and should return the unit matrix */  
   for (i=1;i<=nlstate+ndeath;i++)    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     for (j=1;j<=nlstate+ndeath;j++){    if (!m) nrerror("allocation failure 1 in matrix()");
       oldm[i][j]=(i==j ? 1.0 : 0.0);    m += NR_END;
       po[i][j][0]=(i==j ? 1.0 : 0.0);    m -= nrl;
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   for(h=1; h <=nhstepm; h++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     for(d=1; d <=hstepm; d++){    m[nrl] += NR_END;
       newm=savm;    m[nrl] -= ncl;
       /* Covariates have to be included here again */  
       cov[1]=1.;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       for (k=1; k<=cptcovage;k++)    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m[nrl][ncl] += NR_END;
       for (k=1; k<=cptcovprod;k++)    m[nrl][ncl] -= nll;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for (j=ncl+1; j<=nch; j++) 
       m[nrl][j]=m[nrl][j-1]+nlay;
     
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    for (i=nrl+1; i<=nrh; i++) {
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,      for (j=ncl+1; j<=nch; j++) 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        m[i][j]=m[i][j-1]+nlay;
       savm=oldm;    }
       oldm=newm;    return m; 
     }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     for(i=1; i<=nlstate+ndeath; i++)             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       for(j=1;j<=nlstate+ndeath;j++) {    */
         po[i][j][h]=newm[i][j];  }
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  
          */  /*************************free ma3x ************************/
       }  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   } /* end h */  {
   return po;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
 }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     free((FREE_ARG)(m+nrl-NR_END));
   }
 /*************** log-likelihood *************/  
 double func( double *x)  /*************** function subdirf ***********/
 {  char *subdirf(char fileres[])
   int i, ii, j, k, mi, d, kk;  {
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    /* Caution optionfilefiname is hidden */
   double **out;    strcpy(tmpout,optionfilefiname);
   double sw; /* Sum of weights */    strcat(tmpout,"/"); /* Add to the right */
   double lli; /* Individual log likelihood */    strcat(tmpout,fileres);
   long ipmx;    return tmpout;
   /*extern weight */  }
   /* We are differentiating ll according to initial status */  
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  /*************** function subdirf2 ***********/
   /*for(i=1;i<imx;i++)  char *subdirf2(char fileres[], char *preop)
     printf(" %d\n",s[4][i]);  {
   */    
   cov[1]=1.;    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   for(k=1; k<=nlstate; k++) ll[k]=0.;    strcat(tmpout,"/");
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    strcat(tmpout,preop);
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    strcat(tmpout,fileres);
     for(mi=1; mi<= wav[i]-1; mi++){    return tmpout;
       for (ii=1;ii<=nlstate+ndeath;ii++)  }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
       for(d=0; d<dh[mi][i]; d++){  /*************** function subdirf3 ***********/
         newm=savm;  char *subdirf3(char fileres[], char *preop, char *preop2)
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  {
         for (kk=1; kk<=cptcovage;kk++) {    
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    /* Caution optionfilefiname is hidden */
         }    strcpy(tmpout,optionfilefiname);
            strcat(tmpout,"/");
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    strcat(tmpout,preop);
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    strcat(tmpout,preop2);
         savm=oldm;    strcat(tmpout,fileres);
         oldm=newm;    return tmpout;
          }
          
       } /* end mult */  /***************** f1dim *************************/
        extern int ncom; 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  extern double *pcom,*xicom;
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  extern double (*nrfunc)(double []); 
       ipmx +=1;   
       sw += weight[i];  double f1dim(double x) 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  { 
     } /* end of wave */    int j; 
   } /* end of individual */    double f;
     double *xt; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];   
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    xt=vector(1,ncom); 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   return -l;    f=(*nrfunc)(xt); 
 }    free_vector(xt,1,ncom); 
     return f; 
   } 
 /*********** Maximum Likelihood Estimation ***************/  
   /*****************brent *************************/
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
 {  { 
   int i,j, iter;    int iter; 
   double **xi,*delti;    double a,b,d,etemp;
   double fret;    double fu,fv,fw,fx;
   xi=matrix(1,npar,1,npar);    double ftemp;
   for (i=1;i<=npar;i++)    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     for (j=1;j<=npar;j++)    double e=0.0; 
       xi[i][j]=(i==j ? 1.0 : 0.0);   
   printf("Powell\n");    a=(ax < cx ? ax : cx); 
   powell(p,xi,npar,ftol,&iter,&fret,func);    b=(ax > cx ? ax : cx); 
     x=w=v=bx; 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    fw=fv=fx=(*f)(x); 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    for (iter=1;iter<=ITMAX;iter++) { 
       xm=0.5*(a+b); 
 }      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
 /**** Computes Hessian and covariance matrix ***/      printf(".");fflush(stdout);
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      fprintf(ficlog,".");fflush(ficlog);
 {  #ifdef DEBUG
   double  **a,**y,*x,pd;      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);
   double **hess;      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);
   int i, j,jk;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   int *indx;  #endif
       if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   double hessii(double p[], double delta, int theta, double delti[]);        *xmin=x; 
   double hessij(double p[], double delti[], int i, int j);        return fx; 
   void lubksb(double **a, int npar, int *indx, double b[]) ;      } 
   void ludcmp(double **a, int npar, int *indx, double *d) ;      ftemp=fu;
       if (fabs(e) > tol1) { 
   hess=matrix(1,npar,1,npar);        r=(x-w)*(fx-fv); 
         q=(x-v)*(fx-fw); 
   printf("\nCalculation of the hessian matrix. Wait...\n");        p=(x-v)*q-(x-w)*r; 
   for (i=1;i<=npar;i++){        q=2.0*(q-r); 
     printf("%d",i);fflush(stdout);        if (q > 0.0) p = -p; 
     hess[i][i]=hessii(p,ftolhess,i,delti);        q=fabs(q); 
     /*printf(" %f ",p[i]);*/        etemp=e; 
     /*printf(" %lf ",hess[i][i]);*/        e=d; 
   }        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
            d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   for (i=1;i<=npar;i++) {        else { 
     for (j=1;j<=npar;j++)  {          d=p/q; 
       if (j>i) {          u=x+d; 
         printf(".%d%d",i,j);fflush(stdout);          if (u-a < tol2 || b-u < tol2) 
         hess[i][j]=hessij(p,delti,i,j);            d=SIGN(tol1,xm-x); 
         hess[j][i]=hess[i][j];            } 
         /*printf(" %lf ",hess[i][j]);*/      } else { 
       }        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     }      } 
   }      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   printf("\n");      fu=(*f)(u); 
       if (fu <= fx) { 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        if (u >= x) a=x; else b=x; 
          SHFT(v,w,x,u) 
   a=matrix(1,npar,1,npar);          SHFT(fv,fw,fx,fu) 
   y=matrix(1,npar,1,npar);          } else { 
   x=vector(1,npar);            if (u < x) a=u; else b=u; 
   indx=ivector(1,npar);            if (fu <= fw || w == x) { 
   for (i=1;i<=npar;i++)              v=w; 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];              w=u; 
   ludcmp(a,npar,indx,&pd);              fv=fw; 
               fw=fu; 
   for (j=1;j<=npar;j++) {            } else if (fu <= fv || v == x || v == w) { 
     for (i=1;i<=npar;i++) x[i]=0;              v=u; 
     x[j]=1;              fv=fu; 
     lubksb(a,npar,indx,x);            } 
     for (i=1;i<=npar;i++){          } 
       matcov[i][j]=x[i];    } 
     }    nrerror("Too many iterations in brent"); 
   }    *xmin=x; 
     return fx; 
   printf("\n#Hessian matrix#\n");  } 
   for (i=1;i<=npar;i++) {  
     for (j=1;j<=npar;j++) {  /****************** mnbrak ***********************/
       printf("%.3e ",hess[i][j]);  
     }  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
     printf("\n");              double (*func)(double)) 
   }  { 
     double ulim,u,r,q, dum;
   /* Recompute Inverse */    double fu; 
   for (i=1;i<=npar;i++)   
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    *fa=(*func)(*ax); 
   ludcmp(a,npar,indx,&pd);    *fb=(*func)(*bx); 
     if (*fb > *fa) { 
   /*  printf("\n#Hessian matrix recomputed#\n");      SHFT(dum,*ax,*bx,dum) 
         SHFT(dum,*fb,*fa,dum) 
   for (j=1;j<=npar;j++) {        } 
     for (i=1;i<=npar;i++) x[i]=0;    *cx=(*bx)+GOLD*(*bx-*ax); 
     x[j]=1;    *fc=(*func)(*cx); 
     lubksb(a,npar,indx,x);    while (*fb > *fc) { 
     for (i=1;i<=npar;i++){      r=(*bx-*ax)*(*fb-*fc); 
       y[i][j]=x[i];      q=(*bx-*cx)*(*fb-*fa); 
       printf("%.3e ",y[i][j]);      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     }        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     printf("\n");      ulim=(*bx)+GLIMIT*(*cx-*bx); 
   }      if ((*bx-u)*(u-*cx) > 0.0) { 
   */        fu=(*func)(u); 
       } else if ((*cx-u)*(u-ulim) > 0.0) { 
   free_matrix(a,1,npar,1,npar);        fu=(*func)(u); 
   free_matrix(y,1,npar,1,npar);        if (fu < *fc) { 
   free_vector(x,1,npar);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   free_ivector(indx,1,npar);            SHFT(*fb,*fc,fu,(*func)(u)) 
   free_matrix(hess,1,npar,1,npar);            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
         u=ulim; 
 }        fu=(*func)(u); 
       } else { 
 /*************** hessian matrix ****************/        u=(*cx)+GOLD*(*cx-*bx); 
 double hessii( double x[], double delta, int theta, double delti[])        fu=(*func)(u); 
 {      } 
   int i;      SHFT(*ax,*bx,*cx,u) 
   int l=1, lmax=20;        SHFT(*fa,*fb,*fc,fu) 
   double k1,k2;        } 
   double p2[NPARMAX+1];  } 
   double res;  
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  /*************** linmin ************************/
   double fx;  
   int k=0,kmax=10;  int ncom; 
   double l1;  double *pcom,*xicom;
   double (*nrfunc)(double []); 
   fx=func(x);   
   for (i=1;i<=npar;i++) p2[i]=x[i];  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for(l=0 ; l <=lmax; l++){  { 
     l1=pow(10,l);    double brent(double ax, double bx, double cx, 
     delts=delt;                 double (*f)(double), double tol, double *xmin); 
     for(k=1 ; k <kmax; k=k+1){    double f1dim(double x); 
       delt = delta*(l1*k);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       p2[theta]=x[theta] +delt;                double *fc, double (*func)(double)); 
       k1=func(p2)-fx;    int j; 
       p2[theta]=x[theta]-delt;    double xx,xmin,bx,ax; 
       k2=func(p2)-fx;    double fx,fb,fa;
       /*res= (k1-2.0*fx+k2)/delt/delt; */   
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    ncom=n; 
          pcom=vector(1,n); 
 #ifdef DEBUG    xicom=vector(1,n); 
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);    nrfunc=func; 
 #endif    for (j=1;j<=n;j++) { 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */      pcom[j]=p[j]; 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){      xicom[j]=xi[j]; 
         k=kmax;    } 
       }    ax=0.0; 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    xx=1.0; 
         k=kmax; l=lmax*10.;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       }    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  #ifdef DEBUG
         delts=delt;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       }    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     }  #endif
   }    for (j=1;j<=n;j++) { 
   delti[theta]=delts;      xi[j] *= xmin; 
   return res;      p[j] += xi[j]; 
      } 
 }    free_vector(xicom,1,n); 
     free_vector(pcom,1,n); 
 double hessij( double x[], double delti[], int thetai,int thetaj)  } 
 {  
   int i;  char *asc_diff_time(long time_sec, char ascdiff[])
   int l=1, l1, lmax=20;  {
   double k1,k2,k3,k4,res,fx;    long sec_left, days, hours, minutes;
   double p2[NPARMAX+1];    days = (time_sec) / (60*60*24);
   int k;    sec_left = (time_sec) % (60*60*24);
     hours = (sec_left) / (60*60) ;
   fx=func(x);    sec_left = (sec_left) %(60*60);
   for (k=1; k<=2; k++) {    minutes = (sec_left) /60;
     for (i=1;i<=npar;i++) p2[i]=x[i];    sec_left = (sec_left) % (60);
     p2[thetai]=x[thetai]+delti[thetai]/k;    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    return ascdiff;
     k1=func(p2)-fx;  }
    
     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, 
     k2=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 [])); 
     k3=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;
     k4=func(p2)-fx;    int niterf, itmp;
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  
 #ifdef DEBUG    pt=vector(1,n); 
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);    ptt=vector(1,n); 
 #endif    xit=vector(1,n); 
   }    xits=vector(1,n); 
   return res;    *fret=(*func)(p); 
 }    for (j=1;j<=n;j++) pt[j]=p[j]; 
     for (*iter=1;;++(*iter)) { 
 /************** Inverse of matrix **************/      fp=(*fret); 
 void ludcmp(double **a, int n, int *indx, double *d)      ibig=0; 
 {      del=0.0; 
   int i,imax,j,k;      last_time=curr_time;
   double big,dum,sum,temp;      (void) gettimeofday(&curr_time,&tzp);
   double *vv;      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);
   vv=vector(1,n);  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   *d=1.0;     for (i=1;i<=n;i++) {
   for (i=1;i<=n;i++) {        printf(" %d %.12f",i, p[i]);
     big=0.0;        fprintf(ficlog," %d %.12lf",i, p[i]);
     for (j=1;j<=n;j++)        fprintf(ficrespow," %.12lf", p[i]);
       if ((temp=fabs(a[i][j])) > big) big=temp;      }
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");      printf("\n");
     vv[i]=1.0/big;      fprintf(ficlog,"\n");
   }      fprintf(ficrespow,"\n");fflush(ficrespow);
   for (j=1;j<=n;j++) {      if(*iter <=3){
     for (i=1;i<j;i++) {        tm = *localtime(&curr_time.tv_sec);
       sum=a[i][j];        strcpy(strcurr,asctime(&tm));
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  /*       asctime_r(&tm,strcurr); */
       a[i][j]=sum;        forecast_time=curr_time; 
     }        itmp = strlen(strcurr);
     big=0.0;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
     for (i=j;i<=n;i++) {          strcurr[itmp-1]='\0';
       sum=a[i][j];        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
       for (k=1;k<j;k++)        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         sum -= a[i][k]*a[k][j];        for(niterf=10;niterf<=30;niterf+=10){
       a[i][j]=sum;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
       if ( (dum=vv[i]*fabs(sum)) >= big) {          tmf = *localtime(&forecast_time.tv_sec);
         big=dum;  /*      asctime_r(&tmf,strfor); */
         imax=i;          strcpy(strfor,asctime(&tmf));
       }          itmp = strlen(strfor);
     }          if(strfor[itmp-1]=='\n')
     if (j != imax) {          strfor[itmp-1]='\0';
       for (k=1;k<=n;k++) {          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);
         dum=a[imax][k];          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);
         a[imax][k]=a[j][k];        }
         a[j][k]=dum;      }
       }      for (i=1;i<=n;i++) { 
       *d = -(*d);        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
       vv[imax]=vv[j];        fptt=(*fret); 
     }  #ifdef DEBUG
     indx[j]=imax;        printf("fret=%lf \n",*fret);
     if (a[j][j] == 0.0) a[j][j]=TINY;        fprintf(ficlog,"fret=%lf \n",*fret);
     if (j != n) {  #endif
       dum=1.0/(a[j][j]);        printf("%d",i);fflush(stdout);
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        fprintf(ficlog,"%d",i);fflush(ficlog);
     }        linmin(p,xit,n,fret,func); 
   }        if (fabs(fptt-(*fret)) > del) { 
   free_vector(vv,1,n);  /* Doesn't work */          del=fabs(fptt-(*fret)); 
 ;          ibig=i; 
 }        } 
   #ifdef DEBUG
 void lubksb(double **a, int n, int *indx, double b[])        printf("%d %.12e",i,(*fret));
 {        fprintf(ficlog,"%d %.12e",i,(*fret));
   int i,ii=0,ip,j;        for (j=1;j<=n;j++) {
   double sum;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
            printf(" x(%d)=%.12e",j,xit[j]);
   for (i=1;i<=n;i++) {          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     ip=indx[i];        }
     sum=b[ip];        for(j=1;j<=n;j++) {
     b[ip]=b[i];          printf(" p=%.12e",p[j]);
     if (ii)          fprintf(ficlog," p=%.12e",p[j]);
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        }
     else if (sum) ii=i;        printf("\n");
     b[i]=sum;        fprintf(ficlog,"\n");
   }  #endif
   for (i=n;i>=1;i--) {      } 
     sum=b[i];      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];  #ifdef DEBUG
     b[i]=sum/a[i][i];        int k[2],l;
   }        k[0]=1;
 }        k[1]=-1;
         printf("Max: %.12e",(*func)(p));
 /************ Frequencies ********************/        fprintf(ficlog,"Max: %.12e",(*func)(p));
 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)        for (j=1;j<=n;j++) {
 {  /* Some frequencies */          printf(" %.12e",p[j]);
            fprintf(ficlog," %.12e",p[j]);
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;        }
   double ***freq; /* Frequencies */        printf("\n");
   double *pp;        fprintf(ficlog,"\n");
   double pos, k2, dateintsum=0,k2cpt=0;        for(l=0;l<=1;l++) {
   FILE *ficresp;          for (j=1;j<=n;j++) {
   char fileresp[FILENAMELENGTH];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
              printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   pp=vector(1,nlstate);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          }
   strcpy(fileresp,"p");          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   strcat(fileresp,fileres);          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   if((ficresp=fopen(fileresp,"w"))==NULL) {        }
     printf("Problem with prevalence resultfile: %s\n", fileresp);  #endif
     exit(0);  
   }  
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        free_vector(xit,1,n); 
   j1=0;        free_vector(xits,1,n); 
          free_vector(ptt,1,n); 
   j=cptcoveff;        free_vector(pt,1,n); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        return; 
        } 
   for(k1=1; k1<=j;k1++){      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     for(i1=1; i1<=ncodemax[k1];i1++){      for (j=1;j<=n;j++) { 
       j1++;        ptt[j]=2.0*p[j]-pt[j]; 
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        xit[j]=p[j]-pt[j]; 
         scanf("%d", i);*/        pt[j]=p[j]; 
       for (i=-1; i<=nlstate+ndeath; i++)        } 
         for (jk=-1; jk<=nlstate+ndeath; jk++)        fptt=(*func)(ptt); 
           for(m=agemin; m <= agemax+3; m++)      if (fptt < fp) { 
             freq[i][jk][m]=0;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
              if (t < 0.0) { 
       dateintsum=0;          linmin(p,xit,n,fret,func); 
       k2cpt=0;          for (j=1;j<=n;j++) { 
       for (i=1; i<=imx; i++) {            xi[j][ibig]=xi[j][n]; 
         bool=1;            xi[j][n]=xit[j]; 
         if  (cptcovn>0) {          }
           for (z1=1; z1<=cptcoveff; z1++)  #ifdef DEBUG
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
               bool=0;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         }          for(j=1;j<=n;j++){
         if (bool==1) {            printf(" %.12e",xit[j]);
           for(m=firstpass; m<=lastpass; m++){            fprintf(ficlog," %.12e",xit[j]);
             k2=anint[m][i]+(mint[m][i]/12.);          }
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          printf("\n");
               if(agev[m][i]==0) agev[m][i]=agemax+1;          fprintf(ficlog,"\n");
               if(agev[m][i]==1) agev[m][i]=agemax+2;  #endif
               if (m<lastpass) {        }
                 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];    } 
               }  } 
                
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {  /**** Prevalence limit (stable or period prevalence)  ****************/
                 dateintsum=dateintsum+k2;  
                 k2cpt++;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
               }  {
             }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
           }       matrix by transitions matrix until convergence is reached */
         }  
       }    int i, ii,j,k;
            double min, max, maxmin, maxmax,sumnew=0.;
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    double **matprod2();
     double **out, cov[NCOVMAX+1], **pmij();
       if  (cptcovn>0) {    double **newm;
         fprintf(ficresp, "\n#********** Variable ");    double agefin, delaymax=50 ; /* Max number of years to converge */
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  
         fprintf(ficresp, "**********\n#");    for (ii=1;ii<=nlstate+ndeath;ii++)
       }      for (j=1;j<=nlstate+ndeath;j++){
       for(i=1; i<=nlstate;i++)        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      }
       fprintf(ficresp, "\n");  
           cov[1]=1.;
       for(i=(int)agemin; i <= (int)agemax+3; i++){   
         if(i==(int)agemax+3)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           printf("Total");    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
         else      newm=savm;
           printf("Age %d", i);      /* Covariates have to be included here again */
         for(jk=1; jk <=nlstate ; jk++){      cov[2]=agefin;
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      
             pp[jk] += freq[jk][m][i];      for (k=1; k<=cptcovn;k++) {
         }        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, pos=0; m <=0 ; m++)      }
             pos += freq[jk][m][i];      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           if(pp[jk]>=1.e-10)      for (k=1; k<=cptcovprod;k++)
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           else      
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         }      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
         for(jk=1; jk <=nlstate ; jk++){      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      
             pp[jk] += freq[jk][m][i];      savm=oldm;
         }      oldm=newm;
       maxmax=0.;
         for(jk=1,pos=0; jk <=nlstate ; jk++)      for(j=1;j<=nlstate;j++){
           pos += pp[jk];        min=1.;
         for(jk=1; jk <=nlstate ; jk++){        max=0.;
           if(pos>=1.e-5)        for(i=1; i<=nlstate; i++) {
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          sumnew=0;
           else          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          prlim[i][j]= newm[i][j]/(1-sumnew);
           if( i <= (int) agemax){          max=FMAX(max,prlim[i][j]);
             if(pos>=1.e-5){          min=FMIN(min,prlim[i][j]);
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        }
               probs[i][jk][j1]= pp[jk]/pos;        maxmin=max-min;
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/        maxmax=FMAX(maxmax,maxmin);
             }      }
             else      if(maxmax < ftolpl){
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        return prlim;
           }      }
         }    }
          }
         for(jk=-1; jk <=nlstate+ndeath; jk++)  
           for(m=-1; m <=nlstate+ndeath; m++)  /*************** transition probabilities ***************/ 
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);  
         if(i <= (int) agemax)  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
           fprintf(ficresp,"\n");  {
         printf("\n");    /* According to parameters values stored in x and the covariate's values stored in cov,
       }       computes the probability to be observed in state j being in state i by appying the
     }       model to the ncovmodel covariates (including constant and age).
   }       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
   dateintmean=dateintsum/k2cpt;       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:
   fclose(ficresp);       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
   free_vector(pp,1,nlstate);       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.
   /* End of Freq */       Outputs ps[i][j] the probability to be observed in j being in j according to
 }       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     */
 /************ Prevalence ********************/    double s1, lnpijopii;
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)    /*double t34;*/
 {  /* Some frequencies */    int i,j,j1, nc, ii, jj;
    
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      for(i=1; i<= nlstate; i++){
   double ***freq; /* Frequencies */        for(j=1; j<i;j++){
   double *pp;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   double pos, k2;            /*lnpijopii += param[i][j][nc]*cov[nc];*/
             lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   pp=vector(1,nlstate);  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          }
            ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   j1=0;        }
          for(j=i+1; j<=nlstate+ndeath;j++){
   j=cptcoveff;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
              lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
   for(k1=1; k1<=j;k1++){  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
     for(i1=1; i1<=ncodemax[k1];i1++){          }
       j1++;          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
              }
       for (i=-1; i<=nlstate+ndeath; i++)        }
         for (jk=-1; jk<=nlstate+ndeath; jk++)        
           for(m=agemin; m <= agemax+3; m++)      for(i=1; i<= nlstate; i++){
             freq[i][jk][m]=0;        s1=0;
              for(j=1; j<i; j++){
       for (i=1; i<=imx; i++) {          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         bool=1;          /*printf("debug1 %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++)        for(j=i+1; j<=nlstate+ndeath; j++){
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
               bool=0;          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }        }
         if (bool==1) {        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
           for(m=firstpass; m<=lastpass; m++){        ps[i][i]=1./(s1+1.);
             k2=anint[m][i]+(mint[m][i]/12.);        /* Computing other pijs */
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        for(j=1; j<i; j++)
               if(agev[m][i]==0) agev[m][i]=agemax+1;          ps[i][j]= exp(ps[i][j])*ps[i][i];
               if(agev[m][i]==1) agev[m][i]=agemax+2;        for(j=i+1; j<=nlstate+ndeath; j++)
               if (m<lastpass) {          ps[i][j]= exp(ps[i][j])*ps[i][i];
                 if (calagedate>0)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];      } /* end i */
                 else      
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];        for(jj=1; jj<= nlstate+ndeath; jj++){
               }          ps[ii][jj]=0;
             }          ps[ii][ii]=1;
           }        }
         }      }
       }      
       for(i=(int)agemin; i <= (int)agemax+3; i++){  
         for(jk=1; jk <=nlstate ; jk++){  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
             pp[jk] += freq[jk][m][i];  /*         printf("ddd %lf ",ps[ii][jj]); */
         }  /*       } */
         for(jk=1; jk <=nlstate ; jk++){  /*       printf("\n "); */
           for(m=-1, pos=0; m <=0 ; m++)  /*        } */
             pos += freq[jk][m][i];  /*        printf("\n ");printf("%lf ",cov[2]); */
         }         /*
                for(i=1; i<= npar; i++) printf("%f ",x[i]);
         for(jk=1; jk <=nlstate ; jk++){        goto end;*/
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      return ps;
             pp[jk] += freq[jk][m][i];  }
         }  
          /**************** Product of 2 matrices ******************/
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];  
          double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
         for(jk=1; jk <=nlstate ; jk++){      {
           if( i <= (int) agemax){    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
             if(pos>=1.e-5){       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
               probs[i][jk][j1]= pp[jk]/pos;    /* in, b, out are matrice of pointers which should have been initialized 
             }       before: only the contents of out is modified. The function returns
           }       a pointer to pointers identical to out */
         }    long i, j, k;
            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;
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  }
   free_vector(pp,1,nlstate);  
    
 }  /* End of Freq */  /************* Higher Matrix Product ***************/
   
 /************* Waves Concatenation ***************/  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   {
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    /* Computes the transition matrix starting at age 'age' over 
 {       'nhstepm*hstepm*stepm' months (i.e. until
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
      Death is a valid wave (if date is known).       nhstepm*hstepm matrices. 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]       (typically every 2 years instead of every month which is too big 
      and mw[mi+1][i]. dh depends on stepm.       for the memory).
      */       Model is determined by parameters x and covariates have to be 
        included manually here. 
   int i, mi, m;  
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;       */
      double sum=0., jmean=0.;*/  
     int i, j, d, h, k;
   int j, k=0,jk, ju, jl;    double **out, cov[NCOVMAX+1];
   double sum=0.;    double **newm;
   jmin=1e+5;  
   jmax=-1;    /* Hstepm could be zero and should return the unit matrix */
   jmean=0.;    for (i=1;i<=nlstate+ndeath;i++)
   for(i=1; i<=imx; i++){      for (j=1;j<=nlstate+ndeath;j++){
     mi=0;        oldm[i][j]=(i==j ? 1.0 : 0.0);
     m=firstpass;        po[i][j][0]=(i==j ? 1.0 : 0.0);
     while(s[m][i] <= nlstate){      }
       if(s[m][i]>=1)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         mw[++mi][i]=m;    for(h=1; h <=nhstepm; h++){
       if(m >=lastpass)      for(d=1; d <=hstepm; d++){
         break;        newm=savm;
       else        /* Covariates have to be included here again */
         m++;        cov[1]=1.;
     }/* end while */        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
     if (s[m][i] > nlstate){        for (k=1; k<=cptcovn;k++) 
       mi++;     /* Death is another wave */          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       /* if(mi==0)  never been interviewed correctly before death */        for (k=1; k<=cptcovage;k++)
          /* Only death is a correct wave */          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       mw[mi][i]=m;        for (k=1; k<=cptcovprod;k++)
     }          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
     wav[i]=mi;  
     if(mi==0)        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   }        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
                      pmij(pmmij,cov,ncovmodel,x,nlstate));
   for(i=1; i<=imx; i++){        savm=oldm;
     for(mi=1; mi<wav[i];mi++){        oldm=newm;
       if (stepm <=0)      }
         dh[mi][i]=1;      for(i=1; i<=nlstate+ndeath; i++)
       else{        for(j=1;j<=nlstate+ndeath;j++) {
         if (s[mw[mi+1][i]][i] > nlstate) {          po[i][j][h]=newm[i][j];
           if (agedc[i] < 2*AGESUP) {          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);        }
           if(j==0) j=1;  /* Survives at least one month after exam */      /*printf("h=%d ",h);*/
           k=k+1;    } /* end h */
           if (j >= jmax) jmax=j;  /*     printf("\n H=%d \n",h); */
           if (j <= jmin) jmin=j;    return po;
           sum=sum+j;  }
           /*if (j<0) printf("j=%d num=%d \n",j,i); */  
           }  
         }  /*************** log-likelihood *************/
         else{  double func( double *x)
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  {
           k=k+1;    int i, ii, j, k, mi, d, kk;
           if (j >= jmax) jmax=j;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
           else if (j <= jmin)jmin=j;    double **out;
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    double sw; /* Sum of weights */
           sum=sum+j;    double lli; /* Individual log likelihood */
         }    int s1, s2;
         jk= j/stepm;    double bbh, survp;
         jl= j -jk*stepm;    long ipmx;
         ju= j -(jk+1)*stepm;    /*extern weight */
         if(jl <= -ju)    /* We are differentiating ll according to initial status */
           dh[mi][i]=jk;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         else    /*for(i=1;i<imx;i++) 
           dh[mi][i]=jk+1;      printf(" %d\n",s[4][i]);
         if(dh[mi][i]==0)    */
           dh[mi][i]=1; /* At least one step */    cov[1]=1.;
       }  
     }    for(k=1; k<=nlstate; k++) ll[k]=0.;
   }  
   jmean=sum/k;    if(mle==1){
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
  }        /* Computes the values of the ncovmodel covariates of the model
 /*********** Tricode ****************************/           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
 void tricode(int *Tvar, int **nbcode, int imx)           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
 {           to be observed in j being in i according to the model.
   int Ndum[20],ij=1, k, j, i;         */
   int cptcode=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   cptcoveff=0;        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
             is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
   for (k=0; k<19; k++) Ndum[k]=0;           has been calculated etc */
   for (k=1; k<=7; k++) ncodemax[k]=0;        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {            for (j=1;j<=nlstate+ndeath;j++){
     for (i=1; i<=imx; i++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       ij=(int)(covar[Tvar[j]][i]);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       Ndum[ij]++;            }
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          for(d=0; d<dh[mi][i]; d++){
       if (ij > cptcode) cptcode=ij;            newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
     for (i=0; i<=cptcode; i++) {              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
       if(Ndum[i]!=0) ncodemax[j]++;            }
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     ij=1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
             oldm=newm;
     for (i=1; i<=ncodemax[j]; i++) {          } /* end mult */
       for (k=0; k<=19; k++) {        
         if (Ndum[k] != 0) {          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           nbcode[Tvar[j]][ij]=k;          /* But now since version 0.9 we anticipate for bias at large stepm.
                     * If stepm is larger than one month (smallest stepm) and if the exact delay 
           ij++;           * (in months) between two waves is not a multiple of stepm, we rounded to 
         }           * the nearest (and in case of equal distance, to the lowest) interval but now
         if (ij > ncodemax[j]) break;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       }             * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
     }           * probability in order to take into account the bias as a fraction of the way
   }             * from savm to out if bh is negative or even beyond if bh is positive. bh varies
            * -stepm/2 to stepm/2 .
  for (k=0; k<19; k++) Ndum[k]=0;           * 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. 
  for (i=1; i<=ncovmodel-2; i++) {           */
       ij=Tvar[i];          s1=s[mw[mi][i]][i];
       Ndum[ij]++;          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias bh is positive if real duration
  ij=1;           * is higher than the multiple of stepm and negative otherwise.
  for (i=1; i<=10; i++) {           */
    if((Ndum[i]!=0) && (i<=ncovcol)){          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
      Tvaraff[ij]=i;          if( s2 > nlstate){ 
      ij++;            /* i.e. if s2 is a death state and if the date of death is known 
    }               then the contribution to the likelihood is the probability to 
  }               die between last step unit time and current  step unit time, 
                 which is also equal to probability to die before dh 
     cptcoveff=ij-1;               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 Expectancies ****************/          health state: the date of the interview describes the actual state
           and not the date of a change in health state. The former idea was
 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 )          to consider that at each interview the state was recorded
           (healthy, disable or death) and IMaCh was corrected; but when we
 {          introduced the exact date of death then we should have modified
   /* Health expectancies */          the contribution of an exact death to the likelihood. This new
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;          contribution is smaller and very dependent of the step unit
   double age, agelim, hf;          stepm. It is no more the probability to die between last interview
   double ***p3mat,***varhe;          and month of death but the probability to survive from last
   double **dnewm,**doldm;          interview up to one month before death multiplied by the
   double *xp;          probability to die within a month. Thanks to Chris
   double **gp, **gm;          Jackson for correcting this bug.  Former versions increased
   double ***gradg, ***trgradg;          mortality artificially. The bad side is that we add another loop
   int theta;          which slows down the processing. The difference can be up to 10%
           lower mortality.
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);            */
   xp=vector(1,npar);            lli=log(out[s1][s2] - savm[s1][s2]);
   dnewm=matrix(1,nlstate*2,1,npar);  
   doldm=matrix(1,nlstate*2,1,nlstate*2);  
            } else if  (s2==-2) {
   fprintf(ficreseij,"# Health expectancies\n");            for (j=1,survp=0. ; j<=nlstate; j++) 
   fprintf(ficreseij,"# Age");              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   for(i=1; i<=nlstate;i++)            /*survp += out[s1][j]; */
     for(j=1; j<=nlstate;j++)            lli= log(survp);
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          }
   fprintf(ficreseij,"\n");          
           else if  (s2==-4) { 
   if(estepm < stepm){            for (j=3,survp=0. ; j<=nlstate; j++)  
     printf ("Problem %d lower than %d\n",estepm, stepm);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   }            lli= log(survp); 
   else  hstepm=estepm;            } 
   /* We compute the life expectancy from trapezoids spaced every estepm months  
    * This is mainly to measure the difference between two models: for example          else if  (s2==-5) { 
    * if stepm=24 months pijx are given only every 2 years and by summing them            for (j=1,survp=0. ; j<=2; j++)  
    * we are calculating an estimate of the Life Expectancy assuming a linear              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
    * progression inbetween and thus overestimating or underestimating according            lli= log(survp); 
    * to the curvature of the survival function. If, for the same date, we          } 
    * estimate the model with stepm=1 month, we can keep estepm to 24 months          
    * to compare the new estimate of Life expectancy with the same linear          else{
    * hypothesis. A more precise result, taking into account a more precise            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
    * curvature will be obtained if estepm is as small as stepm. */            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
           } 
   /* For example we decided to compute the life expectancy with the smallest unit */          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          /*if(lli ==000.0)*/
      nhstepm is the number of hstepm from age to agelim          /*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); */
      nstepm is the number of stepm from age to agelin.          ipmx +=1;
      Look at hpijx to understand the reason of that which relies in memory size          sw += weight[i];
      and note for a fixed period like estepm months */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        } /* end of wave */
      survival function given by stepm (the optimization length). Unfortunately it      } /* end of individual */
      means that if the survival funtion is printed only each two years of age and if    }  else if(mle==2){
      you sum them up and add 1 year (area under the trapezoids) you won't get the same      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      results. So we changed our mind and took the option of the best precision.        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   */        for(mi=1; mi<= wav[i]-1; mi++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
   agelim=AGESUP;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     /* nhstepm age range expressed in number of stepm */            }
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          for(d=0; d<=dh[mi][i]; d++){
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */            newm=savm;
     /* if (stepm >= YEARM) hstepm=1;*/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            for (kk=1; kk<=cptcovage;kk++) {
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);            }
     gp=matrix(0,nhstepm,1,nlstate*2);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     gm=matrix(0,nhstepm,1,nlstate*2);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            oldm=newm;
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          } /* end mult */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);          
            s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          bbh=(double)bh[mi][i]/(double)stepm; 
           lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
     /* Computing Variances of health expectancies */          ipmx +=1;
           sw += weight[i];
      for(theta=1; theta <=npar; theta++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1; i<=npar; i++){        } /* end of wave */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      } /* end of individual */
       }    }  else if(mle==3){  /* exponential inter-extrapolation */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       cptj=0;        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j<= nlstate; j++){          for (ii=1;ii<=nlstate+ndeath;ii++)
         for(i=1; i<=nlstate; i++){            for (j=1;j<=nlstate+ndeath;j++){
           cptj=cptj+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            }
           }          for(d=0; d<dh[mi][i]; d++){
         }            newm=savm;
       }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                  for (kk=1; kk<=cptcovage;kk++) {
                    cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for(i=1; i<=npar; i++)            }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                  savm=oldm;
       cptj=0;            oldm=newm;
       for(j=1; j<= nlstate; j++){          } /* end mult */
         for(i=1;i<=nlstate;i++){        
           cptj=cptj+1;          s1=s[mw[mi][i]][i];
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){          s2=s[mw[mi+1][i]][i];
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;          bbh=(double)bh[mi][i]/(double)stepm; 
           }          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
         }          ipmx +=1;
       }          sw += weight[i];
       for(j=1; j<= nlstate*2; j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(h=0; h<=nhstepm-1; h++){        } /* end of wave */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      } /* end of individual */
         }    }else if (mle==4){  /* ml=4 no inter-extrapolation */
      }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
            for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 /* End theta */        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      for(h=0; h<=nhstepm-1; h++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate*2;j++)            }
         for(theta=1; theta <=npar; theta++)          for(d=0; d<dh[mi][i]; d++){
           trgradg[h][j][theta]=gradg[h][theta][j];            newm=savm;
                  cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
      for(i=1;i<=nlstate*2;i++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for(j=1;j<=nlstate*2;j++)            }
         varhe[i][j][(int)age] =0.;          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      printf("%d|",(int)age);fflush(stdout);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
      for(h=0;h<=nhstepm-1;h++){            savm=oldm;
       for(k=0;k<=nhstepm-1;k++){            oldm=newm;
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);          } /* end mult */
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);        
         for(i=1;i<=nlstate*2;i++)          s1=s[mw[mi][i]][i];
           for(j=1;j<=nlstate*2;j++)          s2=s[mw[mi+1][i]][i];
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;          if( s2 > nlstate){ 
       }            lli=log(out[s1][s2] - savm[s1][s2]);
     }          }else{
     /* Computing expectancies */            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     for(i=1; i<=nlstate;i++)          }
       for(j=1; j<=nlstate;j++)          ipmx +=1;
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){          sw += weight[i];
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
            /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
 /* if((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]);*/        } /* end of wave */
       } /* end of individual */
         }    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     fprintf(ficreseij,"%3.0f",age );        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     cptj=0;        for(mi=1; mi<= wav[i]-1; mi++){
     for(i=1; i<=nlstate;i++)          for (ii=1;ii<=nlstate+ndeath;ii++)
       for(j=1; j<=nlstate;j++){            for (j=1;j<=nlstate+ndeath;j++){
         cptj++;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
     fprintf(ficreseij,"\n");          for(d=0; d<dh[mi][i]; d++){
                newm=savm;
     free_matrix(gm,0,nhstepm,1,nlstate*2);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     free_matrix(gp,0,nhstepm,1,nlstate*2);            for (kk=1; kk<=cptcovage;kk++) {
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);            }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          
   }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   printf("\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   free_vector(xp,1,npar);            oldm=newm;
   free_matrix(dnewm,1,nlstate*2,1,npar);          } /* end mult */
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);        
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);          s1=s[mw[mi][i]][i];
 }          s2=s[mw[mi+1][i]][i];
           lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 /************ Variance ******************/          ipmx +=1;
 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)          sw += weight[i];
 {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   /* Variance of health expectancies */          /*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]);*/
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        } /* end of wave */
   double **newm;      } /* end of individual */
   double **dnewm,**doldm;    } /* End of if */
   int i, j, nhstepm, hstepm, h, nstepm ;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   int k, cptcode;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double *xp;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double **gp, **gm;    return -l;
   double ***gradg, ***trgradg;  }
   double ***p3mat;  
   double age,agelim, hf;  /*************** log-likelihood *************/
   int theta;  double funcone( double *x)
   {
   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");    /* Same as likeli but slower because of a lot of printf and if */
   fprintf(ficresvij,"# Age");    int i, ii, j, k, mi, d, kk;
   for(i=1; i<=nlstate;i++)    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     for(j=1; j<=nlstate;j++)    double **out;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    double lli; /* Individual log likelihood */
   fprintf(ficresvij,"\n");    double llt;
     int s1, s2;
   xp=vector(1,npar);    double bbh, survp;
   dnewm=matrix(1,nlstate,1,npar);    /*extern weight */
   doldm=matrix(1,nlstate,1,nlstate);    /* We are differentiating ll according to initial status */
      /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   if(estepm < stepm){    /*for(i=1;i<imx;i++) 
     printf ("Problem %d lower than %d\n",estepm, stepm);      printf(" %d\n",s[4][i]);
   }    */
   else  hstepm=estepm;      cov[1]=1.;
   /* 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.    for(k=1; k<=nlstate; k++) ll[k]=0.;
      nhstepm is the number of hstepm from age to agelim  
      nstepm is the number of stepm from age to agelin.    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      Look at hpijx to understand the reason of that which relies in memory size      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      and note for a fixed period like k years */      for(mi=1; mi<= wav[i]-1; mi++){
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        for (ii=1;ii<=nlstate+ndeath;ii++)
      survival function given by stepm (the optimization length). Unfortunately it          for (j=1;j<=nlstate+ndeath;j++){
      means that if the survival funtion is printed only each two years of age and if            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      you sum them up and add 1 year (area under the trapezoids) you won't get the same            savm[ii][j]=(ii==j ? 1.0 : 0.0);
      results. So we changed our mind and took the option of the best precision.          }
   */        for(d=0; d<dh[mi][i]; d++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          newm=savm;
   agelim = AGESUP;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          for (kk=1; kk<=cptcovage;kk++) {
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          }
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     gp=matrix(0,nhstepm,1,nlstate);          savm=oldm;
     gm=matrix(0,nhstepm,1,nlstate);          oldm=newm;
         } /* end mult */
     for(theta=1; theta <=npar; theta++){        
       for(i=1; i<=npar; i++){ /* Computes gradient */        s1=s[mw[mi][i]][i];
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        s2=s[mw[mi+1][i]][i];
       }        bbh=(double)bh[mi][i]/(double)stepm; 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          /* bias is positive if real duration
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);         * is higher than the multiple of stepm and negative otherwise.
          */
       if (popbased==1) {        if( s2 > nlstate && (mle <5) ){  /* Jackson */
         for(i=1; i<=nlstate;i++)          lli=log(out[s1][s2] - savm[s1][s2]);
           prlim[i][i]=probs[(int)age][i][ij];        } else if  (s2==-2) {
       }          for (j=1,survp=0. ; j<=nlstate; j++) 
              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       for(j=1; j<= nlstate; j++){          lli= log(survp);
         for(h=0; h<=nhstepm; h++){        }else if (mle==1){
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        } else if(mle==2){
         }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       }        } else if(mle==3){  /* exponential inter-extrapolation */
              lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       for(i=1; i<=npar; i++) /* Computes gradient */        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          lli=log(out[s1][s2]); /* Original formula */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          } else{  /* mle=0 back to 1 */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
            /*lli=log(out[s1][s2]); */ /* Original formula */
       if (popbased==1) {        } /* End of if */
         for(i=1; i<=nlstate;i++)        ipmx +=1;
           prlim[i][i]=probs[(int)age][i][ij];        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]); */
       for(j=1; j<= nlstate; j++){        if(globpr){
         for(h=0; h<=nhstepm; h++){          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)   %11.6f %11.6f %11.6f ", \
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
         }                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
             llt +=ll[k]*gipmx/gsw;
       for(j=1; j<= nlstate; j++)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         for(h=0; h<=nhstepm; h++){          }
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          fprintf(ficresilk," %10.6f\n", -llt);
         }        }
     } /* End theta */      } /* end of wave */
     } /* end of individual */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     for(h=0; h<=nhstepm; h++)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       for(j=1; j<=nlstate;j++)    if(globpr==0){ /* First time we count the contributions and weights */
         for(theta=1; theta <=npar; theta++)      gipmx=ipmx;
           trgradg[h][j][theta]=gradg[h][theta][j];      gsw=sw;
     }
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    return -l;
     for(i=1;i<=nlstate;i++)  }
       for(j=1;j<=nlstate;j++)  
         vareij[i][j][(int)age] =0.;  
   /*************** function likelione ***********/
     for(h=0;h<=nhstepm;h++){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       for(k=0;k<=nhstepm;k++){  {
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    /* This routine should help understanding what is done with 
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);       the selection of individuals/waves and
         for(i=1;i<=nlstate;i++)       to check the exact contribution to the likelihood.
           for(j=1;j<=nlstate;j++)       Plotting could be done.
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;     */
       }    int k;
     }  
     if(*globpri !=0){ /* Just counts and sums, no printings */
     fprintf(ficresvij,"%.0f ",age );      strcpy(fileresilk,"ilk"); 
     for(i=1; i<=nlstate;i++)      strcat(fileresilk,fileres);
       for(j=1; j<=nlstate;j++){      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);        printf("Problem with resultfile: %s\n", fileresilk);
       }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     fprintf(ficresvij,"\n");      }
     free_matrix(gp,0,nhstepm,1,nlstate);      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");
     free_matrix(gm,0,nhstepm,1,nlstate);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);      for(k=1; k<=nlstate; k++) 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   } /* End age */      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
      }
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);    *fretone=(*funcone)(p);
   free_matrix(dnewm,1,nlstate,1,nlstate);    if(*globpri !=0){
       fclose(ficresilk);
 }      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       fflush(fichtm); 
 /************ 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)    return;
 {  }
   /* Variance of prevalence limit */  
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  
   double **newm;  /*********** Maximum Likelihood Estimation ***************/
   double **dnewm,**doldm;  
   int i, j, nhstepm, hstepm;  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   int k, cptcode;  {
   double *xp;    int i,j, iter;
   double *gp, *gm;    double **xi;
   double **gradg, **trgradg;    double fret;
   double age,agelim;    double fretone; /* Only one call to likelihood */
   int theta;    /*  char filerespow[FILENAMELENGTH];*/
        xi=matrix(1,npar,1,npar);
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");    for (i=1;i<=npar;i++)
   fprintf(ficresvpl,"# Age");      for (j=1;j<=npar;j++)
   for(i=1; i<=nlstate;i++)        xi[i][j]=(i==j ? 1.0 : 0.0);
       fprintf(ficresvpl," %1d-%1d",i,i);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   fprintf(ficresvpl,"\n");    strcpy(filerespow,"pow"); 
     strcat(filerespow,fileres);
   xp=vector(1,npar);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   dnewm=matrix(1,nlstate,1,npar);      printf("Problem with resultfile: %s\n", filerespow);
   doldm=matrix(1,nlstate,1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
      }
   hstepm=1*YEARM; /* Every year of age */    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    for (i=1;i<=nlstate;i++)
   agelim = AGESUP;      for(j=1;j<=nlstate+ndeath;j++)
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    fprintf(ficrespow,"\n");
     if (stepm >= YEARM) hstepm=1;  
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    powell(p,xi,npar,ftol,&iter,&fret,func);
     gradg=matrix(1,npar,1,nlstate);  
     gp=vector(1,nlstate);    free_matrix(xi,1,npar,1,npar);
     gm=vector(1,nlstate);    fclose(ficrespow);
     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     for(theta=1; theta <=npar; theta++){    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       for(i=1; i<=npar; i++){ /* Computes gradient */    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }  }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)  /**** Computes Hessian and covariance matrix ***/
         gp[i] = prlim[i][i];  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
      {
       for(i=1; i<=npar; i++) /* Computes gradient */    double  **a,**y,*x,pd;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    double **hess;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    int i, j,jk;
       for(i=1;i<=nlstate;i++)    int *indx;
         gm[i] = prlim[i][i];  
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(i=1;i<=nlstate;i++)    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    void lubksb(double **a, int npar, int *indx, double b[]) ;
     } /* End theta */    void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
     trgradg =matrix(1,nlstate,1,npar);    hess=matrix(1,npar,1,npar);
   
     for(j=1; j<=nlstate;j++)    printf("\nCalculation of the hessian matrix. Wait...\n");
       for(theta=1; theta <=npar; theta++)    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
         trgradg[j][theta]=gradg[theta][j];    for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
     for(i=1;i<=nlstate;i++)      fprintf(ficlog,"%d",i);fflush(ficlog);
       varpl[i][(int)age] =0.;     
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);      
     for(i=1;i<=nlstate;i++)      /*  printf(" %f ",p[i]);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
     fprintf(ficresvpl,"%.0f ",age );    
     for(i=1; i<=nlstate;i++)    for (i=1;i<=npar;i++) {
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      for (j=1;j<=npar;j++)  {
     fprintf(ficresvpl,"\n");        if (j>i) { 
     free_vector(gp,1,nlstate);          printf(".%d%d",i,j);fflush(stdout);
     free_vector(gm,1,nlstate);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     free_matrix(gradg,1,npar,1,nlstate);          hess[i][j]=hessij(p,delti,i,j,func,npar);
     free_matrix(trgradg,1,nlstate,1,npar);          
   } /* End age */          hess[j][i]=hess[i][j];    
           /*printf(" %lf ",hess[i][j]);*/
   free_vector(xp,1,npar);        }
   free_matrix(doldm,1,nlstate,1,npar);      }
   free_matrix(dnewm,1,nlstate,1,nlstate);    }
     printf("\n");
 }    fprintf(ficlog,"\n");
   
 /************ Variance of one-step probabilities  ******************/    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 {    
   int i, j,  i1, k1, l1;    a=matrix(1,npar,1,npar);
   int k2, l2, j1,  z1;    y=matrix(1,npar,1,npar);
   int k=0,l, cptcode;    x=vector(1,npar);
   int first=1;    indx=ivector(1,npar);
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;    for (i=1;i<=npar;i++)
   double **dnewm,**doldm;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   double *xp;    ludcmp(a,npar,indx,&pd);
   double *gp, *gm;  
   double **gradg, **trgradg;    for (j=1;j<=npar;j++) {
   double **mu;      for (i=1;i<=npar;i++) x[i]=0;
   double age,agelim, cov[NCOVMAX];      x[j]=1;
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */      lubksb(a,npar,indx,x);
   int theta;      for (i=1;i<=npar;i++){ 
   char fileresprob[FILENAMELENGTH];        matcov[i][j]=x[i];
   char fileresprobcov[FILENAMELENGTH];      }
   char fileresprobcor[FILENAMELENGTH];    }
   
   double ***varpij;    printf("\n#Hessian matrix#\n");
     fprintf(ficlog,"\n#Hessian matrix#\n");
   strcpy(fileresprob,"prob");    for (i=1;i<=npar;i++) { 
   strcat(fileresprob,fileres);      for (j=1;j<=npar;j++) { 
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {        printf("%.3e ",hess[i][j]);
     printf("Problem with resultfile: %s\n", fileresprob);        fprintf(ficlog,"%.3e ",hess[i][j]);
   }      }
   strcpy(fileresprobcov,"probcov");      printf("\n");
   strcat(fileresprobcov,fileres);      fprintf(ficlog,"\n");
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    }
     printf("Problem with resultfile: %s\n", fileresprobcov);  
   }    /* Recompute Inverse */
   strcpy(fileresprobcor,"probcor");    for (i=1;i<=npar;i++)
   strcat(fileresprobcor,fileres);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {    ludcmp(a,npar,indx,&pd);
     printf("Problem with resultfile: %s\n", fileresprobcor);  
   }    /*  printf("\n#Hessian matrix recomputed#\n");
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);  
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    for (j=1;j<=npar;j++) {
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      for (i=1;i<=npar;i++) x[i]=0;
        x[j]=1;
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");      lubksb(a,npar,indx,x);
   fprintf(ficresprob,"# Age");      for (i=1;i<=npar;i++){ 
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");        y[i][j]=x[i];
   fprintf(ficresprobcov,"# Age");        printf("%.3e ",y[i][j]);
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");        fprintf(ficlog,"%.3e ",y[i][j]);
   fprintf(ficresprobcov,"# Age");      }
       printf("\n");
       fprintf(ficlog,"\n");
   for(i=1; i<=nlstate;i++)    }
     for(j=1; j<=(nlstate+ndeath);j++){    */
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);  
       fprintf(ficresprobcov," p%1d-%1d ",i,j);    free_matrix(a,1,npar,1,npar);
       fprintf(ficresprobcor," p%1d-%1d ",i,j);    free_matrix(y,1,npar,1,npar);
     }      free_vector(x,1,npar);
   fprintf(ficresprob,"\n");    free_ivector(indx,1,npar);
   fprintf(ficresprobcov,"\n");    free_matrix(hess,1,npar,1,npar);
   fprintf(ficresprobcor,"\n");  
   xp=vector(1,npar);  
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);  }
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));  
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);  /*************** hessian matrix ****************/
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   first=1;  {
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    int i;
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    int l=1, lmax=20;
     exit(0);    double k1,k2;
   }    double p2[MAXPARM+1]; /* identical to x */
   else{    double res;
     fprintf(ficgp,"\n# Routine varprob");    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   }    double fx;
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    int k=0,kmax=10;
     printf("Problem with html file: %s\n", optionfilehtm);    double l1;
     exit(0);  
   }    fx=func(x);
   else{    for (i=1;i<=npar;i++) p2[i]=x[i];
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");    for(l=0 ; l <=lmax; l++){
     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");      l1=pow(10,l);
     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");      delts=delt;
       for(k=1 ; k <kmax; k=k+1){
   }        delt = delta*(l1*k);
   cov[1]=1;        p2[theta]=x[theta] +delt;
   j=cptcoveff;        k1=func(p2)-fx;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        p2[theta]=x[theta]-delt;
   j1=0;        k2=func(p2)-fx;
   for(k1=1; k1<=1;k1++){        /*res= (k1-2.0*fx+k2)/delt/delt; */
     for(i1=1; i1<=ncodemax[k1];i1++){        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     j1++;        
   #ifdef DEBUGHESS
     if  (cptcovn>0) {        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       fprintf(ficresprob, "\n#********** Variable ");        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       fprintf(ficresprobcov, "\n#********** Variable ");  #endif
       fprintf(ficgp, "\n#********** Variable ");        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       fprintf(ficresprobcor, "\n#********** Variable ");          k=kmax;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        }
       fprintf(ficresprob, "**********\n#");        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          k=kmax; l=lmax*10.;
       fprintf(ficresprobcov, "**********\n#");        }
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       fprintf(ficgp, "**********\n#");          delts=delt;
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        }
       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#");    delti[theta]=delts;
     }    return res; 
        
       for (age=bage; age<=fage; age ++){  }
         cov[2]=age;  
         for (k=1; k<=cptcovn;k++) {  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];  {
         }    int i;
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    int l=1, l1, lmax=20;
         for (k=1; k<=cptcovprod;k++)    double k1,k2,k3,k4,res,fx;
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    double p2[MAXPARM+1];
            int k;
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));  
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);    fx=func(x);
         gp=vector(1,(nlstate)*(nlstate+ndeath));    for (k=1; k<=2; k++) {
         gm=vector(1,(nlstate)*(nlstate+ndeath));      for (i=1;i<=npar;i++) p2[i]=x[i];
          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++)      k1=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;
                k2=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;      k3=func(p2)-fx;
               gp[k]=pmmij[i][j];    
             }      p2[thetai]=x[thetai]-delti[thetai]/k;
           }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                k4=func(p2)-fx;
           for(i=1; i<=npar; i++)      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
             xp[i] = x[i] - (i==theta ?delti[theta]:0);  #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);
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      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);
           k=0;  #endif
           for(i=1; i<=(nlstate); i++){    }
             for(j=1; j<=(nlstate+ndeath);j++){    return res;
               k=k+1;  }
               gm[k]=pmmij[i][j];  
             }  /************** Inverse of matrix **************/
           }  void ludcmp(double **a, int n, int *indx, double *d) 
        { 
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)    int i,imax,j,k; 
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      double big,dum,sum,temp; 
         }    double *vv; 
    
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)    vv=vector(1,n); 
           for(theta=1; theta <=npar; theta++)    *d=1.0; 
             trgradg[j][theta]=gradg[theta][j];    for (i=1;i<=n;i++) { 
              big=0.0; 
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);      for (j=1;j<=n;j++) 
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);        if ((temp=fabs(a[i][j])) > big) big=temp; 
              if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
         pmij(pmmij,cov,ncovmodel,x,nlstate);      vv[i]=1.0/big; 
            } 
         k=0;    for (j=1;j<=n;j++) { 
         for(i=1; i<=(nlstate); i++){      for (i=1;i<j;i++) { 
           for(j=1; j<=(nlstate+ndeath);j++){        sum=a[i][j]; 
             k=k+1;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
             mu[k][(int) age]=pmmij[i][j];        a[i][j]=sum; 
           }      } 
         }      big=0.0; 
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)      for (i=j;i<=n;i++) { 
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)        sum=a[i][j]; 
             varpij[i][j][(int)age] = doldm[i][j];        for (k=1;k<j;k++) 
           sum -= a[i][k]*a[k][j]; 
         /*printf("\n%d ",(int)age);        a[i][j]=sum; 
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){        if ( (dum=vv[i]*fabs(sum)) >= big) { 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));          big=dum; 
      }*/          imax=i; 
         } 
         fprintf(ficresprob,"\n%d ",(int)age);      } 
         fprintf(ficresprobcov,"\n%d ",(int)age);      if (j != imax) { 
         fprintf(ficresprobcor,"\n%d ",(int)age);        for (k=1;k<=n;k++) { 
           dum=a[imax][k]; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)          a[imax][k]=a[j][k]; 
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));          a[j][k]=dum; 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){        } 
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);        *d = -(*d); 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);        vv[imax]=vv[j]; 
         }      } 
         i=0;      indx[j]=imax; 
         for (k=1; k<=(nlstate);k++){      if (a[j][j] == 0.0) a[j][j]=TINY; 
           for (l=1; l<=(nlstate+ndeath);l++){      if (j != n) { 
             i=i++;        dum=1.0/(a[j][j]); 
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
             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]);    free_vector(vv,1,n);  /* Doesn't work */
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));  ;
             }  } 
           }  
         }/* end of loop for state */  void lubksb(double **a, int n, int *indx, double b[]) 
       } /* end of loop for age */  { 
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/    int i,ii=0,ip,j; 
       for (k1=1; k1<=(nlstate);k1++){    double sum; 
         for (l1=1; l1<=(nlstate+ndeath);l1++){   
           if(l1==k1) continue;    for (i=1;i<=n;i++) { 
           i=(k1-1)*(nlstate+ndeath)+l1;      ip=indx[i]; 
           for (k2=1; k2<=(nlstate);k2++){      sum=b[ip]; 
             for (l2=1; l2<=(nlstate+ndeath);l2++){      b[ip]=b[i]; 
               if(l2==k2) continue;      if (ii) 
               j=(k2-1)*(nlstate+ndeath)+l2;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
               if(j<=i) continue;      else if (sum) ii=i; 
               for (age=bage; age<=fage; age ++){      b[i]=sum; 
                 if ((int)age %5==0){    } 
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;    for (i=n;i>=1;i--) { 
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;      sum=b[i]; 
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                   mu1=mu[i][(int) age]/stepm*YEARM ;      b[i]=sum/a[i][i]; 
                   mu2=mu[j][(int) age]/stepm*YEARM;    } 
                   /* Computing eigen value of matrix of covariance */  } 
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));  void pstamp(FILE *fichier)
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);  {
                   /* Eigen vectors */    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));  }
                   v21=sqrt(1.-v11*v11);  
                   v12=-v21;  /************ Frequencies ********************/
                   v22=v11;  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[])
                   /*printf(fignu*/  {  /* Some frequencies */
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */    
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */    int i, m, jk, k1,i1, j1, bool, z1,j;
                   if(first==1){    int first;
                     first=0;    double ***freq; /* Frequencies */
                     fprintf(ficgp,"\nset parametric;set nolabel");    double *pp, **prop;
                     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);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");    char fileresp[FILENAMELENGTH];
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%1d%1d-%1d%1d.png\">varpijgr%s%1d%1d-%1d%1d.png</A>, ",k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1,optionfilefiname,k2,l2,k1,l1);    
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);    pp=vector(1,nlstate);
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);    prop=matrix(1,nlstate,iagemin,iagemax+3);
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);    strcpy(fileresp,"p");
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    strcat(fileresp,fileres);
                     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\"",\    if((ficresp=fopen(fileresp,"w"))==NULL) {
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \      printf("Problem with prevalence resultfile: %s\n", fileresp);
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
                   }else{      exit(0);
                     first=0;    }
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);    j1=0;
                     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\"",\    
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \    j=cptcoveff;
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
                   }/* if first */  
                 } /* age mod 5 */    first=1;
               } /* end loop age */  
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);    for(k1=1; k1<=j;k1++){
               first=1;      for(i1=1; i1<=ncodemax[k1];i1++){
             } /*l12 */        j1++;
           } /* k12 */        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
         } /*l1 */          scanf("%d", i);*/
       }/* k1 */        for (i=-5; i<=nlstate+ndeath; i++)  
     } /* loop covariates */          for (jk=-5; jk<=nlstate+ndeath; jk++)  
     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));              freq[i][jk][m]=0;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));  
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);      for (i=1; i<=nlstate; i++)  
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        for(m=iagemin; m <= iagemax+3; m++)
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          prop[i][m]=0;
   }        
   free_vector(xp,1,npar);        dateintsum=0;
   fclose(ficresprob);        k2cpt=0;
   fclose(ficresprobcov);        for (i=1; i<=imx; i++) {
   fclose(ficresprobcor);          bool=1;
   fclose(ficgp);          if  (cptcovn>0) {
   fclose(fichtm);            for (z1=1; z1<=cptcoveff; z1++) 
 }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
           }
 /******************* Printing html file ***********/          if (bool==1){
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \            for(m=firstpass; m<=lastpass; m++){
                   int lastpass, int stepm, int weightopt, char model[],\              k2=anint[m][i]+(mint[m][i]/12.);
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                   int popforecast, int estepm ,\                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                   double jprev1, double mprev1,double anprev1, \                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                   double jprev2, double mprev2,double anprev2){                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
   int jj1, k1, i1, cpt;                if (m<lastpass) {
   /*char optionfilehtm[FILENAMELENGTH];*/                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
     printf("Problem with %s \n",optionfilehtm), exit(0);                }
   }                
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n                  dateintsum=dateintsum+k2;
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n                  k2cpt++;
  - 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):            }
    <a href=\"e%s\">e%s</a> <br>\n</li>", \          }
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);        }
          
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n        pstamp(ficresp);
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n        if  (cptcovn>0) {
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n          fprintf(ficresp, "\n#********** Variable "); 
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  - 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=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
  if(popforecast==1) fprintf(fichtm,"\n        fprintf(ficresp, "\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        for(i=iagemin; i <= iagemax+3; i++){
         <br>",fileres,fileres,fileres,fileres);          if(i==iagemax+3){
  else            fprintf(ficlog,"Total");
    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);          }else{
 fprintf(fichtm," <li>Graphs</li><p>");            if(first==1){
               first=0;
  m=cptcoveff;              printf("See log file for details...\n");
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}            }
             fprintf(ficlog,"Age %d", 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, pp[jk]=0; m <=nlstate+ndeath ; m++)
      jj1++;              pp[jk] += freq[jk][m][i]; 
      if (cptcovn > 0) {          }
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");          for(jk=1; jk <=nlstate ; jk++){
        for (cpt=1; cpt<=cptcoveff;cpt++)            for(m=-1, pos=0; m <=0 ; m++)
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);              pos += freq[jk][m][i];
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");            if(pp[jk]>=1.e-10){
      }              if(first==1){
      /* Pij */                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>              }
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                  fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
      /* Quasi-incidences */            }else{
      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>              if(first==1)
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
        /* Stable prevalence in each health state */              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
        for(cpt=1; cpt<nlstate;cpt++){            }
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>          }
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
        }          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>- Observed and stationary prevalence (with confident              pp[jk] += freq[jk][m][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,pos=0,posprop=0; jk <=nlstate ; jk++){
      }            pos += pp[jk];
      for(cpt=1; cpt<=nlstate;cpt++) {            posprop += prop[jk][i];
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>          }
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          for(jk=1; jk <=nlstate ; jk++){
      }            if(pos>=1.e-5){
      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]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
    }            }else{
  }              if(first==1)
 fclose(fichtm);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 }              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }
 /******************* Gnuplot file **************/            if( i <= iagemax){
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){              if(pos>=1.e-5){
                 fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;                /*probs[i][jk][j1]= pp[jk]/pos;*/
   int ng;                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {              }
     printf("Problem with file %s",optionfilegnuplot);              else
   }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             }
 #ifdef windows          }
     fprintf(ficgp,"cd \"%s\" \n",pathc);          
 #endif          for(jk=-1; jk <=nlstate+ndeath; jk++)
 m=pow(2,cptcoveff);            for(m=-1; m <=nlstate+ndeath; m++)
                if(freq[jk][m][i] !=0 ) {
  /* 1eme*/              if(first==1)
   for (cpt=1; cpt<= nlstate ; cpt ++) {                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
    for (k1=1; k1<= m ; k1 ++) {                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
 #ifdef windows          if(i <= iagemax)
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            fprintf(ficresp,"\n");
      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);          if(first==1)
 #endif            printf("Others in log...\n");
 #ifdef unix          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\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);      }
 #endif    }
     dateintmean=dateintsum/k2cpt; 
 for (i=1; i<= nlstate ; i ++) {   
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    fclose(ficresp);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 }    free_vector(pp,1,nlstate);
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     for (i=1; i<= nlstate ; i ++) {    /* End of Freq */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }  /************ Prevalence ********************/
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
      for (i=1; i<= nlstate ; i ++) {  {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   else fprintf(ficgp," \%%*lf (\%%*lf)");       in each health status at the date of interview (if between dateprev1 and dateprev2).
 }         We still use firstpass and lastpass as another selection.
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    */
 #ifdef unix   
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");    int i, m, jk, k1, i1, j1, bool, z1,j;
 #endif    double ***freq; /* Frequencies */
    }    double *pp, **prop;
   }    double pos,posprop; 
   /*2 eme*/    double  y2; /* in fractional years */
     int iagemin, iagemax;
   for (k1=1; k1<= m ; k1 ++) {  
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);    iagemin= (int) agemin;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    iagemax= (int) agemax;
        /*pp=vector(1,nlstate);*/
     for (i=1; i<= nlstate+1 ; i ++) {    prop=matrix(1,nlstate,iagemin,iagemax+3); 
       k=2*i;    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    j1=0;
       for (j=1; j<= nlstate+1 ; j ++) {    
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    j=cptcoveff;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    if (cptcovn<1) {j=1;ncodemax[1]=1;}
 }      
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    for(k1=1; k1<=j;k1++){
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);      for(i1=1; i1<=ncodemax[k1];i1++){
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);        j1++;
       for (j=1; j<= nlstate+1 ; j ++) {        
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        for (i=1; i<=nlstate; i++)  
         else fprintf(ficgp," \%%*lf (\%%*lf)");          for(m=iagemin; m <= iagemax+3; m++)
 }              prop[i][m]=0.0;
       fprintf(ficgp,"\" t\"\" w l 0,");       
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);        for (i=1; i<=imx; i++) { /* Each individual */
       for (j=1; j<= nlstate+1 ; j ++) {          bool=1;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          if  (cptcovn>0) {
   else fprintf(ficgp," \%%*lf (\%%*lf)");            for (z1=1; z1<=cptcoveff; z1++) 
 }                if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");                bool=0;
       else fprintf(ficgp,"\" t\"\" w l 0,");          } 
     }          if (bool==1) { 
   }            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
                y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
   /*3eme*/              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
   for (k1=1; k1<= m ; k1 ++) {                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     for (cpt=1; cpt<= nlstate ; cpt ++) {                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
       k=2+nlstate*(2*cpt-2);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);                  prop[s[m][i]][iagemax+3] += weight[i]; 
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");                } 
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);              }
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);            } /* end selection of waves */
  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++){  
 */          
       for (i=1; i< nlstate ; i ++) {          for(jk=1,posprop=0; 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);            posprop += prop[jk][i]; 
           } 
       }  
     }          for(jk=1; jk <=nlstate ; jk++){     
   }            if( i <=  iagemax){ 
                if(posprop>=1.e-5){ 
   /* CV preval stat */                probs[i][jk][j1]= prop[jk][i]/posprop;
     for (k1=1; k1<= m ; k1 ++) {              } else
     for (cpt=1; cpt<nlstate ; cpt ++) {                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
       k=3;            } 
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          }/* end jk */ 
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);        }/* end i */ 
       } /* end i1 */
       for (i=1; i< nlstate ; i ++)    } /* end k1 */
         fprintf(ficgp,"+$%d",k+i+1);    
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
          /*free_vector(pp,1,nlstate);*/
       l=3+(nlstate+ndeath)*cpt;    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  }  /* End of prevalence */
       for (i=1; i< nlstate ; i ++) {  
         l=3+(nlstate+ndeath)*cpt;  /************* Waves Concatenation ***************/
         fprintf(ficgp,"+$%d",l+i+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)
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);    {
     }    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   }         Death is a valid wave (if date is known).
         mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   /* proba elementaires */       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
    for(i=1,jk=1; i <=nlstate; i++){       and mw[mi+1][i]. dh depends on stepm.
     for(k=1; k <=(nlstate+ndeath); k++){       */
       if (k != i) {  
         for(j=1; j <=ncovmodel; j++){    int i, mi, m;
            /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);       double sum=0., jmean=0.;*/
           jk++;    int first;
           fprintf(ficgp,"\n");    int j, k=0,jk, ju, jl;
         }    double sum=0.;
       }    first=0;
     }    jmin=1e+5;
    }    jmax=-1;
     jmean=0.;
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/    for(i=1; i<=imx; i++){
      for(jk=1; jk <=m; jk++) {      mi=0;
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);      m=firstpass;
        if (ng==2)      while(s[m][i] <= nlstate){
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
        else          mw[++mi][i]=m;
          fprintf(ficgp,"\nset title \"Probability\"\n");        if(m >=lastpass)
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);          break;
        i=1;        else
        for(k2=1; k2<=nlstate; k2++) {          m++;
          k3=i;      }/* end while */
          for(k=1; k<=(nlstate+ndeath); k++) {      if (s[m][i] > nlstate){
            if (k != k2){        mi++;     /* Death is another wave */
              if(ng==2)        /* if(mi==0)  never been interviewed correctly before death */
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);           /* Only death is a correct wave */
              else        mw[mi][i]=m;
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);      }
              ij=1;  
              for(j=3; j <=ncovmodel; j++) {      wav[i]=mi;
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {      if(mi==0){
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        nbwarn++;
                  ij++;        if(first==0){
                }          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
                else          first=1;
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        }
              }        if(first==1){
              fprintf(ficgp,")/(1");          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
                      }
              for(k1=1; k1 <=nlstate; k1++){        } /* end mi==0 */
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    } /* End individuals */
                ij=1;  
                for(j=3; j <=ncovmodel; j++){    for(i=1; i<=imx; i++){
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {      for(mi=1; mi<wav[i];mi++){
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        if (stepm <=0)
                    ij++;          dh[mi][i]=1;
                  }        else{
                  else          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);            if (agedc[i] < 2*AGESUP) {
                }              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
                fprintf(ficgp,")");              if(j==0) j=1;  /* Survives at least one month after exam */
              }              else if(j<0){
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);                nberr++;
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
              i=i+ncovmodel;                j=1; /* Temporary Dangerous patch */
            }                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
          }                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
        }                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
      }              }
    }              k=k+1;
    fclose(ficgp);              if (j >= jmax){
 }  /* end gnuplot */                jmax=j;
                 ijmax=i;
               }
 /*************** Moving average **************/              if (j <= jmin){
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){                jmin=j;
                 ijmin=i;
   int i, cpt, cptcod;              }
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)              sum=sum+j;
       for (i=1; i<=nlstate;i++)              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
           mobaverage[(int)agedeb][i][cptcod]=0.;            }
              }
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){          else{
       for (i=1; i<=nlstate;i++){            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  /*        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 (cpt=0;cpt<=4;cpt++){  
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];            k=k+1;
           }            if (j >= jmax) {
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;              jmax=j;
         }              ijmax=i;
       }            }
     }            else if (j <= jmin){
                  jmin=j;
 }              ijmin=i;
             }
             /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
 /************** Forecasting ******************/            /*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]);*/
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){            if(j<0){
                nberr++;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;              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]);
   int *popage;              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]);
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;            }
   double *popeffectif,*popcount;            sum=sum+j;
   double ***p3mat;          }
   char fileresf[FILENAMELENGTH];          jk= j/stepm;
           jl= j -jk*stepm;
  agelim=AGESUP;          ju= j -(jk+1)*stepm;
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
             if(jl==0){
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              dh[mi][i]=jk;
                bh[mi][i]=0;
              }else{ /* We want a negative bias in order to only have interpolation ie
   strcpy(fileresf,"f");                    * to avoid the price of an extra matrix product in likelihood */
   strcat(fileresf,fileres);              dh[mi][i]=jk+1;
   if((ficresf=fopen(fileresf,"w"))==NULL) {              bh[mi][i]=ju;
     printf("Problem with forecast resultfile: %s\n", fileresf);            }
   }          }else{
   printf("Computing forecasting: result on file '%s' \n", fileresf);            if(jl <= -ju){
               dh[mi][i]=jk;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;              bh[mi][i]=jl;       /* bias is positive if real duration
                                    * is higher than the multiple of stepm and negative otherwise.
   if (mobilav==1) {                                   */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            }
     movingaverage(agedeb, fage, ageminpar, mobaverage);            else{
   }              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
   stepsize=(int) (stepm+YEARM-1)/YEARM;            }
   if (stepm<=12) stepsize=1;            if(dh[mi][i]==0){
                dh[mi][i]=1; /* At least one step */
   agelim=AGESUP;              bh[mi][i]=ju; /* At least one step */
                /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
   hstepm=1;            }
   hstepm=hstepm/stepm;          } /* end if mle */
   yp1=modf(dateintmean,&yp);        }
   anprojmean=yp;      } /* end wave */
   yp2=modf((yp1*12),&yp);    }
   mprojmean=yp;    jmean=sum/k;
   yp1=modf((yp2*30.5),&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);
   jprojmean=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);
   if(jprojmean==0) jprojmean=1;   }
   if(mprojmean==0) jprojmean=1;  
    /*********** Tricode ****************************/
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  void tricode(int *Tvar, int **nbcode, int imx)
    {
   for(cptcov=1;cptcov<=i2;cptcov++){    /* Uses cptcovn+2*cptcovprod as the number of covariates */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
       k=k+1;  
       fprintf(ficresf,"\n#******");    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
       for(j=1;j<=cptcoveff;j++) {    int modmaxcovj=0; /* Modality max of covariates j */
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    cptcoveff=0; 
       }   
       fprintf(ficresf,"******\n");    for (k=0; k<maxncov; k++) Ndum[k]=0;
       fprintf(ficresf,"# StartingAge FinalAge");    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  
          for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
            for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {                                 modality of this covariate Vj*/ 
         fprintf(ficresf,"\n");        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);                                          modality of the nth covariate of individual i. */
         Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        if (ij > modmaxcovj) modmaxcovj=ij; 
           nhstepm = nhstepm/hstepm;        /* 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
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           female is 1, then modmaxcovj=1.*/
           oldm=oldms;savm=savms;      }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        /* 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 */
           for (h=0; h<=nhstepm; h++){        if( Ndum[i] != 0 )
             if (h==(int) (calagedate+YEARM*cpt)) {          ncodemax[j]++; 
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);        /* Number of modalities of the j th covariate. In fact
             }           ncodemax[j]=2 (dichotom. variables only) but it could be more for
             for(j=1; j<=nlstate+ndeath;j++) {           historical reasons */
               kk1=0.;kk2=0;      } /* Ndum[-1] number of undefined modalities */
               for(i=1; i<=nlstate;i++) {                
                 if (mobilav==1)      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      ij=1; 
                 else {      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];        for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
                 }          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
                            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
               }                                       k is a modality. If we have model=V1+V1*sex 
               if (h==(int)(calagedate+12*cpt)){                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
                 fprintf(ficresf," %.3f", kk1);            ij++;
                                  }
               }          if (ij > ncodemax[j]) break; 
             }        }  /* end of loop on */
           }      } /* end of loop on modality */ 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    } /* 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;
     }    
   }    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.*/
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
      Ndum[ij]++;
   fclose(ficresf);   }
 }  
 /************** Forecasting ******************/   ij=1;
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
       if((Ndum[i]!=0) && (i<=ncovcol)){
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;       Tvaraff[ij]=i; /*For printing */
   int *popage;       ij++;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;     }
   double *popeffectif,*popcount;   }
   double ***p3mat,***tabpop,***tabpopprev;   ij--;
   char filerespop[FILENAMELENGTH];   cptcoveff=ij; /*Number of simple covariates*/
   }
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  /*********** Health Expectancies ****************/
   agelim=AGESUP;  
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
    
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  {
      /* Health expectancies, no variances */
      int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
   strcpy(filerespop,"pop");    int nhstepma, nstepma; /* Decreasing with age */
   strcat(filerespop,fileres);    double age, agelim, hf;
   if((ficrespop=fopen(filerespop,"w"))==NULL) {    double ***p3mat;
     printf("Problem with forecast resultfile: %s\n", filerespop);    double eip;
   }  
   printf("Computing forecasting: result on file '%s' \n", filerespop);    pstamp(ficreseij);
     fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    fprintf(ficreseij,"# Age");
     for(i=1; i<=nlstate;i++){
   if (mobilav==1) {      for(j=1; j<=nlstate;j++){
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        fprintf(ficreseij," e%1d%1d ",i,j);
     movingaverage(agedeb, fage, ageminpar, mobaverage);      }
   }      fprintf(ficreseij," e%1d. ",i);
     }
   stepsize=(int) (stepm+YEARM-1)/YEARM;    fprintf(ficreseij,"\n");
   if (stepm<=12) stepsize=1;  
      
   agelim=AGESUP;    if(estepm < stepm){
        printf ("Problem %d lower than %d\n",estepm, stepm);
   hstepm=1;    }
   hstepm=hstepm/stepm;    else  hstepm=estepm;   
      /* We compute the life expectancy from trapezoids spaced every estepm months
   if (popforecast==1) {     * This is mainly to measure the difference between two models: for example
     if((ficpop=fopen(popfile,"r"))==NULL) {     * if stepm=24 months pijx are given only every 2 years and by summing them
       printf("Problem with population file : %s\n",popfile);exit(0);     * we are calculating an estimate of the Life Expectancy assuming a linear 
     }     * progression in between and thus overestimating or underestimating according
     popage=ivector(0,AGESUP);     * to the curvature of the survival function. If, for the same date, we 
     popeffectif=vector(0,AGESUP);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     popcount=vector(0,AGESUP);     * to compare the new estimate of Life expectancy with the same linear 
         * hypothesis. A more precise result, taking into account a more precise
     i=1;       * curvature will be obtained if estepm is as small as stepm. */
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;  
        /* For example we decided to compute the life expectancy with the smallest unit */
     imx=i;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];       nhstepm is the number of hstepm from age to agelim 
   }       nstepm is the number of stepm from age to agelin. 
        Look at hpijx to understand the reason of that which relies in memory size
   for(cptcov=1;cptcov<=i2;cptcov++){       and note for a fixed period like estepm months */
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       k=k+1;       survival function given by stepm (the optimization length). Unfortunately it
       fprintf(ficrespop,"\n#******");       means that if the survival funtion is printed only each two years of age and if
       for(j=1;j<=cptcoveff;j++) {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       results. So we changed our mind and took the option of the best precision.
       }    */
       fprintf(ficrespop,"******\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       fprintf(ficrespop,"# Age");  
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    agelim=AGESUP;
       if (popforecast==1)  fprintf(ficrespop," [Population]");    /* If stepm=6 months */
            /* Computed by stepm unit matrices, product of hstepm matrices, stored
       for (cpt=0; cpt<=0;cpt++) {         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        
          /* nhstepm age range expressed in number of stepm */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           nhstepm = nhstepm/hstepm;    /* if (stepm >= YEARM) hstepm=1;*/
              nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    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 (age=bage; age<=fage; age ++){ 
              nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           for (h=0; h<=nhstepm; h++){      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             if (h==(int) (calagedate+YEARM*cpt)) {      /* if (stepm >= YEARM) hstepm=1;*/
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
             }  
             for(j=1; j<=nlstate+ndeath;j++) {      /* If stepm=6 months */
               kk1=0.;kk2=0;      /* Computed by stepm unit matrices, product of hstepma matrices, stored
               for(i=1; i<=nlstate;i++) {                       in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
                 if (mobilav==1)      
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
                 else {      
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
                 }      
               }      printf("%d|",(int)age);fflush(stdout);
               if (h==(int)(calagedate+12*cpt)){      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;      
                   /*fprintf(ficrespop," %.3f", kk1);      /* Computing expectancies */
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/      for(i=1; i<=nlstate;i++)
               }        for(j=1; j<=nlstate;j++)
             }          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             for(i=1; i<=nlstate;i++){            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
               kk1=0.;            
                 for(j=1; j<=nlstate;j++){            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];  
                 }          }
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];  
             }      fprintf(ficreseij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)        eip=0;
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        for(j=1; j<=nlstate;j++){
           }          eip +=eij[i][j][(int)age];
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
         }        }
       }        fprintf(ficreseij,"%9.4f", eip );
        }
   /******/      fprintf(ficreseij,"\n");
       
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    }
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    printf("\n");
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    fprintf(ficlog,"\n");
           nhstepm = nhstepm/hstepm;    
            }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
           oldm=oldms;savm=savms;  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[] )
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    
           for (h=0; h<=nhstepm; h++){  {
             if (h==(int) (calagedate+YEARM*cpt)) {    /* Covariances of health expectancies eij and of total life expectancies according
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);     to initial status i, ei. .
             }    */
             for(j=1; j<=nlstate+ndeath;j++) {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
               kk1=0.;kk2=0;    int nhstepma, nstepma; /* Decreasing with age */
               for(i=1; i<=nlstate;i++) {                  double age, agelim, hf;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        double ***p3matp, ***p3matm, ***varhe;
               }    double **dnewm,**doldm;
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    double *xp, *xm;
             }    double **gp, **gm;
           }    double ***gradg, ***trgradg;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int theta;
         }  
       }    double eip, vip;
    }  
   }    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
      xp=vector(1,npar);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
   if (popforecast==1) {    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     free_ivector(popage,0,AGESUP);    
     free_vector(popeffectif,0,AGESUP);    pstamp(ficresstdeij);
     free_vector(popcount,0,AGESUP);    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   }    fprintf(ficresstdeij,"# Age");
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    for(i=1; i<=nlstate;i++){
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(j=1; j<=nlstate;j++)
   fclose(ficrespop);        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
 }      fprintf(ficresstdeij," e%1d. ",i);
     }
 /***********************************************/    fprintf(ficresstdeij,"\n");
 /**************** Main Program *****************/  
 /***********************************************/    pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
 int main(int argc, char *argv[])    fprintf(ficrescveij,"# Age");
 {    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++){
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;        cptj= (j-1)*nlstate+i;
   double agedeb, agefin,hf;        for(i2=1; i2<=nlstate;i2++)
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
   double fret;            if(cptj2 <= cptj)
   double **xi,tmp,delta;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
   double dum; /* Dummy variable */      }
   double ***p3mat;    fprintf(ficrescveij,"\n");
   int *indx;    
   char line[MAXLINE], linepar[MAXLINE];    if(estepm < stepm){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      printf ("Problem %d lower than %d\n",estepm, stepm);
   int firstobs=1, lastobs=10;    }
   int sdeb, sfin; /* Status at beginning and end */    else  hstepm=estepm;   
   int c,  h , cpt,l;    /* We compute the life expectancy from trapezoids spaced every estepm months
   int ju,jl, mi;     * This is mainly to measure the difference between two models: for example
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;     * if stepm=24 months pijx are given only every 2 years and by summing them
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;     * we are calculating an estimate of the Life Expectancy assuming a linear 
   int mobilav=0,popforecast=0;     * progression in between and thus overestimating or underestimating according
   int hstepm, nhstepm;     * to the curvature of the survival function. If, for the same date, we 
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;     * 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 
   double bage, fage, age, agelim, agebase;     * hypothesis. A more precise result, taking into account a more precise
   double ftolpl=FTOL;     * curvature will be obtained if estepm is as small as stepm. */
   double **prlim;  
   double *severity;    /* For example we decided to compute the life expectancy with the smallest unit */
   double ***param; /* Matrix of parameters */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   double  *p;       nhstepm is the number of hstepm from age to agelim 
   double **matcov; /* Matrix of covariance */       nstepm is the number of stepm from age to agelin. 
   double ***delti3; /* Scale */       Look at hpijx to understand the reason of that which relies in memory size
   double *delti; /* Scale */       and note for a fixed period like estepm months */
   double ***eij, ***vareij;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   double **varpl; /* Variances of prevalence limits by age */       survival function given by stepm (the optimization length). Unfortunately it
   double *epj, vepp;       means that if the survival funtion is printed only each two years of age and if
   double kk1, kk2;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;       results. So we changed our mind and took the option of the best precision.
      */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   char *alph[]={"a","a","b","c","d","e"}, str[4];  
     /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
   char z[1]="c", occ;    agelim=AGESUP;
 #include <sys/time.h>    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
 #include <time.h>    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    /* if (stepm >= YEARM) hstepm=1;*/
      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   /* long total_usecs;    
   struct timeval start_time, end_time;    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   getcwd(pathcd, size);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     gp=matrix(0,nhstepm,1,nlstate*nlstate);
   printf("\n%s",version);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   if(argc <=1){  
     printf("\nEnter the parameter file name: ");    for (age=bage; age<=fage; age ++){ 
     scanf("%s",pathtot);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   else{      /* if (stepm >= YEARM) hstepm=1;*/
     strcpy(pathtot,argv[1]);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   }  
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      /* If stepm=6 months */
   /*cygwin_split_path(pathtot,path,optionfile);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   /* cutv(path,optionfile,pathtot,'\\');*/      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);  
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);      /* Computing  Variances of health expectancies */
   chdir(path);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   replace(pathc,path);         decrease memory allocation */
       for(theta=1; theta <=npar; theta++){
 /*-------- arguments in the command line --------*/        for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
   strcpy(fileres,"r");          xm[i] = x[i] - (i==theta ?delti[theta]:0);
   strcat(fileres, optionfilefiname);        }
   strcat(fileres,".txt");    /* Other files have txt extension */        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   /*---------arguments file --------*/    
         for(j=1; j<= nlstate; j++){
   if((ficpar=fopen(optionfile,"r"))==NULL)    {          for(i=1; i<=nlstate; i++){
     printf("Problem with optionfile %s\n",optionfile);            for(h=0; h<=nhstepm-1; h++){
     goto end;              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.;
             }
   strcpy(filereso,"o");          }
   strcat(filereso,fileres);        }
   if((ficparo=fopen(filereso,"w"))==NULL) {       
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        for(ij=1; ij<= nlstate*nlstate; ij++)
   }          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   /* Reads comments: lines beginning with '#' */          }
   while((c=getc(ficpar))=='#' && c!= EOF){      }/* End theta */
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      
     puts(line);      for(h=0; h<=nhstepm-1; h++)
     fputs(line,ficparo);        for(j=1; j<=nlstate*nlstate;j++)
   }          for(theta=1; theta <=npar; theta++)
   ungetc(c,ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
       
   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);       for(ij=1;ij<=nlstate*nlstate;ij++)
   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);        for(ji=1;ji<=nlstate*nlstate;ji++)
 while((c=getc(ficpar))=='#' && c!= EOF){          varhe[ij][ji][(int)age] =0.;
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);       printf("%d|",(int)age);fflush(stdout);
     puts(line);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     fputs(line,ficparo);       for(h=0;h<=nhstepm-1;h++){
   }        for(k=0;k<=nhstepm-1;k++){
   ungetc(c,ficpar);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
            matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
              for(ij=1;ij<=nlstate*nlstate;ij++)
   covar=matrix(0,NCOVMAX,1,n);            for(ji=1;ji<=nlstate*nlstate;ji++)
   cptcovn=0;              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;        }
       }
   ncovmodel=2+cptcovn;  
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      /* Computing expectancies */
        hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   /* Read guess parameters */      for(i=1; i<=nlstate;i++)
   /* Reads comments: lines beginning with '#' */        for(j=1; j<=nlstate;j++)
   while((c=getc(ficpar))=='#' && c!= EOF){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     ungetc(c,ficpar);            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     fgets(line, MAXLINE, ficpar);            
     puts(line);            /* 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]);*/
     fputs(line,ficparo);  
   }          }
   ungetc(c,ficpar);  
        fprintf(ficresstdeij,"%3.0f",age );
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      for(i=1; i<=nlstate;i++){
     for(i=1; i <=nlstate; i++)        eip=0.;
     for(j=1; j <=nlstate+ndeath-1; j++){        vip=0.;
       fscanf(ficpar,"%1d%1d",&i1,&j1);        for(j=1; j<=nlstate;j++){
       fprintf(ficparo,"%1d%1d",i1,j1);          eip += eij[i][j][(int)age];
       printf("%1d%1d",i,j);          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
       for(k=1; k<=ncovmodel;k++){            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
         fscanf(ficpar," %lf",&param[i][j][k]);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         printf(" %lf",param[i][j][k]);        }
         fprintf(ficparo," %lf",param[i][j][k]);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }      }
       fscanf(ficpar,"\n");      fprintf(ficresstdeij,"\n");
       printf("\n");  
       fprintf(ficparo,"\n");      fprintf(ficrescveij,"%3.0f",age );
     }      for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++){
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;          cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
   p=param[1][1];            for(j2=1; j2<=nlstate;j2++){
                cptj2= (j2-1)*nlstate+i2;
   /* Reads comments: lines beginning with '#' */              if(cptj2 <= cptj)
   while((c=getc(ficpar))=='#' && c!= EOF){                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
     ungetc(c,ficpar);            }
     fgets(line, MAXLINE, ficpar);        }
     puts(line);      fprintf(ficrescveij,"\n");
     fputs(line,ficparo);     
   }    }
   ungetc(c,ficpar);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
   for(i=1; i <=nlstate; i++){    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for(j=1; j <=nlstate+ndeath-1; j++){    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    printf("\n");
       printf("%1d%1d",i,j);    fprintf(ficlog,"\n");
       fprintf(ficparo,"%1d%1d",i1,j1);  
       for(k=1; k<=ncovmodel;k++){    free_vector(xm,1,npar);
         fscanf(ficpar,"%le",&delti3[i][j][k]);    free_vector(xp,1,npar);
         printf(" %le",delti3[i][j][k]);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
         fprintf(ficparo," %le",delti3[i][j][k]);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
       }    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
       fscanf(ficpar,"\n");  }
       printf("\n");  
       fprintf(ficparo,"\n");  /************ 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[])
   }  {
   delti=delti3[1][1];    /* Variance of health expectancies */
      /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   /* Reads comments: lines beginning with '#' */    /* double **newm;*/
   while((c=getc(ficpar))=='#' && c!= EOF){    double **dnewm,**doldm;
     ungetc(c,ficpar);    double **dnewmp,**doldmp;
     fgets(line, MAXLINE, ficpar);    int i, j, nhstepm, hstepm, h, nstepm ;
     puts(line);    int k, cptcode;
     fputs(line,ficparo);    double *xp;
   }    double **gp, **gm;  /* for var eij */
   ungetc(c,ficpar);    double ***gradg, ***trgradg; /*for var eij */
      double **gradgp, **trgradgp; /* for var p point j */
   matcov=matrix(1,npar,1,npar);    double *gpp, *gmp; /* for var p point j */
   for(i=1; i <=npar; i++){    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     fscanf(ficpar,"%s",&str);    double ***p3mat;
     printf("%s",str);    double age,agelim, hf;
     fprintf(ficparo,"%s",str);    double ***mobaverage;
     for(j=1; j <=i; j++){    int theta;
       fscanf(ficpar," %le",&matcov[i][j]);    char digit[4];
       printf(" %.5le",matcov[i][j]);    char digitp[25];
       fprintf(ficparo," %.5le",matcov[i][j]);  
     }    char fileresprobmorprev[FILENAMELENGTH];
     fscanf(ficpar,"\n");  
     printf("\n");    if(popbased==1){
     fprintf(ficparo,"\n");      if(mobilav!=0)
   }        strcpy(digitp,"-populbased-mobilav-");
   for(i=1; i <=npar; i++)      else strcpy(digitp,"-populbased-nomobil-");
     for(j=i+1;j<=npar;j++)    }
       matcov[i][j]=matcov[j][i];    else 
          strcpy(digitp,"-stablbased-");
   printf("\n");  
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     /*-------- Rewriting paramater file ----------*/      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
      strcpy(rfileres,"r");    /* "Rparameterfile */        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/        printf(" Error in movingaverage mobilav=%d\n",mobilav);
      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;    strcpy(fileresprobmorprev,"prmorprev"); 
     }    sprintf(digit,"%-d",ij);
     fprintf(ficres,"#%s\n",version);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
        strcat(fileresprobmorprev,digit); /* Tvar to be done */
     /*-------- data file ----------*/    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     if((fic=fopen(datafile,"r"))==NULL)    {    strcat(fileresprobmorprev,fileres);
       printf("Problem with datafile: %s\n", datafile);goto end;    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     }      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     n= lastobs;    }
     severity = vector(1,maxwav);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     outcome=imatrix(1,maxwav+1,1,n);   
     num=ivector(1,n);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     moisnais=vector(1,n);    pstamp(ficresprobmorprev);
     annais=vector(1,n);    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     moisdc=vector(1,n);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     andc=vector(1,n);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     agedc=vector(1,n);      fprintf(ficresprobmorprev," p.%-d SE",j);
     cod=ivector(1,n);      for(i=1; i<=nlstate;i++)
     weight=vector(1,n);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    }  
     mint=matrix(1,maxwav,1,n);    fprintf(ficresprobmorprev,"\n");
     anint=matrix(1,maxwav,1,n);    fprintf(ficgp,"\n# Routine varevsij");
     s=imatrix(1,maxwav+1,1,n);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     adl=imatrix(1,maxwav+1,1,n);        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");
     tab=ivector(1,NCOVMAX);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     ncodemax=ivector(1,8);  /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     i=1;    pstamp(ficresvij);
     while (fgets(line, MAXLINE, fic) != NULL)    {    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
       if ((i >= firstobs) && (i <=lastobs)) {    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);
         for (j=maxwav;j>=1;j--){    else
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
           strcpy(line,stra);    fprintf(ficresvij,"# Age");
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    for(i=1; i<=nlstate;i++)
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      for(j=1; j<=nlstate;j++)
         }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
            fprintf(ficresvij,"\n");
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    doldm=matrix(1,nlstate,1,nlstate);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);  
         for (j=ncovcol;j>=1;j--){    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    gpp=vector(nlstate+1,nlstate+ndeath);
         }    gmp=vector(nlstate+1,nlstate+ndeath);
         num[i]=atol(stra);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
            
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    if(estepm < stepm){
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
         i=i+1;    else  hstepm=estepm;   
       }    /* For example we decided to compute the life expectancy with the smallest unit */
     }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     /* printf("ii=%d", ij);       nhstepm is the number of hstepm from age to agelim 
        scanf("%d",i);*/       nstepm is the number of stepm from age to agelin. 
   imx=i-1; /* Number of individuals */       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
   /* for (i=1; i<=imx; i++){       survival function given by stepm (the optimization length). Unfortunately it
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;       means that if the survival funtion is printed every two years of age and if
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;       results. So we changed our mind and took the option of the best precision.
     }*/    */
    /*  for (i=1; i<=imx; i++){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
      if (s[4][i]==9)  s[4][i]=-1;    agelim = AGESUP;
      printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
        nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   /* Calculation of the number of parameter from char model*/      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   Tvar=ivector(1,15);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   Tprod=ivector(1,15);      gp=matrix(0,nhstepm,1,nlstate);
   Tvaraff=ivector(1,15);      gm=matrix(0,nhstepm,1,nlstate);
   Tvard=imatrix(1,15,1,2);  
   Tage=ivector(1,15);        
          for(theta=1; theta <=npar; theta++){
   if (strlen(model) >1){        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     j=0, j1=0, k1=1, k2=1;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     j=nbocc(model,'+');        }
     j1=nbocc(model,'*');        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     cptcovn=j+1;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     cptcovprod=j1;  
            if (popbased==1) {
     strcpy(modelsav,model);          if(mobilav ==0){
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){            for(i=1; i<=nlstate;i++)
       printf("Error. Non available option model=%s ",model);              prlim[i][i]=probs[(int)age][i][ij];
       goto end;          }else{ /* mobilav */ 
     }            for(i=1; i<=nlstate;i++)
                  prlim[i][i]=mobaverage[(int)age][i][ij];
     for(i=(j+1); i>=1;i--){          }
       cutv(stra,strb,modelsav,'+');        }
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        for(j=1; j<= nlstate; j++){
       /*scanf("%d",i);*/          for(h=0; h<=nhstepm; h++){
       if (strchr(strb,'*')) {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
         cutv(strd,strc,strb,'*');              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
         if (strcmp(strc,"age")==0) {          }
           cptcovprod--;        }
           cutv(strb,stre,strd,'V');        /* This for computing probability of death (h=1 means
           Tvar[i]=atoi(stre);           computed over hstepm matrices product = hstepm*stepm months) 
           cptcovage++;           as a weighted average of prlim.
             Tage[cptcovage]=i;        */
             /*printf("stre=%s ", stre);*/        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
         else if (strcmp(strd,"age")==0) {            gpp[j] += prlim[i][i]*p3mat[i][j][1];
           cptcovprod--;        }    
           cutv(strb,stre,strc,'V');        /* end probability of death */
           Tvar[i]=atoi(stre);  
           cptcovage++;        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           Tage[cptcovage]=i;          xp[i] = x[i] - (i==theta ?delti[theta]:0);
         }        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         else {        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           cutv(strb,stre,strc,'V');   
           Tvar[i]=ncovcol+k1;        if (popbased==1) {
           cutv(strb,strc,strd,'V');          if(mobilav ==0){
           Tprod[k1]=i;            for(i=1; i<=nlstate;i++)
           Tvard[k1][1]=atoi(strc);              prlim[i][i]=probs[(int)age][i][ij];
           Tvard[k1][2]=atoi(stre);          }else{ /* mobilav */ 
           Tvar[cptcovn+k2]=Tvard[k1][1];            for(i=1; i<=nlstate;i++)
           Tvar[cptcovn+k2+1]=Tvard[k1][2];              prlim[i][i]=mobaverage[(int)age][i][ij];
           for (k=1; k<=lastobs;k++)          }
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        }
           k1++;  
           k2=k2+2;        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
         }          for(h=0; h<=nhstepm; h++){
       }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
       else {              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          }
        /*  scanf("%d",i);*/        }
       cutv(strd,strc,strb,'V');        /* This for computing probability of death (h=1 means
       Tvar[i]=atoi(strc);           computed over hstepm matrices product = hstepm*stepm months) 
       }           as a weighted average of prlim.
       strcpy(modelsav,stra);          */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         scanf("%d",i);*/          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
 }        }    
          /* end probability of death */
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);  
   printf("cptcovprod=%d ", cptcovprod);        for(j=1; j<= nlstate; j++) /* vareij */
   scanf("%d ",i);*/          for(h=0; h<=nhstepm; h++){
     fclose(fic);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
     /*  if(mle==1){*/  
     if (weightopt != 1) { /* Maximisation without weights*/        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
       for(i=1;i<=n;i++) weight[i]=1.0;          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     }        }
     /*-calculation of age at interview from date of interview and age at death -*/  
     agev=matrix(1,maxwav,1,imx);      } /* End theta */
   
     for (i=1; i<=imx; i++) {      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
       for(m=2; (m<= maxwav); m++) {  
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){      for(h=0; h<=nhstepm; h++) /* veij */
          anint[m][i]=9999;        for(j=1; j<=nlstate;j++)
          s[m][i]=-1;          for(theta=1; theta <=npar; theta++)
        }            trgradg[h][j][theta]=gradg[h][theta][j];
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;  
       }      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     }        for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     for (i=1; i<=imx; i++)  {    
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  
       for(m=1; (m<= maxwav); m++){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         if(s[m][i] >0){      for(i=1;i<=nlstate;i++)
           if (s[m][i] >= nlstate+1) {        for(j=1;j<=nlstate;j++)
             if(agedc[i]>0)          vareij[i][j][(int)age] =0.;
               if(moisdc[i]!=99 && andc[i]!=9999)  
                 agev[m][i]=agedc[i];      for(h=0;h<=nhstepm;h++){
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/        for(k=0;k<=nhstepm;k++){
            else {          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
               if (andc[i]!=9999){          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          for(i=1;i<=nlstate;i++)
               agev[m][i]=-1;            for(j=1;j<=nlstate;j++)
               }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
             }        }
           }      }
           else if(s[m][i] !=9){ /* Should no more exist */    
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);      /* pptj */
             if(mint[m][i]==99 || anint[m][i]==9999)      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
               agev[m][i]=1;      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
             else if(agev[m][i] <agemin){      for(j=nlstate+1;j<=nlstate+ndeath;j++)
               agemin=agev[m][i];        for(i=nlstate+1;i<=nlstate+ndeath;i++)
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/          varppt[j][i]=doldmp[j][i];
             }      /* end ppptj */
             else if(agev[m][i] >agemax){      /*  x centered again */
               agemax=agev[m][i];      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
             }   
             /*agev[m][i]=anint[m][i]-annais[i];*/      if (popbased==1) {
             /*   agev[m][i] = age[i]+2*m;*/        if(mobilav ==0){
           }          for(i=1; i<=nlstate;i++)
           else { /* =9 */            prlim[i][i]=probs[(int)age][i][ij];
             agev[m][i]=1;        }else{ /* mobilav */ 
             s[m][i]=-1;          for(i=1; i<=nlstate;i++)
           }            prlim[i][i]=mobaverage[(int)age][i][ij];
         }        }
         else /*= 0 Unknown */      }
           agev[m][i]=1;               
       }      /* This for computing probability of death (h=1 means
             computed over hstepm (estepm) matrices product = hstepm*stepm months) 
     }         as a weighted average of prlim.
     for (i=1; i<=imx; i++)  {      */
       for(m=1; (m<= maxwav); m++){      for(j=nlstate+1;j<=nlstate+ndeath;j++){
         if (s[m][i] > (nlstate+ndeath)) {        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           printf("Error: Wrong value in nlstate or ndeath\n");            gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
           goto end;      }    
         }      /* end probability of death */
       }  
     }      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
     free_vector(severity,1,maxwav);          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     free_imatrix(outcome,1,maxwav+1,1,n);        }
     free_vector(moisnais,1,n);      } 
     free_vector(annais,1,n);      fprintf(ficresprobmorprev,"\n");
     /* free_matrix(mint,1,maxwav,1,n);  
        free_matrix(anint,1,maxwav,1,n);*/      fprintf(ficresvij,"%.0f ",age );
     free_vector(moisdc,1,n);      for(i=1; i<=nlstate;i++)
     free_vector(andc,1,n);        for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
            }
     wav=ivector(1,imx);      fprintf(ficresvij,"\n");
     dh=imatrix(1,lastpass-firstpass+1,1,imx);      free_matrix(gp,0,nhstepm,1,nlstate);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);      free_matrix(gm,0,nhstepm,1,nlstate);
          free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
     /* Concatenates waves */      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
       Tcode=ivector(1,100);    free_vector(gmp,nlstate+1,nlstate+ndeath);
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
       ncodemax[1]=1;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
          /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
    codtab=imatrix(1,100,1,10);    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
    h=0;  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
    m=pow(2,cptcoveff);  /*   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); */
    for(k=1;k<=cptcoveff; k++){    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
      for(i=1; i <=(m/pow(2,k));i++){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
        for(j=1; j <= ncodemax[k]; j++){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
            h++;    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);
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/  */
          }  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
        }    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
      }  
    }    free_vector(xp,1,npar);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    free_matrix(doldm,1,nlstate,1,nlstate);
       codtab[1][2]=1;codtab[2][2]=2; */    free_matrix(dnewm,1,nlstate,1,npar);
    /* for(i=1; i <=m ;i++){    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       for(k=1; k <=cptcovn; k++){    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       }    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       printf("\n");    fclose(ficresprobmorprev);
       }    fflush(ficgp);
       scanf("%d",i);*/    fflush(fichtm); 
      }  /* end varevsij */
    /* Calculates basic frequencies. Computes observed prevalence at single age  
        and prints on file fileres'p'. */  /************ 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, char strstart[])
      {
        /* Variance of prevalence limit */
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **newm;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **dnewm,**doldm;
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    int i, j, nhstepm, hstepm;
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    int k, cptcode;
          double *xp;
     /* For Powell, parameters are in a vector p[] starting at p[1]    double *gp, *gm;
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    double **gradg, **trgradg;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    double age,agelim;
     int theta;
     if(mle==1){    
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    pstamp(ficresvpl);
     }    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
        fprintf(ficresvpl,"# Age");
     /*--------- results files --------------*/    for(i=1; i<=nlstate;i++)
     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(ficresvpl," %1d-%1d",i,i);
      fprintf(ficresvpl,"\n");
   
    jk=1;    xp=vector(1,npar);
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    dnewm=matrix(1,nlstate,1,npar);
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    doldm=matrix(1,nlstate,1,nlstate);
    for(i=1,jk=1; i <=nlstate; i++){    
      for(k=1; k <=(nlstate+ndeath); k++){    hstepm=1*YEARM; /* Every year of age */
        if (k != i)    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
          {    agelim = AGESUP;
            printf("%d%d ",i,k);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
            fprintf(ficres,"%1d%1d ",i,k);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
            for(j=1; j <=ncovmodel; j++){      if (stepm >= YEARM) hstepm=1;
              printf("%f ",p[jk]);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
              fprintf(ficres,"%f ",p[jk]);      gradg=matrix(1,npar,1,nlstate);
              jk++;      gp=vector(1,nlstate);
            }      gm=vector(1,nlstate);
            printf("\n");  
            fprintf(ficres,"\n");      for(theta=1; theta <=npar; theta++){
          }        for(i=1; i<=npar; i++){ /* Computes gradient */
      }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
    }        }
  if(mle==1){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     /* Computing hessian and covariance matrix */        for(i=1;i<=nlstate;i++)
     ftolhess=ftol; /* Usually correct */          gp[i] = prlim[i][i];
     hesscov(matcov, p, npar, delti, ftolhess, func);      
  }        for(i=1; i<=npar; i++) /* Computes gradient */
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     printf("# Scales (for hessian or gradient estimation)\n");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
      for(i=1,jk=1; i <=nlstate; i++){        for(i=1;i<=nlstate;i++)
       for(j=1; j <=nlstate+ndeath; j++){          gm[i] = prlim[i][i];
         if (j!=i) {  
           fprintf(ficres,"%1d%1d",i,j);        for(i=1;i<=nlstate;i++)
           printf("%1d%1d",i,j);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
           for(k=1; k<=ncovmodel;k++){      } /* End theta */
             printf(" %.5e",delti[jk]);  
             fprintf(ficres," %.5e",delti[jk]);      trgradg =matrix(1,nlstate,1,npar);
             jk++;  
           }      for(j=1; j<=nlstate;j++)
           printf("\n");        for(theta=1; theta <=npar; theta++)
           fprintf(ficres,"\n");          trgradg[j][theta]=gradg[theta][j];
         }  
       }      for(i=1;i<=nlstate;i++)
      }        varpl[i][(int)age] =0.;
          matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
     k=1;      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
     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");        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     for(i=1;i<=npar;i++){  
       /*  if (k>nlstate) k=1;      fprintf(ficresvpl,"%.0f ",age );
       i1=(i-1)/(ncovmodel*nlstate)+1;      for(i=1; i<=nlstate;i++)
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       printf("%s%d%d",alph[k],i1,tab[i]);*/      fprintf(ficresvpl,"\n");
       fprintf(ficres,"%3d",i);      free_vector(gp,1,nlstate);
       printf("%3d",i);      free_vector(gm,1,nlstate);
       for(j=1; j<=i;j++){      free_matrix(gradg,1,npar,1,nlstate);
         fprintf(ficres," %.5e",matcov[i][j]);      free_matrix(trgradg,1,nlstate,1,npar);
         printf(" %.5e",matcov[i][j]);    } /* End age */
       }  
       fprintf(ficres,"\n");    free_vector(xp,1,npar);
       printf("\n");    free_matrix(doldm,1,nlstate,1,npar);
       k++;    free_matrix(dnewm,1,nlstate,1,nlstate);
     }  
      }
     while((c=getc(ficpar))=='#' && c!= EOF){  
       ungetc(c,ficpar);  /************ Variance of one-step probabilities  ******************/
       fgets(line, MAXLINE, ficpar);  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[])
       puts(line);  {
       fputs(line,ficparo);    int i, j=0,  i1, k1, l1, t, tj;
     }    int k2, l2, j1,  z1;
     ungetc(c,ficpar);    int k=0,l, cptcode;
     estepm=0;    int first=1, first1;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     if (estepm==0 || estepm < stepm) estepm=stepm;    double **dnewm,**doldm;
     if (fage <= 2) {    double *xp;
       bage = ageminpar;    double *gp, *gm;
       fage = agemaxpar;    double **gradg, **trgradg;
     }    double **mu;
        double age,agelim, cov[NCOVMAX];
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    int theta;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    char fileresprob[FILENAMELENGTH];
      char fileresprobcov[FILENAMELENGTH];
     while((c=getc(ficpar))=='#' && c!= EOF){    char fileresprobcor[FILENAMELENGTH];
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    double ***varpij;
     puts(line);  
     fputs(line,ficparo);    strcpy(fileresprob,"prob"); 
   }    strcat(fileresprob,fileres);
   ungetc(c,ficpar);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprob);
   fscanf(ficpar,"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", fileresprob);
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    }
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    strcpy(fileresprobcov,"probcov"); 
          strcat(fileresprobcov,fileres);
   while((c=getc(ficpar))=='#' && c!= EOF){    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
     ungetc(c,ficpar);      printf("Problem with resultfile: %s\n", fileresprobcov);
     fgets(line, MAXLINE, ficpar);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     puts(line);    }
     fputs(line,ficparo);    strcpy(fileresprobcor,"probcor"); 
   }    strcat(fileresprobcor,fileres);
   ungetc(c,ficpar);    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    }
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   fscanf(ficpar,"pop_based=%d\n",&popbased);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficparo,"pop_based=%d\n",popbased);      fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficres,"pop_based=%d\n",popbased);      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);
   while((c=getc(ficpar))=='#' && c!= EOF){    pstamp(ficresprob);
     ungetc(c,ficpar);    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprob,"# Age");
     puts(line);    pstamp(ficresprobcov);
     fputs(line,ficparo);    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   }    fprintf(ficresprobcov,"# Age");
   ungetc(c,ficpar);    pstamp(ficresprobcor);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);    fprintf(ficresprobcor,"# Age");
 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(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);  
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
 while((c=getc(ficpar))=='#' && c!= EOF){        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
     ungetc(c,ficpar);        fprintf(ficresprobcov," p%1d-%1d ",i,j);
     fgets(line, MAXLINE, ficpar);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
     puts(line);      }  
     fputs(line,ficparo);   /* fprintf(ficresprob,"\n");
   }    fprintf(ficresprobcov,"\n");
   ungetc(c,ficpar);    fprintf(ficresprobcor,"\n");
    */
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    xp=vector(1,npar);
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
 /*------------ gnuplot -------------*/    fprintf(ficgp,"\n# Routine varprob");
   strcpy(optionfilegnuplot,optionfilefiname);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   strcat(optionfilegnuplot,".gp");    fprintf(fichtm,"\n");
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {  
     printf("Problem with file %s",optionfilegnuplot);    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
   }    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
   fclose(ficgp);    file %s<br>\n",optionfilehtmcov);
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
 /*--------- index.htm --------*/  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");
   strcpy(optionfilehtm,optionfile);    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. \
   strcat(optionfilehtm,".htm");  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
     printf("Problem with %s \n",optionfilehtm), exit(0);  standard deviations wide on each axis. <br>\
   }   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n  
 \n    cov[1]=1;
 Total number of observations=%d <br>\n    tj=cptcoveff;
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
 <hr  size=\"2\" color=\"#EC5E5E\">    j1=0;
  <ul><li>Parameter files<br>\n    for(t=1; t<=tj;t++){
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n      for(i1=1; i1<=ncodemax[t];i1++){ 
  - 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);        j1++;
   fclose(fichtm);        if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprob, "**********\n#\n");
 /*------------ free_vector  -------------*/          fprintf(ficresprobcov, "\n#********** Variable "); 
  chdir(path);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprobcov, "**********\n#\n");
  free_ivector(wav,1,imx);          
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);          fprintf(ficgp, "\n#********** Variable "); 
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);            for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
  free_ivector(num,1,n);          fprintf(ficgp, "**********\n#\n");
  free_vector(agedc,1,n);          
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          
  fclose(ficparo);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
  fclose(ficres);          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
   /*--------------- Prevalence limit --------------*/          fprintf(ficresprobcor, "\n#********** Variable ");    
            for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcpy(filerespl,"pl");          fprintf(ficresprobcor, "**********\n#");    
   strcat(filerespl,fileres);        }
   if((ficrespl=fopen(filerespl,"w"))==NULL) {        
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        for (age=bage; age<=fage; age ++){ 
   }          cov[2]=age;
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          for (k=1; k<=cptcovn;k++) {
   fprintf(ficrespl,"#Prevalence limit\n");            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
   fprintf(ficrespl,"#Age ");          }
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   fprintf(ficrespl,"\n");          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]]];
   prlim=matrix(1,nlstate,1,nlstate);          
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          gp=vector(1,(nlstate)*(nlstate+ndeath));
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          gm=vector(1,(nlstate)*(nlstate+ndeath));
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      
   k=0;          for(theta=1; theta <=npar; theta++){
   agebase=ageminpar;            for(i=1; i<=npar; i++)
   agelim=agemaxpar;              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
   ftolpl=1.e-10;            
   i1=cptcoveff;            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   if (cptcovn < 1){i1=1;}            
             k=0;
   for(cptcov=1;cptcov<=i1;cptcov++){            for(i=1; i<= (nlstate); i++){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              for(j=1; j<=(nlstate+ndeath);j++){
         k=k+1;                k=k+1;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/                gp[k]=pmmij[i][j];
         fprintf(ficrespl,"\n#******");              }
         for(j=1;j<=cptcoveff;j++)            }
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            
         fprintf(ficrespl,"******\n");            for(i=1; i<=npar; i++)
                      xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
         for (age=agebase; age<=agelim; age++){      
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
           fprintf(ficrespl,"%.0f",age );            k=0;
           for(i=1; i<=nlstate;i++)            for(i=1; i<=(nlstate); i++){
           fprintf(ficrespl," %.5f", prlim[i][i]);              for(j=1; j<=(nlstate+ndeath);j++){
           fprintf(ficrespl,"\n");                k=k+1;
         }                gm[k]=pmmij[i][j];
       }              }
     }            }
   fclose(ficrespl);       
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
   /*------------- h Pij x at various ages ------------*/              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
            }
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  
   if((ficrespij=fopen(filerespij,"w"))==NULL) {          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;            for(theta=1; theta <=npar; theta++)
   }              trgradg[j][theta]=gradg[theta][j];
   printf("Computing pij: result on file '%s' \n", filerespij);          
            matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
   stepsize=(int) (stepm+YEARM-1)/YEARM;          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
   /*if (stepm<=24) stepsize=2;*/          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
   agelim=AGESUP;          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   hstepm=stepsize*YEARM; /* Every year of age */          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
            pmij(pmmij,cov,ncovmodel,x,nlstate);
   k=0;          
   for(cptcov=1;cptcov<=i1;cptcov++){          k=0;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for(i=1; i<=(nlstate); i++){
       k=k+1;            for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficrespij,"\n#****** ");              k=k+1;
         for(j=1;j<=cptcoveff;j++)              mu[k][(int) age]=pmmij[i][j];
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            }
         fprintf(ficrespij,"******\n");          }
                  for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */              varpij[i][j][(int)age] = doldm[i][j];
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          /*printf("\n%d ",(int)age);
           oldm=oldms;savm=savms;            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           fprintf(ficrespij,"# Age");            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
           for(i=1; i<=nlstate;i++)            }*/
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);          fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficrespij,"\n");          fprintf(ficresprobcov,"\n%d ",(int)age);
            for (h=0; h<=nhstepm; h++){          fprintf(ficresprobcor,"\n%d ",(int)age);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );  
             for(i=1; i<=nlstate;i++)          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
               for(j=1; j<=nlstate+ndeath;j++)            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficrespij,"\n");            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
              }            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          }
           fprintf(ficrespij,"\n");          i=0;
         }          for (k=1; k<=(nlstate);k++){
     }            for (l=1; l<=(nlstate+ndeath);l++){ 
   }              i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
   fclose(ficrespij);                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]));
               }
   /*---------- Forecasting ------------------*/            }
   if((stepm == 1) && (strcmp(model,".")==0)){          }/* end of loop for state */
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);        } /* end of loop for age */
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);  
   }        /* Confidence intervalle of pij  */
   else{        /*
     erreur=108;          fprintf(ficgp,"\nunset parametric;unset label");
     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 log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   }          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
            fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
   /*---------- Health expectancies and variances ------------*/          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
   strcpy(filerest,"t");        */
   strcat(filerest,fileres);  
   if((ficrest=fopen(filerest,"w"))==NULL) {        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;        first1=1;
   }        for (k2=1; k2<=(nlstate);k2++){
   printf("Computing Total LEs with variances: file '%s' \n", filerest);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
   strcpy(filerese,"e");            for (k1=1; k1<=(nlstate);k1++){
   strcat(filerese,fileres);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   if((ficreseij=fopen(filerese,"w"))==NULL) {                if(l1==k1) continue;
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);                i=(k1-1)*(nlstate+ndeath)+l1;
   }                if(i<=j) continue;
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);                for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
  strcpy(fileresv,"v");                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
   strcat(fileresv,fileres);                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
   if((ficresvij=fopen(fileresv,"w"))==NULL) {                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);                    mu1=mu[i][(int) age]/stepm*YEARM ;
   }                    mu2=mu[j][(int) age]/stepm*YEARM;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);                    c12=cv12/sqrt(v1*v2);
   calagedate=-1;                    /* Computing eigen value of matrix of covariance */
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);                    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.;
   k=0;                    if ((lc2 <0) || (lc1 <0) ){
   for(cptcov=1;cptcov<=i1;cptcov++){                      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);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                      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);
       k=k+1;                      lc1=fabs(lc1);
       fprintf(ficrest,"\n#****** ");                      lc2=fabs(lc2);
       for(j=1;j<=cptcoveff;j++)                    }
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficrest,"******\n");                    /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       fprintf(ficreseij,"\n#****** ");                    /*v21=sqrt(1.-v11*v11); *//* error */
       for(j=1;j<=cptcoveff;j++)                    v21=(lc1-v1)/cv12*v11;
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    v12=-v21;
       fprintf(ficreseij,"******\n");                    v22=v11;
                     tnalp=v21/v11;
       fprintf(ficresvij,"\n#****** ");                    if(first1==1){
       for(j=1;j<=cptcoveff;j++)                      first1=0;
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      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);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                    /*printf(fignu*/
       oldm=oldms;savm=savms;                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);                      /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                      if(first==1){
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);                      first=0;
       oldm=oldms;savm=savms;                      fprintf(ficgp,"\nset parametric;unset label");
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);                      fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
     :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
       fprintf(ficrest,"\n");                              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);
       epj=vector(1,nlstate+1);                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
       for(age=bage; age <=fage ;age++){                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
         if (popbased==1) {                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
           for(i=1; i<=nlstate;i++)                      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",\
             prlim[i][i]=probs[(int)age][i][k];                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         }                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                            }else{
         fprintf(ficrest," %4.0f",age);                      first=0;
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
             epj[j] += prlim[i][i]*eij[i][j][(int)age];                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)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",\
           }                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
           epj[nlstate+1] +=epj[j];                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
         }                    }/* if first */
                   } /* age mod 5 */
         for(i=1, vepp=0.;i <=nlstate;i++)                } /* end loop age */
           for(j=1;j <=nlstate;j++)                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
             vepp += vareij[i][j][(int)age];                first=1;
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));              } /*l12 */
         for(j=1;j <=nlstate;j++){            } /* k12 */
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));          } /*l1 */
         }        }/* k1 */
         fprintf(ficrest,"\n");      } /* loop covariates */
       }    }
     }    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
   }    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
 free_matrix(mint,1,maxwav,1,n);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(weight,1,n);    free_vector(xp,1,npar);
   fclose(ficreseij);    fclose(ficresprob);
   fclose(ficresvij);    fclose(ficresprobcov);
   fclose(ficrest);    fclose(ficresprobcor);
   fclose(ficpar);    fflush(ficgp);
   free_vector(epj,1,nlstate+1);    fflush(fichtmcov);
    }
   /*------- Variance limit prevalence------*/    
   
   strcpy(fileresvpl,"vpl");  /******************* Printing html file ***********/
   strcat(fileresvpl,fileres);  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {                    int lastpass, int stepm, int weightopt, char model[],\
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
     exit(0);                    int popforecast, int estepm ,\
   }                    double jprev1, double mprev1,double anprev1, \
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);                    double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
       k=k+1;  </ul>");
       fprintf(ficresvpl,"\n#****** ");     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
       for(j=1;j<=cptcoveff;j++)   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
       fprintf(ficresvpl,"******\n");     fprintf(fichtm,"\
         - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
       varpl=matrix(1,nlstate,(int) bage, (int) fage);             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
       oldm=oldms;savm=savms;     fprintf(fichtm,"\
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
     }             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
  }     fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
   fclose(ficresvpl);     <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   /*---------- End : free ----------------*/     fprintf(fichtm,"\
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);   - Population projections by age and states: \
       <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
    
     m=cptcoveff;
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);   jj1=0;
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);   for(k1=1; k1<=m;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
   free_matrix(matcov,1,npar,1,npar);       jj1++;
   free_vector(delti,1,npar);       if (cptcovn > 0) {
   free_matrix(agev,1,maxwav,1,imx);         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);         for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   fprintf(fichtm,"\n</body>");         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
   fclose(fichtm);       }
   fclose(ficgp);       /* Pij */
         fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
   if(erreur >0)       /* Quasi-incidences */
     printf("End of Imach with error or warning %d\n",erreur);       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
   else   printf("End of Imach\n");   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> \
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
           /* Period (stable) prevalence in each health state */
   /* 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,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   /*------ End -----------*/  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
  end:          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> \
 #ifdef windows  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
   /* chdir(pathcd);*/       }
 #endif     } /* end i1 */
  /*system("wgnuplot graph.plt");*/   }/* End k1 */
  /*system("../gp37mgw/wgnuplot graph.plt");*/   fprintf(fichtm,"</ul>");
  /*system("cd ../gp37mgw");*/  
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/  
  strcpy(plotcmd,GNUPLOTPROGRAM);   fprintf(fichtm,"\
  strcat(plotcmd," ");  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
  strcat(plotcmd,optionfilegnuplot);   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
  system(plotcmd);  
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
 #ifdef windows           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
   while (z[0] != 'q') {   fprintf(fichtm,"\
     /* chdir(path); */   - Variance-covariance 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,"probcov"),subdirf2(fileres,"probcov"));
     scanf("%s",z);  
     if (z[0] == 'c') system("./imach");   fprintf(fichtm,"\
     else if (z[0] == 'e') system(optionfilehtm);   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     else if (z[0] == 'g') system(plotcmd);           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
     else if (z[0] == 'q') exit(0);   fprintf(fichtm,"\
   }   - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
 #endif     <a href=\"%s\">%s</a> <br>\n</li>",
 }             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else        fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                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.1.140


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