Diff for /imach/src/imach.c between versions 1.48 and 1.136

version 1.48, 2002/06/10 13:12:49 version 1.136, 2010/04/26 20:30:53
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.136  2010/04/26 20:30:53  brouard
      (Module): merging some libgsl code. Fixing computation
   This program computes Healthy Life Expectancies from    of likelione (using inter/intrapolation if mle = 0) in order to
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    get same likelihood as if mle=1.
   first survey ("cross") where individuals from different ages are    Some cleaning of code and comments added.
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.135  2009/10/29 15:33:14  brouard
   second wave of interviews ("longitudinal") which measure each change    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   (if any) in individual health status.  Health expectancies are  
   computed from the time spent in each health state according to a    Revision 1.134  2009/10/29 13:18:53  brouard
   model. More health states you consider, more time is necessary to reach the    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   Maximum Likelihood of the parameters involved in the model.  The  
   simplest model is the multinomial logistic model where pij is the    Revision 1.133  2009/07/06 10:21:25  brouard
   probability to be observed in state j at the second wave    just nforces
   conditional to be observed in state i at the first wave. Therefore  
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Revision 1.132  2009/07/06 08:22:05  brouard
   'age' is age and 'sex' is a covariate. If you want to have a more    Many tings
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.131  2009/06/20 16:22:47  brouard
   you to do it.  More covariates you add, slower the    Some dimensions resccaled
   convergence.  
     Revision 1.130  2009/05/26 06:44:34  brouard
   The advantage of this computer programme, compared to a simple    (Module): Max Covariate is now set to 20 instead of 8. A
   multinomial logistic model, is clear when the delay between waves is not    lot of cleaning with variables initialized to 0. Trying to make
   identical for each individual. Also, if a individual missed an    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.129  2007/08/31 13:49:27  lievre
     Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   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 1.128  2006/06/30 13:02:05  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    (Module): Clarifications on computing e.j
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.127  2006/04/28 18:11:50  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    (Module): Yes the sum of survivors was wrong since
   and the contribution of each individual to the likelihood is simply    imach-114 because nhstepm was no more computed in the age
   hPijx.    loop. Now we define nhstepma in the age loop.
     (Module): In order to speed up (in case of numerous covariates) we
   Also this programme outputs the covariance matrix of the parameters but also    compute health expectancies (without variances) in a first step
   of the life expectancies. It also computes the prevalence limits.    and then all the health expectancies with variances or standard
      deviation (needs data from the Hessian matrices) which slows the
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    computation.
            Institut national d'études démographiques, Paris.    In the future we should be able to stop the program is only health
   This software have been partly granted by Euro-REVES, a concerted action    expectancies and graph are needed without standard deviations.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.126  2006/04/28 17:23:28  brouard
   software can be distributed freely for non commercial use. Latest version    (Module): Yes the sum of survivors was wrong since
   can be accessed at http://euroreves.ined.fr/imach .    imach-114 because nhstepm was no more computed in the age
   **********************************************************************/    loop. Now we define nhstepma in the age loop.
      Version 0.98h
 #include <math.h>  
 #include <stdio.h>    Revision 1.125  2006/04/04 15:20:31  lievre
 #include <stdlib.h>    Errors in calculation of health expectancies. Age was not initialized.
 #include <unistd.h>    Forecasting file added.
   
 #define MAXLINE 256    Revision 1.124  2006/03/22 17:13:53  lievre
 #define GNUPLOTPROGRAM "gnuplot"    Parameters are printed with %lf instead of %f (more numbers after the comma).
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    The log-likelihood is printed in the log file
 #define FILENAMELENGTH 80  
 /*#define DEBUG*/    Revision 1.123  2006/03/20 10:52:43  brouard
 #define windows    * imach.c (Module): <title> changed, corresponds to .htm file
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    name. <head> headers where missing.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     * imach.c (Module): Weights can have a decimal point as for
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    English (a comma might work with a correct LC_NUMERIC environment,
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
 #define NINTERVMAX 8    1.
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Version 0.98g
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  
 #define NCOVMAX 8 /* Maximum number of covariates */    Revision 1.122  2006/03/20 09:45:41  brouard
 #define MAXN 20000    (Module): Weights can have a decimal point as for
 #define YEARM 12. /* Number of months per year */    English (a comma might work with a correct LC_NUMERIC environment,
 #define AGESUP 130    otherwise the weight is truncated).
 #define AGEBASE 40    Modification of warning when the covariates values are not 0 or
 #ifdef windows    1.
 #define DIRSEPARATOR '\\'    Version 0.98g
 #else  
 #define DIRSEPARATOR '/'    Revision 1.121  2006/03/16 17:45:01  lievre
 #endif    * imach.c (Module): Comments concerning covariates added
   
 char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES ";    * imach.c (Module): refinements in the computation of lli if
 int erreur; /* Error number */    status=-2 in order to have more reliable computation if stepm is
 int nvar;    not 1 month. Version 0.98f
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.120  2006/03/16 15:10:38  lievre
 int nlstate=2; /* Number of live states */    (Module): refinements in the computation of lli if
 int ndeath=1; /* Number of dead states */    status=-2 in order to have more reliable computation if stepm is
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    not 1 month. Version 0.98f
 int popbased=0;  
     Revision 1.119  2006/03/15 17:42:26  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): Bug if status = -2, the loglikelihood was
 int maxwav; /* Maxim number of waves */    computed as likelihood omitting the logarithm. Version O.98e
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.118  2006/03/14 18:20:07  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): varevsij Comments added explaining the second
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    table of variances if popbased=1 .
 double jmean; /* Mean space between 2 waves */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Function pstamp added
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    (Module): Version 0.98d
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    Revision 1.117  2006/03/14 17:16:22  brouard
 FILE *fichtm; /* Html File */    (Module): varevsij Comments added explaining the second
 FILE *ficreseij;    table of variances if popbased=1 .
 char filerese[FILENAMELENGTH];    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 FILE  *ficresvij;    (Module): Function pstamp added
 char fileresv[FILENAMELENGTH];    (Module): Version 0.98d
 FILE  *ficresvpl;  
 char fileresvpl[FILENAMELENGTH];    Revision 1.116  2006/03/06 10:29:27  brouard
 char title[MAXLINE];    (Module): Variance-covariance wrong links and
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    varian-covariance of ej. is needed (Saito).
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];  
     Revision 1.115  2006/02/27 12:17:45  brouard
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    (Module): One freematrix added in mlikeli! 0.98c
   
 char filerest[FILENAMELENGTH];    Revision 1.114  2006/02/26 12:57:58  brouard
 char fileregp[FILENAMELENGTH];    (Module): Some improvements in processing parameter
 char popfile[FILENAMELENGTH];    filename with strsep.
   
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    Revision 1.113  2006/02/24 14:20:24  brouard
     (Module): Memory leaks checks with valgrind and:
 #define NR_END 1    datafile was not closed, some imatrix were not freed and on matrix
 #define FREE_ARG char*    allocation too.
 #define FTOL 1.0e-10  
     Revision 1.112  2006/01/30 09:55:26  brouard
 #define NRANSI    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define ITMAX 200  
     Revision 1.111  2006/01/25 20:38:18  brouard
 #define TOL 2.0e-4    (Module): Lots of cleaning and bugs added (Gompertz)
     (Module): Comments can be added in data file. Missing date values
 #define CGOLD 0.3819660    can be a simple dot '.'.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.109  2006/01/24 19:37:15  brouard
 #define TINY 1.0e-20    (Module): Comments (lines starting with a #) are allowed in data.
   
 static double maxarg1,maxarg2;    Revision 1.108  2006/01/19 18:05:42  lievre
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Gnuplot problem appeared...
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    To be fixed
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.107  2006/01/19 16:20:37  brouard
 #define rint(a) floor(a+0.5)    Test existence of gnuplot in imach path
   
 static double sqrarg;    Revision 1.106  2006/01/19 13:24:36  brouard
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Some cleaning and links added in html output
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     Revision 1.105  2006/01/05 20:23:19  lievre
 int imx;    *** empty log message ***
 int stepm;  
 /* Stepm, step in month: minimum step interpolation*/    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 int estepm;    (Module): If the status is missing at the last wave but we know
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 int m,nb;    contributions to the likelihood is 1 - Prob of dying from last
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    the healthy state at last known wave). Version is 0.98
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.103  2005/09/30 15:54:49  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 double *weight;  
 int **s; /* Status */    Revision 1.102  2004/09/15 17:31:30  brouard
 double *agedc, **covar, idx;    Add the possibility to read data file including tab characters.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.101  2004/09/15 10:38:38  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Fix on curr_time
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.100  2004/07/12 18:29:06  brouard
 /**************** split *************************/    Add version for Mac OS X. Just define UNIX in Makefile
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.99  2004/06/05 08:57:40  brouard
    char *s;                             /* pointer */    *** empty log message ***
    int  l1, l2;                         /* length counters */  
     Revision 1.98  2004/05/16 15:05:56  brouard
    l1 = strlen( path );                 /* length of path */    New version 0.97 . First attempt to estimate force of mortality
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    directly from the data i.e. without the need of knowing the health
    s = strrchr( path,  DIRSEPARATOR );          /* find last / */    state at each age, but using a Gompertz model: log u =a + b*age .
    if ( s == NULL ) {                   /* no directory, so use current */    This is the basic analysis of mortality and should be done before any
 #if     defined(__bsd__)                /* get current working directory */    other analysis, in order to test if the mortality estimated from the
       extern char       *getwd( );    cross-longitudinal survey is different from the mortality estimated
     from other sources like vital statistic data.
       if ( getwd( dirc ) == NULL ) {  
 #else    The same imach parameter file can be used but the option for mle should be -3.
       extern char       *getcwd( );  
     Agnès, who wrote this part of the code, tried to keep most of the
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    former routines in order to include the new code within the former code.
 #endif  
          return( GLOCK_ERROR_GETCWD );    The output is very simple: only an estimate of the intercept and of
       }    the slope with 95% confident intervals.
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Current limitations:
       s++;                              /* after this, the filename */    A) Even if you enter covariates, i.e. with the
       l2 = strlen( s );                 /* length of filename */    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    B) There is no computation of Life Expectancy nor Life Table.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.97  2004/02/20 13:25:42  lievre
       dirc[l1-l2] = 0;                  /* add zero */    Version 0.96d. Population forecasting command line is (temporarily)
    }    suppressed.
    l1 = strlen( dirc );                 /* length of directory */  
 #ifdef windows    Revision 1.96  2003/07/15 15:38:55  brouard
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 #else    rewritten within the same printf. Workaround: many printfs.
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }  
 #endif    Revision 1.95  2003/07/08 07:54:34  brouard
    s = strrchr( name, '.' );            /* find last / */    * imach.c (Repository):
    s++;    (Repository): Using imachwizard code to output a more meaningful covariance
    strcpy(ext,s);                       /* save extension */    matrix (cov(a12,c31) instead of numbers.
    l1= strlen( name);  
    l2= strlen( s)+1;    Revision 1.94  2003/06/27 13:00:02  brouard
    strncpy( finame, name, l1-l2);    Just cleaning
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    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
 /******************************************/  
     Revision 1.92  2003/06/25 16:30:45  brouard
 void replace(char *s, char*t)    (Module): On windows (cygwin) function asctime_r doesn't
 {    exist so I changed back to asctime which exists.
   int i;  
   int lg=20;    Revision 1.91  2003/06/25 15:30:29  brouard
   i=0;    * imach.c (Repository): Duplicated warning errors corrected.
   lg=strlen(t);    (Repository): Elapsed time after each iteration is now output. It
   for(i=0; i<= lg; i++) {    helps to forecast when convergence will be reached. Elapsed time
     (s[i] = t[i]);    is stamped in powell.  We created a new html file for the graphs
     if (t[i]== '\\') s[i]='/';    concerning matrix of covariance. It has extension -cov.htm.
   }  
 }    Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
 int nbocc(char *s, char occ)    mle=-1 a template is output in file "or"mypar.txt with the design
 {    of the covariance matrix to be input.
   int i,j=0;  
   int lg=20;    Revision 1.89  2003/06/24 12:30:52  brouard
   i=0;    (Module): Some bugs corrected for windows. Also, when
   lg=strlen(s);    mle=-1 a template is output in file "or"mypar.txt with the design
   for(i=0; i<= lg; i++) {    of the covariance matrix to be input.
   if  (s[i] == occ ) j++;  
   }    Revision 1.88  2003/06/23 17:54:56  brouard
   return j;    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 }  
     Revision 1.87  2003/06/18 12:26:01  brouard
 void cutv(char *u,char *v, char*t, char occ)    Version 0.96
 {  
   int i,lg,j,p=0;    Revision 1.86  2003/06/17 20:04:08  brouard
   i=0;    (Module): Change position of html and gnuplot routines and added
   for(j=0; j<=strlen(t)-1; j++) {    routine fileappend.
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  
   }    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
   lg=strlen(t);    current date of interview. It may happen when the death was just
   for(j=0; j<p; j++) {    prior to the death. In this case, dh was negative and likelihood
     (u[j] = t[j]);    was wrong (infinity). We still send an "Error" but patch by
   }    assuming that the date of death was just one stepm after the
      u[p]='\0';    interview.
     (Repository): Because some people have very long ID (first column)
    for(j=0; j<= lg; j++) {    we changed int to long in num[] and we added a new lvector for
     if (j>=(p+1))(v[j-p-1] = t[j]);    memory allocation. But we also truncated to 8 characters (left
   }    truncation)
 }    (Repository): No more line truncation errors.
   
 /********************** nrerror ********************/    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 void nrerror(char error_text[])    place. It differs from routine "prevalence" which may be called
 {    many times. Probs is memory consuming and must be used with
   fprintf(stderr,"ERREUR ...\n");    parcimony.
   fprintf(stderr,"%s\n",error_text);    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   exit(1);  
 }    Revision 1.83  2003/06/10 13:39:11  lievre
 /*********************** vector *******************/    *** empty log message ***
 double *vector(int nl, int nh)  
 {    Revision 1.82  2003/06/05 15:57:20  brouard
   double *v;    Add log in  imach.c and  fullversion number is now printed.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");  */
   return v-nl+NR_END;  /*
 }     Interpolated Markov Chain
   
 /************************ free vector ******************/    Short summary of the programme:
 void free_vector(double*v, int nl, int nh)    
 {    This program computes Healthy Life Expectancies from
   free((FREE_ARG)(v+nl-NR_END));    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 }    first survey ("cross") where individuals from different ages are
     interviewed on their health status or degree of disability (in the
 /************************ivector *******************************/    case of a health survey which is our main interest) -2- at least a
 int *ivector(long nl,long nh)    second wave of interviews ("longitudinal") which measure each change
 {    (if any) in individual health status.  Health expectancies are
   int *v;    computed from the time spent in each health state according to a
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    model. More health states you consider, more time is necessary to reach the
   if (!v) nrerror("allocation failure in ivector");    Maximum Likelihood of the parameters involved in the model.  The
   return v-nl+NR_END;    simplest model is the multinomial logistic model where pij is the
 }    probability to be observed in state j at the second wave
     conditional to be observed in state i at the first wave. Therefore
 /******************free ivector **************************/    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 void free_ivector(int *v, long nl, long nh)    'age' is age and 'sex' is a covariate. If you want to have a more
 {    complex model than "constant and age", you should modify the program
   free((FREE_ARG)(v+nl-NR_END));    where the markup *Covariates have to be included here again* invites
 }    you to do it.  More covariates you add, slower the
     convergence.
 /******************* imatrix *******************************/  
 int **imatrix(long nrl, long nrh, long ncl, long nch)    The advantage of this computer programme, compared to a simple
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    multinomial logistic model, is clear when the delay between waves is not
 {    identical for each individual. Also, if a individual missed an
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    intermediate interview, the information is lost, but taken into
   int **m;    account using an interpolation or extrapolation.  
    
   /* allocate pointers to rows */    hPijx is the probability to be observed in state i at age x+h
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    conditional to the observed state i at age x. The delay 'h' can be
   if (!m) nrerror("allocation failure 1 in matrix()");    split into an exact number (nh*stepm) of unobserved intermediate
   m += NR_END;    states. This elementary transition (by month, quarter,
   m -= nrl;    semester or year) is modelled as a multinomial logistic.  The hPx
      matrix is simply the matrix product of nh*stepm elementary matrices
      and the contribution of each individual to the likelihood is simply
   /* allocate rows and set pointers to them */    hPijx.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Also this programme outputs the covariance matrix of the parameters but also
   m[nrl] += NR_END;    of the life expectancies. It also computes the period (stable) prevalence. 
   m[nrl] -= ncl;    
      Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;             Institut national d'études démographiques, Paris.
      This software have been partly granted by Euro-REVES, a concerted action
   /* return pointer to array of pointers to rows */    from the European Union.
   return m;    It is copyrighted identically to a GNU software product, ie programme and
 }    software can be distributed freely for non commercial use. Latest version
     can be accessed at http://euroreves.ined.fr/imach .
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
       int **m;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
       long nch,ncl,nrh,nrl;    
      /* free an int matrix allocated by imatrix() */    **********************************************************************/
 {  /*
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    main
   free((FREE_ARG) (m+nrl-NR_END));    read parameterfile
 }    read datafile
     concatwav
 /******************* matrix *******************************/    freqsummary
 double **matrix(long nrl, long nrh, long ncl, long nch)    if (mle >= 1)
 {      mlikeli
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    print results files
   double **m;    if mle==1 
        computes hessian
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    read end of parameter file: agemin, agemax, bage, fage, estepm
   if (!m) nrerror("allocation failure 1 in matrix()");        begin-prev-date,...
   m += NR_END;    open gnuplot file
   m -= nrl;    open html file
     period (stable) prevalence
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));     for age prevalim()
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    h Pij x
   m[nrl] += NR_END;    variance of p varprob
   m[nrl] -= ncl;    forecasting if prevfcast==1 prevforecast call prevalence()
     health expectancies
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    Variance-covariance of DFLE
   return m;    prevalence()
 }     movingaverage()
     varevsij() 
 /*************************free matrix ************************/    if popbased==1 varevsij(,popbased)
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    total life expectancies
 {    Variance of period (stable) prevalence
   free((FREE_ARG)(m[nrl]+ncl-NR_END));   end
   free((FREE_ARG)(m+nrl-NR_END));  */
 }  
   
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)   
 {  #include <math.h>
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #include <stdio.h>
   double ***m;  #include <stdlib.h>
   #include <string.h>
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #include <unistd.h>
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;  #include <limits.h>
   m -= nrl;  #include <sys/types.h>
   #include <sys/stat.h>
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #include <errno.h>
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  extern int errno;
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /* #include <sys/time.h> */
   #include <time.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include "timeval.h"
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #ifdef GSL
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #include <gsl/gsl_errno.h>
   m[nrl][ncl] += NR_END;  #include <gsl/gsl_multimin.h>
   m[nrl][ncl] -= nll;  #endif
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  /* #include <libintl.h> */
    /* #define _(String) gettext (String) */
   for (i=nrl+1; i<=nrh; i++) {  
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #define MAXLINE 256
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;  #define GNUPLOTPROGRAM "gnuplot"
   }  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   return m;  #define FILENAMELENGTH 132
 }  
   #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 /*************************free ma3x ************************/  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  
 {  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define NINTERVMAX 8
 }  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
 /***************** f1dim *************************/  #define NCOVMAX 20 /* Maximum number of covariates */
 extern int ncom;  #define MAXN 20000
 extern double *pcom,*xicom;  #define YEARM 12. /* Number of months per year */
 extern double (*nrfunc)(double []);  #define AGESUP 130
    #define AGEBASE 40
 double f1dim(double x)  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 {  #ifdef UNIX
   int j;  #define DIRSEPARATOR '/'
   double f;  #define CHARSEPARATOR "/"
   double *xt;  #define ODIRSEPARATOR '\\'
    #else
   xt=vector(1,ncom);  #define DIRSEPARATOR '\\'
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define CHARSEPARATOR "\\"
   f=(*nrfunc)(xt);  #define ODIRSEPARATOR '/'
   free_vector(xt,1,ncom);  #endif
   return f;  
 }  /* $Id$ */
   /* $State$ */
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
 {  char fullversion[]="$Revision$ $Date$"; 
   int iter;  char strstart[80];
   double a,b,d,etemp;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   double fu,fv,fw,fx;  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   double ftemp;  int nvar=0, nforce=0; /* Number of variables, number of forces */
   double p,q,r,tol1,tol2,u,v,w,x,xm;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
   double e=0.0;  int npar=NPARMAX;
    int nlstate=2; /* Number of live states */
   a=(ax < cx ? ax : cx);  int ndeath=1; /* Number of dead states */
   b=(ax > cx ? ax : cx);  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   x=w=v=bx;  int popbased=0;
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {  int *wav; /* Number of waves for this individuual 0 is possible */
     xm=0.5*(a+b);  int maxwav=0; /* Maxim number of waves */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
     printf(".");fflush(stdout);  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
 #ifdef DEBUG                     to the likelihood and the sum of weights (done by funcone)*/
     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 mle=1, weightopt=0;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 #endif  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       *xmin=x;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       return fx;  double jmean=1; /* Mean space between 2 waves */
     }  double **oldm, **newm, **savm; /* Working pointers to matrices */
     ftemp=fu;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
     if (fabs(e) > tol1) {  /*FILE *fic ; */ /* Used in readdata only */
       r=(x-w)*(fx-fv);  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
       q=(x-v)*(fx-fw);  FILE *ficlog, *ficrespow;
       p=(x-v)*q-(x-w)*r;  int globpr=0; /* Global variable for printing or not */
       q=2.0*(q-r);  double fretone; /* Only one call to likelihood */
       if (q > 0.0) p = -p;  long ipmx=0; /* Number of contributions */
       q=fabs(q);  double sw; /* Sum of weights */
       etemp=e;  char filerespow[FILENAMELENGTH];
       e=d;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  FILE *ficresilk;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       else {  FILE *ficresprobmorprev;
         d=p/q;  FILE *fichtm, *fichtmcov; /* Html File */
         u=x+d;  FILE *ficreseij;
         if (u-a < tol2 || b-u < tol2)  char filerese[FILENAMELENGTH];
           d=SIGN(tol1,xm-x);  FILE *ficresstdeij;
       }  char fileresstde[FILENAMELENGTH];
     } else {  FILE *ficrescveij;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  char filerescve[FILENAMELENGTH];
     }  FILE  *ficresvij;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  char fileresv[FILENAMELENGTH];
     fu=(*f)(u);  FILE  *ficresvpl;
     if (fu <= fx) {  char fileresvpl[FILENAMELENGTH];
       if (u >= x) a=x; else b=x;  char title[MAXLINE];
       SHFT(v,w,x,u)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
         SHFT(fv,fw,fx,fu)  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
         } else {  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
           if (u < x) a=u; else b=u;  char command[FILENAMELENGTH];
           if (fu <= fw || w == x) {  int  outcmd=0;
             v=w;  
             w=u;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
             fv=fw;  
             fw=fu;  char filelog[FILENAMELENGTH]; /* Log file */
           } else if (fu <= fv || v == x || v == w) {  char filerest[FILENAMELENGTH];
             v=u;  char fileregp[FILENAMELENGTH];
             fv=fu;  char popfile[FILENAMELENGTH];
           }  
         }  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   }  
   nrerror("Too many iterations in brent");  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   *xmin=x;  struct timezone tzp;
   return fx;  extern int gettimeofday();
 }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   long time_value;
 /****************** mnbrak ***********************/  extern long time();
   char strcurr[80], strfor[80];
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))  char *endptr;
 {  long lval;
   double ulim,u,r,q, dum;  double dval;
   double fu;  
    #define NR_END 1
   *fa=(*func)(*ax);  #define FREE_ARG char*
   *fb=(*func)(*bx);  #define FTOL 1.0e-10
   if (*fb > *fa) {  
     SHFT(dum,*ax,*bx,dum)  #define NRANSI 
       SHFT(dum,*fb,*fa,dum)  #define ITMAX 200 
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);  #define TOL 2.0e-4 
   *fc=(*func)(*cx);  
   while (*fb > *fc) {  #define CGOLD 0.3819660 
     r=(*bx-*ax)*(*fb-*fc);  #define ZEPS 1.0e-10 
     q=(*bx-*cx)*(*fb-*fa);  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #define GOLD 1.618034 
     ulim=(*bx)+GLIMIT*(*cx-*bx);  #define GLIMIT 100.0 
     if ((*bx-u)*(u-*cx) > 0.0) {  #define TINY 1.0e-20 
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {  static double maxarg1,maxarg2;
       fu=(*func)(u);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       if (fu < *fc) {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    
           SHFT(*fb,*fc,fu,(*func)(u))  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
           }  #define rint(a) floor(a+0.5)
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  static double sqrarg;
       fu=(*func)(u);  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
     } else {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
       u=(*cx)+GOLD*(*cx-*bx);  int agegomp= AGEGOMP;
       fu=(*func)(u);  
     }  int imx; 
     SHFT(*ax,*bx,*cx,u)  int stepm=1;
       SHFT(*fa,*fb,*fc,fu)  /* Stepm, step in month: minimum step interpolation*/
       }  
 }  int estepm;
   /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 /*************** linmin ************************/  
   int m,nb;
 int ncom;  long *num;
 double *pcom,*xicom;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 double (*nrfunc)(double []);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
    double **pmmij, ***probs;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  double *ageexmed,*agecens;
 {  double dateintmean=0;
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);  double *weight;
   double f1dim(double x);  int **s; /* Status */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  double *agedc, **covar, idx;
               double *fc, double (*func)(double));  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   int j;  double *lsurv, *lpop, *tpop;
   double xx,xmin,bx,ax;  
   double fx,fb,fa;  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
    double ftolhess; /* Tolerance for computing hessian */
   ncom=n;  
   pcom=vector(1,n);  /**************** split *************************/
   xicom=vector(1,n);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   nrfunc=func;  {
   for (j=1;j<=n;j++) {    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
     pcom[j]=p[j];       the name of the file (name), its extension only (ext) and its first part of the name (finame)
     xicom[j]=xi[j];    */ 
   }    char  *ss;                            /* pointer */
   ax=0.0;    int   l1, l2;                         /* length counters */
   xx=1.0;  
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    l1 = strlen(path );                   /* length of path */
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
 #ifdef DEBUG    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
 #endif      strcpy( name, path );               /* we got the fullname name because no directory */
   for (j=1;j<=n;j++) {      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     xi[j] *= xmin;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     p[j] += xi[j];      /* get current working directory */
   }      /*    extern  char* getcwd ( char *buf , int len);*/
   free_vector(xicom,1,n);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   free_vector(pcom,1,n);        return( GLOCK_ERROR_GETCWD );
 }      }
       /* got dirc from getcwd*/
 /*************** powell ************************/      printf(" DIRC = %s \n",dirc);
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    } else {                              /* strip direcotry from path */
             double (*func)(double []))      ss++;                               /* after this, the filename */
 {      l2 = strlen( ss );                  /* length of filename */
   void linmin(double p[], double xi[], int n, double *fret,      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
               double (*func)(double []));      strcpy( name, ss );         /* save file name */
   int i,ibig,j;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   double del,t,*pt,*ptt,*xit;      dirc[l1-l2] = 0;                    /* add zero */
   double fp,fptt;      printf(" DIRC2 = %s \n",dirc);
   double *xits;    }
   pt=vector(1,n);    /* We add a separator at the end of dirc if not exists */
   ptt=vector(1,n);    l1 = strlen( dirc );                  /* length of directory */
   xit=vector(1,n);    if( dirc[l1-1] != DIRSEPARATOR ){
   xits=vector(1,n);      dirc[l1] =  DIRSEPARATOR;
   *fret=(*func)(p);      dirc[l1+1] = 0; 
   for (j=1;j<=n;j++) pt[j]=p[j];      printf(" DIRC3 = %s \n",dirc);
   for (*iter=1;;++(*iter)) {    }
     fp=(*fret);    ss = strrchr( name, '.' );            /* find last / */
     ibig=0;    if (ss >0){
     del=0.0;      ss++;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      strcpy(ext,ss);                     /* save extension */
     for (i=1;i<=n;i++)      l1= strlen( name);
       printf(" %d %.12f",i, p[i]);      l2= strlen(ss)+1;
     printf("\n");      strncpy( finame, name, l1-l2);
     for (i=1;i<=n;i++) {      finame[l1-l2]= 0;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    }
       fptt=(*fret);  
 #ifdef DEBUG    return( 0 );                          /* we're done */
       printf("fret=%lf \n",*fret);  }
 #endif  
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);  /******************************************/
       if (fabs(fptt-(*fret)) > del) {  
         del=fabs(fptt-(*fret));  void replace_back_to_slash(char *s, char*t)
         ibig=i;  {
       }    int i;
 #ifdef DEBUG    int lg=0;
       printf("%d %.12e",i,(*fret));    i=0;
       for (j=1;j<=n;j++) {    lg=strlen(t);
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    for(i=0; i<= lg; i++) {
         printf(" x(%d)=%.12e",j,xit[j]);      (s[i] = t[i]);
       }      if (t[i]== '\\') s[i]='/';
       for(j=1;j<=n;j++)    }
         printf(" p=%.12e",p[j]);  }
       printf("\n");  
 #endif  char *trimbb(char *out, char *in)
     }  { /* Trim multiple blanks in line */
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {    char *s;
 #ifdef DEBUG    s=out;
       int k[2],l;    while (*in != '\0'){
       k[0]=1;      while( *in == ' ' && *(in+1) == ' ' && *(in+1) != '\0'){
       k[1]=-1;        in++;
       printf("Max: %.12e",(*func)(p));      }
       for (j=1;j<=n;j++)      *out++ = *in++;
         printf(" %.12e",p[j]);    }
       printf("\n");    *out='\0';
       for(l=0;l<=1;l++) {    return s;
         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]);  int nbocc(char *s, char occ)
         }  {
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    int i,j=0;
       }    int lg=20;
 #endif    i=0;
     lg=strlen(s);
     for(i=0; i<= lg; i++) {
       free_vector(xit,1,n);    if  (s[i] == occ ) j++;
       free_vector(xits,1,n);    }
       free_vector(ptt,1,n);    return j;
       free_vector(pt,1,n);  }
       return;  
     }  void cutv(char *u,char *v, char*t, char occ)
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  {
     for (j=1;j<=n;j++) {    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
       ptt[j]=2.0*p[j]-pt[j];       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       xit[j]=p[j]-pt[j];       gives u="abcedf" and v="ghi2j" */
       pt[j]=p[j];    int i,lg,j,p=0;
     }    i=0;
     fptt=(*func)(ptt);    for(j=0; j<=strlen(t)-1; j++) {
     if (fptt < fp) {      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    }
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);    lg=strlen(t);
         for (j=1;j<=n;j++) {    for(j=0; j<p; j++) {
           xi[j][ibig]=xi[j][n];      (u[j] = t[j]);
           xi[j][n]=xit[j];    }
         }       u[p]='\0';
 #ifdef DEBUG  
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);     for(j=0; j<= lg; j++) {
         for(j=1;j<=n;j++)      if (j>=(p+1))(v[j-p-1] = t[j]);
           printf(" %.12e",xit[j]);    }
         printf("\n");  }
 #endif  
       }  /********************** nrerror ********************/
     }  
   }  void nrerror(char error_text[])
 }  {
     fprintf(stderr,"ERREUR ...\n");
 /**** Prevalence limit ****************/    fprintf(stderr,"%s\n",error_text);
     exit(EXIT_FAILURE);
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  }
 {  /*********************** vector *******************/
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  double *vector(int nl, int nh)
      matrix by transitions matrix until convergence is reached */  {
     double *v;
   int i, ii,j,k;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   double min, max, maxmin, maxmax,sumnew=0.;    if (!v) nrerror("allocation failure in vector");
   double **matprod2();    return v-nl+NR_END;
   double **out, cov[NCOVMAX], **pmij();  }
   double **newm;  
   double agefin, delaymax=50 ; /* Max number of years to converge */  /************************ free vector ******************/
   void free_vector(double*v, int nl, int nh)
   for (ii=1;ii<=nlstate+ndeath;ii++)  {
     for (j=1;j<=nlstate+ndeath;j++){    free((FREE_ARG)(v+nl-NR_END));
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  }
     }  
   /************************ivector *******************************/
    cov[1]=1.;  int *ivector(long nl,long nh)
    {
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    int *v;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     newm=savm;    if (!v) nrerror("allocation failure in ivector");
     /* Covariates have to be included here again */    return v-nl+NR_END;
      cov[2]=agefin;  }
    
       for (k=1; k<=cptcovn;k++) {  /******************free ivector **************************/
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  void free_ivector(int *v, long nl, long nh)
         /*      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]]);*/  {
       }    free((FREE_ARG)(v+nl-NR_END));
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  }
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /************************lvector *******************************/
   long *lvector(long nl,long nh)
       /*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]);*/    long *v;
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    if (!v) nrerror("allocation failure in ivector");
     return v-nl+NR_END;
     savm=oldm;  }
     oldm=newm;  
     maxmax=0.;  /******************free lvector **************************/
     for(j=1;j<=nlstate;j++){  void free_lvector(long *v, long nl, long nh)
       min=1.;  {
       max=0.;    free((FREE_ARG)(v+nl-NR_END));
       for(i=1; i<=nlstate; i++) {  }
         sumnew=0;  
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /******************* imatrix *******************************/
         prlim[i][j]= newm[i][j]/(1-sumnew);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         max=FMAX(max,prlim[i][j]);       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
         min=FMIN(min,prlim[i][j]);  { 
       }    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       maxmin=max-min;    int **m; 
       maxmax=FMAX(maxmax,maxmin);    
     }    /* allocate pointers to rows */ 
     if(maxmax < ftolpl){    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       return prlim;    if (!m) nrerror("allocation failure 1 in matrix()"); 
     }    m += NR_END; 
   }    m -= nrl; 
 }    
     
 /*************** transition probabilities ***************/    /* allocate rows and set pointers to them */ 
     m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 {    m[nrl] += NR_END; 
   double s1, s2;    m[nrl] -= ncl; 
   /*double t34;*/    
   int i,j,j1, nc, ii, jj;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     
     for(i=1; i<= nlstate; i++){    /* return pointer to array of pointers to rows */ 
     for(j=1; j<i;j++){    return m; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  } 
         /*s2 += param[i][j][nc]*cov[nc];*/  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  /****************** free_imatrix *************************/
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  void free_imatrix(m,nrl,nrh,ncl,nch)
       }        int **m;
       ps[i][j]=s2;        long nch,ncl,nrh,nrl; 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/       /* free an int matrix allocated by imatrix() */ 
     }  { 
     for(j=i+1; j<=nlstate+ndeath;j++){    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    free((FREE_ARG) (m+nrl-NR_END)); 
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  } 
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }  /******************* matrix *******************************/
       ps[i][j]=s2;  double **matrix(long nrl, long nrh, long ncl, long nch)
     }  {
   }    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     /*ps[3][2]=1;*/    double **m;
   
   for(i=1; i<= nlstate; i++){    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      s1=0;    if (!m) nrerror("allocation failure 1 in matrix()");
     for(j=1; j<i; j++)    m += NR_END;
       s1+=exp(ps[i][j]);    m -= nrl;
     for(j=i+1; j<=nlstate+ndeath; j++)  
       s1+=exp(ps[i][j]);    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     ps[i][i]=1./(s1+1.);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     for(j=1; j<i; j++)    m[nrl] += NR_END;
       ps[i][j]= exp(ps[i][j])*ps[i][i];    m[nrl] -= ncl;
     for(j=i+1; j<=nlstate+ndeath; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    return m;
   } /* end i */    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
      */
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
       ps[ii][jj]=0;  /*************************free matrix ************************/
       ps[ii][ii]=1;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     }  {
   }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     free((FREE_ARG)(m+nrl-NR_END));
   }
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){  /******************* ma3x *******************************/
      printf("%lf ",ps[ii][jj]);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
    }  {
     printf("\n ");    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     }    double ***m;
     printf("\n ");printf("%lf ",cov[2]);*/  
 /*    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    if (!m) nrerror("allocation failure 1 in matrix()");
   goto end;*/    m += NR_END;
     return ps;    m -= nrl;
 }  
     m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
 /**************** Product of 2 matrices ******************/    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    m[nrl] -= ncl;
 {  
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  
   /* in, b, out are matrice of pointers which should have been initialized    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
      before: only the contents of out is modified. The function returns    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
      a pointer to pointers identical to out */    m[nrl][ncl] += NR_END;
   long i, j, k;    m[nrl][ncl] -= nll;
   for(i=nrl; i<= nrh; i++)    for (j=ncl+1; j<=nch; j++) 
     for(k=ncolol; k<=ncoloh; k++)      m[nrl][j]=m[nrl][j-1]+nlay;
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    
         out[i][k] +=in[i][j]*b[j][k];    for (i=nrl+1; i<=nrh; i++) {
       m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   return out;      for (j=ncl+1; j<=nch; j++) 
 }        m[i][j]=m[i][j-1]+nlay;
     }
     return m; 
 /************* Higher Matrix Product ***************/    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
              &(m[i][j][k]) <=> *((*(m+i) + j)+k)
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    */
 {  }
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until  /*************************free ma3x ************************/
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  {
      (typically every 2 years instead of every month which is too big).    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
      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));
   }
      */  
   /*************** function subdirf ***********/
   int i, j, d, h, k;  char *subdirf(char fileres[])
   double **out, cov[NCOVMAX];  {
   double **newm;    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   /* Hstepm could be zero and should return the unit matrix */    strcat(tmpout,"/"); /* Add to the right */
   for (i=1;i<=nlstate+ndeath;i++)    strcat(tmpout,fileres);
     for (j=1;j<=nlstate+ndeath;j++){    return tmpout;
       oldm[i][j]=(i==j ? 1.0 : 0.0);  }
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }  /*************** function subdirf2 ***********/
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  char *subdirf2(char fileres[], char *preop)
   for(h=1; h <=nhstepm; h++){  {
     for(d=1; d <=hstepm; d++){    
       newm=savm;    /* Caution optionfilefiname is hidden */
       /* Covariates have to be included here again */    strcpy(tmpout,optionfilefiname);
       cov[1]=1.;    strcat(tmpout,"/");
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    strcat(tmpout,preop);
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    strcat(tmpout,fileres);
       for (k=1; k<=cptcovage;k++)    return tmpout;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  }
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /*************** function subdirf3 ***********/
   char *subdirf3(char fileres[], char *preop, char *preop2)
   {
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    /* Caution optionfilefiname is hidden */
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    strcpy(tmpout,optionfilefiname);
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    strcat(tmpout,"/");
       savm=oldm;    strcat(tmpout,preop);
       oldm=newm;    strcat(tmpout,preop2);
     }    strcat(tmpout,fileres);
     for(i=1; i<=nlstate+ndeath; i++)    return tmpout;
       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]);  /***************** f1dim *************************/
          */  extern int ncom; 
       }  extern double *pcom,*xicom;
   } /* end h */  extern double (*nrfunc)(double []); 
   return po;   
 }  double f1dim(double x) 
   { 
     int j; 
 /*************** log-likelihood *************/    double f;
 double func( double *x)    double *xt; 
 {   
   int i, ii, j, k, mi, d, kk;    xt=vector(1,ncom); 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   double **out;    f=(*nrfunc)(xt); 
   double sw; /* Sum of weights */    free_vector(xt,1,ncom); 
   double lli; /* Individual log likelihood */    return f; 
   long ipmx;  } 
   /*extern weight */  
   /* We are differentiating ll according to initial status */  /*****************brent *************************/
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   /*for(i=1;i<imx;i++)  { 
     printf(" %d\n",s[4][i]);    int iter; 
   */    double a,b,d,etemp;
   cov[1]=1.;    double fu,fv,fw,fx;
     double ftemp;
   for(k=1; k<=nlstate; k++) ll[k]=0.;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    double e=0.0; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];   
     for(mi=1; mi<= wav[i]-1; mi++){    a=(ax < cx ? ax : cx); 
       for (ii=1;ii<=nlstate+ndeath;ii++)    b=(ax > cx ? ax : cx); 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    x=w=v=bx; 
       for(d=0; d<dh[mi][i]; d++){    fw=fv=fx=(*f)(x); 
         newm=savm;    for (iter=1;iter<=ITMAX;iter++) { 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      xm=0.5*(a+b); 
         for (kk=1; kk<=cptcovage;kk++) {      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
         }      printf(".");fflush(stdout);
              fprintf(ficlog,".");fflush(ficlog);
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  #ifdef DEBUG
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));      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);
         savm=oldm;      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);
         oldm=newm;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
          #endif
              if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
       } /* end mult */        *xmin=x; 
              return fx; 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      } 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      ftemp=fu;
       ipmx +=1;      if (fabs(e) > tol1) { 
       sw += weight[i];        r=(x-w)*(fx-fv); 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        q=(x-v)*(fx-fw); 
     } /* end of wave */        p=(x-v)*q-(x-w)*r; 
   } /* end of individual */        q=2.0*(q-r); 
         if (q > 0.0) p = -p; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];        q=fabs(q); 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */        etemp=e; 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */        e=d; 
   return -l;        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)); 
         else { 
           d=p/q; 
 /*********** Maximum Likelihood Estimation ***************/          u=x+d; 
           if (u-a < tol2 || b-u < tol2) 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))            d=SIGN(tol1,xm-x); 
 {        } 
   int i,j, iter;      } else { 
   double **xi,*delti;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   double fret;      } 
   xi=matrix(1,npar,1,npar);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   for (i=1;i<=npar;i++)      fu=(*f)(u); 
     for (j=1;j<=npar;j++)      if (fu <= fx) { 
       xi[i][j]=(i==j ? 1.0 : 0.0);        if (u >= x) a=x; else b=x; 
   printf("Powell\n");        SHFT(v,w,x,u) 
   powell(p,xi,npar,ftol,&iter,&fret,func);          SHFT(fv,fw,fx,fu) 
           } else { 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));            if (u < x) a=u; else b=u; 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));            if (fu <= fw || w == x) { 
               v=w; 
 }              w=u; 
               fv=fw; 
 /**** Computes Hessian and covariance matrix ***/              fw=fu; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))            } else if (fu <= fv || v == x || v == w) { 
 {              v=u; 
   double  **a,**y,*x,pd;              fv=fu; 
   double **hess;            } 
   int i, j,jk;          } 
   int *indx;    } 
     nrerror("Too many iterations in brent"); 
   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) ;  
   /****************** mnbrak ***********************/
   hess=matrix(1,npar,1,npar);  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   printf("\nCalculation of the hessian matrix. Wait...\n");              double (*func)(double)) 
   for (i=1;i<=npar;i++){  { 
     printf("%d",i);fflush(stdout);    double ulim,u,r,q, dum;
     hess[i][i]=hessii(p,ftolhess,i,delti);    double fu; 
     /*printf(" %f ",p[i]);*/   
     /*printf(" %lf ",hess[i][i]);*/    *fa=(*func)(*ax); 
   }    *fb=(*func)(*bx); 
      if (*fb > *fa) { 
   for (i=1;i<=npar;i++) {      SHFT(dum,*ax,*bx,dum) 
     for (j=1;j<=npar;j++)  {        SHFT(dum,*fb,*fa,dum) 
       if (j>i) {        } 
         printf(".%d%d",i,j);fflush(stdout);    *cx=(*bx)+GOLD*(*bx-*ax); 
         hess[i][j]=hessij(p,delti,i,j);    *fc=(*func)(*cx); 
         hess[j][i]=hess[i][j];        while (*fb > *fc) { 
         /*printf(" %lf ",hess[i][j]);*/      r=(*bx-*ax)*(*fb-*fc); 
       }      q=(*bx-*cx)*(*fb-*fa); 
     }      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) { 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");        fu=(*func)(u); 
        } else if ((*cx-u)*(u-ulim) > 0.0) { 
   a=matrix(1,npar,1,npar);        fu=(*func)(u); 
   y=matrix(1,npar,1,npar);        if (fu < *fc) { 
   x=vector(1,npar);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   indx=ivector(1,npar);            SHFT(*fb,*fc,fu,(*func)(u)) 
   for (i=1;i<=npar;i++)            } 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   ludcmp(a,npar,indx,&pd);        u=ulim; 
         fu=(*func)(u); 
   for (j=1;j<=npar;j++) {      } else { 
     for (i=1;i<=npar;i++) x[i]=0;        u=(*cx)+GOLD*(*cx-*bx); 
     x[j]=1;        fu=(*func)(u); 
     lubksb(a,npar,indx,x);      } 
     for (i=1;i<=npar;i++){      SHFT(*ax,*bx,*cx,u) 
       matcov[i][j]=x[i];        SHFT(*fa,*fb,*fc,fu) 
     }        } 
   }  } 
   
   printf("\n#Hessian matrix#\n");  /*************** linmin ************************/
   for (i=1;i<=npar;i++) {  
     for (j=1;j<=npar;j++) {  int ncom; 
       printf("%.3e ",hess[i][j]);  double *pcom,*xicom;
     }  double (*nrfunc)(double []); 
     printf("\n");   
   }  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   { 
   /* Recompute Inverse */    double brent(double ax, double bx, double cx, 
   for (i=1;i<=npar;i++)                 double (*f)(double), double tol, double *xmin); 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    double f1dim(double x); 
   ludcmp(a,npar,indx,&pd);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
                 double *fc, double (*func)(double)); 
   /*  printf("\n#Hessian matrix recomputed#\n");    int j; 
     double xx,xmin,bx,ax; 
   for (j=1;j<=npar;j++) {    double fx,fb,fa;
     for (i=1;i<=npar;i++) x[i]=0;   
     x[j]=1;    ncom=n; 
     lubksb(a,npar,indx,x);    pcom=vector(1,n); 
     for (i=1;i<=npar;i++){    xicom=vector(1,n); 
       y[i][j]=x[i];    nrfunc=func; 
       printf("%.3e ",y[i][j]);    for (j=1;j<=n;j++) { 
     }      pcom[j]=p[j]; 
     printf("\n");      xicom[j]=xi[j]; 
   }    } 
   */    ax=0.0; 
     xx=1.0; 
   free_matrix(a,1,npar,1,npar);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   free_matrix(y,1,npar,1,npar);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   free_vector(x,1,npar);  #ifdef DEBUG
   free_ivector(indx,1,npar);    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   free_matrix(hess,1,npar,1,npar);    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
     for (j=1;j<=n;j++) { 
 }      xi[j] *= xmin; 
       p[j] += xi[j]; 
 /*************** hessian matrix ****************/    } 
 double hessii( double x[], double delta, int theta, double delti[])    free_vector(xicom,1,n); 
 {    free_vector(pcom,1,n); 
   int i;  } 
   int l=1, lmax=20;  
   double k1,k2;  char *asc_diff_time(long time_sec, char ascdiff[])
   double p2[NPARMAX+1];  {
   double res;    long sec_left, days, hours, minutes;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    days = (time_sec) / (60*60*24);
   double fx;    sec_left = (time_sec) % (60*60*24);
   int k=0,kmax=10;    hours = (sec_left) / (60*60) ;
   double l1;    sec_left = (sec_left) %(60*60);
     minutes = (sec_left) /60;
   fx=func(x);    sec_left = (sec_left) % (60);
   for (i=1;i<=npar;i++) p2[i]=x[i];    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   for(l=0 ; l <=lmax; l++){    return ascdiff;
     l1=pow(10,l);  }
     delts=delt;  
     for(k=1 ; k <kmax; k=k+1){  /*************** powell ************************/
       delt = delta*(l1*k);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       p2[theta]=x[theta] +delt;              double (*func)(double [])) 
       k1=func(p2)-fx;  { 
       p2[theta]=x[theta]-delt;    void linmin(double p[], double xi[], int n, double *fret, 
       k2=func(p2)-fx;                double (*func)(double [])); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */    int i,ibig,j; 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    double del,t,*pt,*ptt,*xit;
          double fp,fptt;
 #ifdef DEBUG    double *xits;
       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);    int niterf, itmp;
 #endif  
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    pt=vector(1,n); 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    ptt=vector(1,n); 
         k=kmax;    xit=vector(1,n); 
       }    xits=vector(1,n); 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    *fret=(*func)(p); 
         k=kmax; l=lmax*10.;    for (j=1;j<=n;j++) pt[j]=p[j]; 
       }    for (*iter=1;;++(*iter)) { 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){      fp=(*fret); 
         delts=delt;      ibig=0; 
       }      del=0.0; 
     }      last_time=curr_time;
   }      (void) gettimeofday(&curr_time,&tzp);
   delti[theta]=delts;      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);
   return res;      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);
    /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
 }     for (i=1;i<=n;i++) {
         printf(" %d %.12f",i, p[i]);
 double hessij( double x[], double delti[], int thetai,int thetaj)        fprintf(ficlog," %d %.12lf",i, p[i]);
 {        fprintf(ficrespow," %.12lf", p[i]);
   int i;      }
   int l=1, l1, lmax=20;      printf("\n");
   double k1,k2,k3,k4,res,fx;      fprintf(ficlog,"\n");
   double p2[NPARMAX+1];      fprintf(ficrespow,"\n");fflush(ficrespow);
   int k;      if(*iter <=3){
         tm = *localtime(&curr_time.tv_sec);
   fx=func(x);        strcpy(strcurr,asctime(&tm));
   for (k=1; k<=2; k++) {  /*       asctime_r(&tm,strcurr); */
     for (i=1;i<=npar;i++) p2[i]=x[i];        forecast_time=curr_time; 
     p2[thetai]=x[thetai]+delti[thetai]/k;        itmp = strlen(strcurr);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
     k1=func(p2)-fx;          strcurr[itmp-1]='\0';
          printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     p2[thetai]=x[thetai]+delti[thetai]/k;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        for(niterf=10;niterf<=30;niterf+=10){
     k2=func(p2)-fx;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
            tmf = *localtime(&forecast_time.tv_sec);
     p2[thetai]=x[thetai]-delti[thetai]/k;  /*      asctime_r(&tmf,strfor); */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          strcpy(strfor,asctime(&tmf));
     k3=func(p2)-fx;          itmp = strlen(strfor);
            if(strfor[itmp-1]=='\n')
     p2[thetai]=x[thetai]-delti[thetai]/k;          strfor[itmp-1]='\0';
     p2[thetaj]=x[thetaj]-delti[thetaj]/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);
     k4=func(p2)-fx;          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);
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        }
 #ifdef DEBUG      }
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);      for (i=1;i<=n;i++) { 
 #endif        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   }        fptt=(*fret); 
   return res;  #ifdef DEBUG
 }        printf("fret=%lf \n",*fret);
         fprintf(ficlog,"fret=%lf \n",*fret);
 /************** Inverse of matrix **************/  #endif
 void ludcmp(double **a, int n, int *indx, double *d)        printf("%d",i);fflush(stdout);
 {        fprintf(ficlog,"%d",i);fflush(ficlog);
   int i,imax,j,k;        linmin(p,xit,n,fret,func); 
   double big,dum,sum,temp;        if (fabs(fptt-(*fret)) > del) { 
   double *vv;          del=fabs(fptt-(*fret)); 
            ibig=i; 
   vv=vector(1,n);        } 
   *d=1.0;  #ifdef DEBUG
   for (i=1;i<=n;i++) {        printf("%d %.12e",i,(*fret));
     big=0.0;        fprintf(ficlog,"%d %.12e",i,(*fret));
     for (j=1;j<=n;j++)        for (j=1;j<=n;j++) {
       if ((temp=fabs(a[i][j])) > big) big=temp;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          printf(" x(%d)=%.12e",j,xit[j]);
     vv[i]=1.0/big;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   }        }
   for (j=1;j<=n;j++) {        for(j=1;j<=n;j++) {
     for (i=1;i<j;i++) {          printf(" p=%.12e",p[j]);
       sum=a[i][j];          fprintf(ficlog," p=%.12e",p[j]);
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        }
       a[i][j]=sum;        printf("\n");
     }        fprintf(ficlog,"\n");
     big=0.0;  #endif
     for (i=j;i<=n;i++) {      } 
       sum=a[i][j];      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       for (k=1;k<j;k++)  #ifdef DEBUG
         sum -= a[i][k]*a[k][j];        int k[2],l;
       a[i][j]=sum;        k[0]=1;
       if ( (dum=vv[i]*fabs(sum)) >= big) {        k[1]=-1;
         big=dum;        printf("Max: %.12e",(*func)(p));
         imax=i;        fprintf(ficlog,"Max: %.12e",(*func)(p));
       }        for (j=1;j<=n;j++) {
     }          printf(" %.12e",p[j]);
     if (j != imax) {          fprintf(ficlog," %.12e",p[j]);
       for (k=1;k<=n;k++) {        }
         dum=a[imax][k];        printf("\n");
         a[imax][k]=a[j][k];        fprintf(ficlog,"\n");
         a[j][k]=dum;        for(l=0;l<=1;l++) {
       }          for (j=1;j<=n;j++) {
       *d = -(*d);            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
       vv[imax]=vv[j];            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     }            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     indx[j]=imax;          }
     if (a[j][j] == 0.0) a[j][j]=TINY;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     if (j != n) {          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       dum=1.0/(a[j][j]);        }
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  #endif
     }  
   }  
   free_vector(vv,1,n);  /* Doesn't work */        free_vector(xit,1,n); 
 ;        free_vector(xits,1,n); 
 }        free_vector(ptt,1,n); 
         free_vector(pt,1,n); 
 void lubksb(double **a, int n, int *indx, double b[])        return; 
 {      } 
   int i,ii=0,ip,j;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   double sum;      for (j=1;j<=n;j++) { 
          ptt[j]=2.0*p[j]-pt[j]; 
   for (i=1;i<=n;i++) {        xit[j]=p[j]-pt[j]; 
     ip=indx[i];        pt[j]=p[j]; 
     sum=b[ip];      } 
     b[ip]=b[i];      fptt=(*func)(ptt); 
     if (ii)      if (fptt < fp) { 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     else if (sum) ii=i;        if (t < 0.0) { 
     b[i]=sum;          linmin(p,xit,n,fret,func); 
   }          for (j=1;j<=n;j++) { 
   for (i=n;i>=1;i--) {            xi[j][ibig]=xi[j][n]; 
     sum=b[i];            xi[j][n]=xit[j]; 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          }
     b[i]=sum/a[i][i];  #ifdef DEBUG
   }          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
 }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           for(j=1;j<=n;j++){
 /************ Frequencies ********************/            printf(" %.12e",xit[j]);
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)            fprintf(ficlog," %.12e",xit[j]);
 {  /* Some frequencies */          }
            printf("\n");
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;          fprintf(ficlog,"\n");
   double ***freq; /* Frequencies */  #endif
   double *pp;        }
   double pos, k2, dateintsum=0,k2cpt=0;      } 
   FILE *ficresp;    } 
   char fileresp[FILENAMELENGTH];  } 
    
   pp=vector(1,nlstate);  /**** Prevalence limit (stable or period prevalence)  ****************/
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   strcpy(fileresp,"p");  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   strcat(fileresp,fileres);  {
   if((ficresp=fopen(fileresp,"w"))==NULL) {    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     printf("Problem with prevalence resultfile: %s\n", fileresp);       matrix by transitions matrix until convergence is reached */
     exit(0);  
   }    int i, ii,j,k;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    double min, max, maxmin, maxmax,sumnew=0.;
   j1=0;    double **matprod2();
      double **out, cov[NCOVMAX+1], **pmij();
   j=cptcoveff;    double **newm;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    double agefin, delaymax=50 ; /* Max number of years to converge */
    
   for(k1=1; k1<=j;k1++){    for (ii=1;ii<=nlstate+ndeath;ii++)
     for(i1=1; i1<=ncodemax[k1];i1++){      for (j=1;j<=nlstate+ndeath;j++){
       j1++;        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      }
         scanf("%d", i);*/  
       for (i=-1; i<=nlstate+ndeath; i++)       cov[1]=1.;
         for (jk=-1; jk<=nlstate+ndeath; jk++)     
           for(m=agemin; m <= agemax+3; m++)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
             freq[i][jk][m]=0;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
            newm=savm;
       dateintsum=0;      /* Covariates have to be included here again */
       k2cpt=0;       cov[2]=agefin;
       for (i=1; i<=imx; i++) {    
         bool=1;        for (k=1; k<=cptcovn;k++) {
         if  (cptcovn>0) {          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           for (z1=1; z1<=cptcoveff; z1++)          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        }
               bool=0;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         }        for (k=1; k<=cptcovprod;k++)
         if (bool==1) {          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           for(m=firstpass; m<=lastpass; m++){  
             k2=anint[m][i]+(mint[m][i]/12.);        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
               if(agev[m][i]==0) agev[m][i]=agemax+1;        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
               if(agev[m][i]==1) agev[m][i]=agemax+2;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
               if (m<lastpass) {  
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      savm=oldm;
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      oldm=newm;
               }      maxmax=0.;
                    for(j=1;j<=nlstate;j++){
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        min=1.;
                 dateintsum=dateintsum+k2;        max=0.;
                 k2cpt++;        for(i=1; i<=nlstate; i++) {
               }          sumnew=0;
             }          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
           }          prlim[i][j]= newm[i][j]/(1-sumnew);
         }          max=FMAX(max,prlim[i][j]);
       }          min=FMIN(min,prlim[i][j]);
                }
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
       if  (cptcovn>0) {      }
         fprintf(ficresp, "\n#********** Variable ");      if(maxmax < ftolpl){
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        return prlim;
         fprintf(ficresp, "**********\n#");      }
       }    }
       for(i=1; i<=nlstate;i++)  }
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  
       fprintf(ficresp, "\n");  /*************** transition probabilities ***************/ 
        
       for(i=(int)agemin; i <= (int)agemax+3; i++){  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         if(i==(int)agemax+3)  {
           printf("Total");    double s1, s2;
         else    /*double t34;*/
           printf("Age %d", i);    int i,j,j1, nc, ii, jj;
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for(i=1; i<= nlstate; i++){
             pp[jk] += freq[jk][m][i];        for(j=1; j<i;j++){
         }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
         for(jk=1; jk <=nlstate ; jk++){            /*s2 += param[i][j][nc]*cov[nc];*/
           for(m=-1, pos=0; m <=0 ; m++)            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
             pos += freq[jk][m][i];  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
           if(pp[jk]>=1.e-10)          }
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          ps[i][j]=s2;
           else  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        }
         }        for(j=i+1; j<=nlstate+ndeath;j++){
           for (nc=1, s2=0.;nc <=ncovmodel; nc++){
         for(jk=1; jk <=nlstate ; jk++){            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
             pp[jk] += freq[jk][m][i];          }
         }          ps[i][j]=s2;
         }
         for(jk=1,pos=0; jk <=nlstate ; jk++)      }
           pos += pp[jk];      /*ps[3][2]=1;*/
         for(jk=1; jk <=nlstate ; jk++){      
           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);        s1=0;
           else        for(j=1; j<i; j++){
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          s1+=exp(ps[i][j]);
           if( i <= (int) agemax){          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
             if(pos>=1.e-5){        }
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);        for(j=i+1; j<=nlstate+ndeath; j++){
               probs[i][jk][j1]= pp[jk]/pos;          s1+=exp(ps[i][j]);
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
             }        }
             else        ps[i][i]=1./(s1+1.);
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        for(j=1; j<i; j++)
           }          ps[i][j]= exp(ps[i][j])*ps[i][i];
         }        for(j=i+1; j<=nlstate+ndeath; j++)
                  ps[i][j]= exp(ps[i][j])*ps[i][i];
         for(jk=-1; jk <=nlstate+ndeath; jk++)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
           for(m=-1; m <=nlstate+ndeath; m++)      } /* end i */
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      
         if(i <= (int) agemax)      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
           fprintf(ficresp,"\n");        for(jj=1; jj<= nlstate+ndeath; jj++){
         printf("\n");          ps[ii][jj]=0;
       }          ps[ii][ii]=1;
     }        }
   }      }
   dateintmean=dateintsum/k2cpt;      
    
   fclose(ficresp);  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   free_vector(pp,1,nlstate);  /*         printf("ddd %lf ",ps[ii][jj]); */
    /*       } */
   /* End of Freq */  /*       printf("\n "); */
 }  /*        } */
   /*        printf("\n ");printf("%lf ",cov[2]); */
 /************ Prevalence ********************/         /*
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)        for(i=1; i<= npar; i++) printf("%f ",x[i]);
 {  /* Some frequencies */        goto end;*/
        return ps;
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  }
   double ***freq; /* Frequencies */  
   double *pp;  /**************** Product of 2 matrices ******************/
   double pos, k2;  
   double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
   pp=vector(1,nlstate);  {
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
         b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    /* in, b, out are matrice of pointers which should have been initialized 
   j1=0;       before: only the contents of out is modified. The function returns
         a pointer to pointers identical to out */
   j=cptcoveff;    long i, j, k;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    for(i=nrl; i<= nrh; i++)
        for(k=ncolol; k<=ncoloh; k++)
   for(k1=1; k1<=j;k1++){        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     for(i1=1; i1<=ncodemax[k1];i1++){          out[i][k] +=in[i][j]*b[j][k];
       j1++;  
          return out;
       for (i=-1; i<=nlstate+ndeath; i++)    }
         for (jk=-1; jk<=nlstate+ndeath; jk++)    
           for(m=agemin; m <= agemax+3; m++)  
             freq[i][jk][m]=0;  /************* Higher Matrix Product ***************/
        
       for (i=1; i<=imx; i++) {  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
         bool=1;  {
         if  (cptcovn>0) {    /* Computes the transition matrix starting at age 'age' over 
           for (z1=1; z1<=cptcoveff; z1++)       'nhstepm*hstepm*stepm' months (i.e. until
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
               bool=0;       nhstepm*hstepm matrices. 
         }       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         if (bool==1) {       (typically every 2 years instead of every month which is too big 
           for(m=firstpass; m<=lastpass; m++){       for the memory).
             k2=anint[m][i]+(mint[m][i]/12.);       Model is determined by parameters x and covariates have to be 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {       included manually here. 
               if(agev[m][i]==0) agev[m][i]=agemax+1;  
               if(agev[m][i]==1) agev[m][i]=agemax+2;       */
               if (m<lastpass) {  
                 if (calagedate>0)    int i, j, d, h, k;
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];    double **out, cov[NCOVMAX+1];
                 else    double **newm;
                   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];    /* Hstepm could be zero and should return the unit matrix */
               }    for (i=1;i<=nlstate+ndeath;i++)
             }      for (j=1;j<=nlstate+ndeath;j++){
           }        oldm[i][j]=(i==j ? 1.0 : 0.0);
         }        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }      }
       for(i=(int)agemin; i <= (int)agemax+3; i++){    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         for(jk=1; jk <=nlstate ; jk++){    for(h=1; h <=nhstepm; h++){
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for(d=1; d <=hstepm; d++){
             pp[jk] += freq[jk][m][i];        newm=savm;
         }        /* Covariates have to be included here again */
         for(jk=1; jk <=nlstate ; jk++){        cov[1]=1.;
           for(m=-1, pos=0; m <=0 ; m++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
             pos += freq[jk][m][i];        for (k=1; k<=cptcovn;k++) 
         }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
                for (k=1; k<=cptcovage;k++)
         for(jk=1; jk <=nlstate ; jk++){          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        for (k=1; k<=cptcovprod;k++)
             pp[jk] += freq[jk][m][i];          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
         }  
          
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
                /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         for(jk=1; jk <=nlstate ; jk++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           if( i <= (int) agemax){                     pmij(pmmij,cov,ncovmodel,x,nlstate));
             if(pos>=1.e-5){        savm=oldm;
               probs[i][jk][j1]= pp[jk]/pos;        oldm=newm;
             }      }
           }      for(i=1; i<=nlstate+ndeath; i++)
         }        for(j=1;j<=nlstate+ndeath;j++) {
                  po[i][j][h]=newm[i][j];
       }          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
     }        }
   }      /*printf("h=%d ",h);*/
     } /* end h */
    /*     printf("\n H=%d \n",h); */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    return po;
   free_vector(pp,1,nlstate);  }
    
 }  /* End of Freq */  
   /*************** log-likelihood *************/
 /************* Waves Concatenation ***************/  double func( double *x)
   {
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)    int i, ii, j, k, mi, d, kk;
 {    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    double **out;
      Death is a valid wave (if date is known).    double sw; /* Sum of weights */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    double lli; /* Individual log likelihood */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]    int s1, s2;
      and mw[mi+1][i]. dh depends on stepm.    double bbh, survp;
      */    long ipmx;
     /*extern weight */
   int i, mi, m;    /* We are differentiating ll according to initial status */
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
      double sum=0., jmean=0.;*/    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
   int j, k=0,jk, ju, jl;    */
   double sum=0.;    cov[1]=1.;
   jmin=1e+5;  
   jmax=-1;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   jmean=0.;  
   for(i=1; i<=imx; i++){    if(mle==1){
     mi=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     m=firstpass;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     while(s[m][i] <= nlstate){        for(mi=1; mi<= wav[i]-1; mi++){
       if(s[m][i]>=1)          for (ii=1;ii<=nlstate+ndeath;ii++)
         mw[++mi][i]=m;            for (j=1;j<=nlstate+ndeath;j++){
       if(m >=lastpass)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         break;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       else            }
         m++;          for(d=0; d<dh[mi][i]; d++){
     }/* end while */            newm=savm;
     if (s[m][i] > nlstate){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       mi++;     /* Death is another wave */            for (kk=1; kk<=cptcovage;kk++) {
       /* if(mi==0)  never been interviewed correctly before death */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
          /* Only death is a correct wave */            }
       mw[mi][i]=m;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
     wav[i]=mi;            oldm=newm;
     if(mi==0)          } /* end mult */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        
   }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           /* But now since version 0.9 we anticipate for bias at large stepm.
   for(i=1; i<=imx; i++){           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     for(mi=1; mi<wav[i];mi++){           * (in months) between two waves is not a multiple of stepm, we rounded to 
       if (stepm <=0)           * the nearest (and in case of equal distance, to the lowest) interval but now
         dh[mi][i]=1;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       else{           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
         if (s[mw[mi+1][i]][i] > nlstate) {           * probability in order to take into account the bias as a fraction of the way
           if (agedc[i] < 2*AGESUP) {           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);           * -stepm/2 to stepm/2 .
           if(j==0) j=1;  /* Survives at least one month after exam */           * For stepm=1 the results are the same as for previous versions of Imach.
           k=k+1;           * For stepm > 1 the results are less biased than in previous versions. 
           if (j >= jmax) jmax=j;           */
           if (j <= jmin) jmin=j;          s1=s[mw[mi][i]][i];
           sum=sum+j;          s2=s[mw[mi+1][i]][i];
           /*if (j<0) printf("j=%d num=%d \n",j,i); */          bbh=(double)bh[mi][i]/(double)stepm; 
           }          /* bias bh is positive if real duration
         }           * is higher than the multiple of stepm and negative otherwise.
         else{           */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           k=k+1;          if( s2 > nlstate){ 
           if (j >= jmax) jmax=j;            /* i.e. if s2 is a death state and if the date of death is known 
           else if (j <= jmin)jmin=j;               then the contribution to the likelihood is the probability to 
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */               die between last step unit time and current  step unit time, 
           sum=sum+j;               which is also equal to probability to die before dh 
         }               minus probability to die before dh-stepm . 
         jk= j/stepm;               In version up to 0.92 likelihood was computed
         jl= j -jk*stepm;          as if date of death was unknown. Death was treated as any other
         ju= j -(jk+1)*stepm;          health state: the date of the interview describes the actual state
         if(jl <= -ju)          and not the date of a change in health state. The former idea was
           dh[mi][i]=jk;          to consider that at each interview the state was recorded
         else          (healthy, disable or death) and IMaCh was corrected; but when we
           dh[mi][i]=jk+1;          introduced the exact date of death then we should have modified
         if(dh[mi][i]==0)          the contribution of an exact death to the likelihood. This new
           dh[mi][i]=1; /* At least one step */          contribution is smaller and very dependent of the step unit
       }          stepm. It is no more the probability to die between last interview
     }          and month of death but the probability to survive from last
   }          interview up to one month before death multiplied by the
   jmean=sum/k;          probability to die within a month. Thanks to Chris
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          Jackson for correcting this bug.  Former versions increased
  }          mortality artificially. The bad side is that we add another loop
 /*********** Tricode ****************************/          which slows down the processing. The difference can be up to 10%
 void tricode(int *Tvar, int **nbcode, int imx)          lower mortality.
 {            */
   int Ndum[20],ij=1, k, j, i;            lli=log(out[s1][s2] - savm[s1][s2]);
   int cptcode=0;  
   cptcoveff=0;  
            } else if  (s2==-2) {
   for (k=0; k<19; k++) Ndum[k]=0;            for (j=1,survp=0. ; j<=nlstate; j++) 
   for (k=1; k<=7; k++) ncodemax[k]=0;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             /*survp += out[s1][j]; */
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {            lli= log(survp);
     for (i=1; i<=imx; i++) {          }
       ij=(int)(covar[Tvar[j]][i]);          
       Ndum[ij]++;          else if  (s2==-4) { 
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            for (j=3,survp=0. ; j<=nlstate; j++)  
       if (ij > cptcode) cptcode=ij;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     }            lli= log(survp); 
           } 
     for (i=0; i<=cptcode; i++) {  
       if(Ndum[i]!=0) ncodemax[j]++;          else if  (s2==-5) { 
     }            for (j=1,survp=0. ; j<=2; j++)  
     ij=1;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             lli= log(survp); 
           } 
     for (i=1; i<=ncodemax[j]; i++) {          
       for (k=0; k<=19; k++) {          else{
         if (Ndum[k] != 0) {            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           nbcode[Tvar[j]][ij]=k;            /*  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 */
                    } 
           ij++;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         }          /*if(lli ==000.0)*/
         if (ij > ncodemax[j]) break;          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       }            ipmx +=1;
     }          sw += weight[i];
   }            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
  for (k=0; k<19; k++) Ndum[k]=0;      } /* end of individual */
     }  else if(mle==2){
  for (i=1; i<=ncovmodel-2; i++) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       ij=Tvar[i];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       Ndum[ij]++;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
  ij=1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  for (i=1; i<=10; i++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    if((Ndum[i]!=0) && (i<=ncovcol)){            }
      Tvaraff[ij]=i;          for(d=0; d<=dh[mi][i]; d++){
      ij++;            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];
     cptcoveff=ij-1;            }
 }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 /*********** Health Expectancies ****************/            savm=oldm;
             oldm=newm;
 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 )          } /* end mult */
         
 {          s1=s[mw[mi][i]][i];
   /* Health expectancies */          s2=s[mw[mi+1][i]][i];
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;          bbh=(double)bh[mi][i]/(double)stepm; 
   double age, agelim, hf;          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 */
   double ***p3mat,***varhe;          ipmx +=1;
   double **dnewm,**doldm;          sw += weight[i];
   double *xp;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **gp, **gm;        } /* end of wave */
   double ***gradg, ***trgradg;      } /* end of individual */
   int theta;    }  else if(mle==3){  /* exponential inter-extrapolation */
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   xp=vector(1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
   dnewm=matrix(1,nlstate*2,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
   doldm=matrix(1,nlstate*2,1,nlstate*2);            for (j=1;j<=nlstate+ndeath;j++){
                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficreseij,"# Health expectancies\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficreseij,"# Age");            }
   for(i=1; i<=nlstate;i++)          for(d=0; d<dh[mi][i]; d++){
     for(j=1; j<=nlstate;j++)            newm=savm;
       fprintf(ficreseij," %1d-%1d (SE)",i,j);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficreseij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   if(estepm < stepm){            }
     printf ("Problem %d lower than %d\n",estepm, stepm);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   else  hstepm=estepm;              savm=oldm;
   /* We compute the life expectancy from trapezoids spaced every estepm months            oldm=newm;
    * This is mainly to measure the difference between two models: for example          } /* end mult */
    * if stepm=24 months pijx are given only every 2 years and by summing them        
    * we are calculating an estimate of the Life Expectancy assuming a linear          s1=s[mw[mi][i]][i];
    * progression inbetween and thus overestimating or underestimating according          s2=s[mw[mi+1][i]][i];
    * to the curvature of the survival function. If, for the same date, we          bbh=(double)bh[mi][i]/(double)stepm; 
    * estimate the model with stepm=1 month, we can keep estepm to 24 months          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 */
    * to compare the new estimate of Life expectancy with the same linear          ipmx +=1;
    * hypothesis. A more precise result, taking into account a more precise          sw += weight[i];
    * curvature will be obtained if estepm is as small as stepm. */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
   /* For example we decided to compute the life expectancy with the smallest unit */      } /* end of individual */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.    }else if (mle==4){  /* ml=4 no inter-extrapolation */
      nhstepm is the number of hstepm from age to agelim      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      nstepm is the number of stepm from age to agelin.        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      Look at hpijx to understand the reason of that which relies in memory size        for(mi=1; mi<= wav[i]-1; mi++){
      and note for a fixed period like estepm months */          for (ii=1;ii<=nlstate+ndeath;ii++)
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the            for (j=1;j<=nlstate+ndeath;j++){
      survival function given by stepm (the optimization length). Unfortunately it              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      means that if the survival funtion is printed only each two years of age and if              savm[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            }
      results. So we changed our mind and took the option of the best precision.          for(d=0; d<dh[mi][i]; d++){
   */            newm=savm;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
   agelim=AGESUP;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            }
     /* nhstepm age range expressed in number of stepm */          
     nstepm=(int) rint((agelim-age)*YEARM/stepm);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     /* if (stepm >= YEARM) hstepm=1;*/            savm=oldm;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            oldm=newm;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          } /* end mult */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);        
     gp=matrix(0,nhstepm,1,nlstate*2);          s1=s[mw[mi][i]][i];
     gm=matrix(0,nhstepm,1,nlstate*2);          s2=s[mw[mi+1][i]][i];
           if( s2 > nlstate){ 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            lli=log(out[s1][s2] - savm[s1][s2]);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          }else{
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
            }
           ipmx +=1;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     /* Computing Variances 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]); */
         } /* end of wave */
      for(theta=1; theta <=npar; theta++){      } /* end of individual */
       for(i=1; i<=npar; i++){    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
       cptj=0;            for (j=1;j<=nlstate+ndeath;j++){
       for(j=1; j<= nlstate; j++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(i=1; i<=nlstate; i++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           cptj=cptj+1;            }
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          for(d=0; d<dh[mi][i]; d++){
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            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++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         xp[i] = x[i] - (i==theta ?delti[theta]:0);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              savm=oldm;
                  oldm=newm;
       cptj=0;          } /* end mult */
       for(j=1; j<= nlstate; j++){        
         for(i=1;i<=nlstate;i++){          s1=s[mw[mi][i]][i];
           cptj=cptj+1;          s2=s[mw[mi+1][i]][i];
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;          ipmx +=1;
           }          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*2; j++)        } /* end of wave */
         for(h=0; h<=nhstepm-1; h++){      } /* end of individual */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    } /* End of if */
         }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
        l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
 /* End theta */    return -l;
   }
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);  
   /*************** log-likelihood *************/
      for(h=0; h<=nhstepm-1; h++)  double funcone( double *x)
       for(j=1; j<=nlstate*2;j++)  {
         for(theta=1; theta <=npar; theta++)    /* Same as likeli but slower because of a lot of printf and if */
           trgradg[h][j][theta]=gradg[h][theta][j];    int i, ii, j, k, mi, d, kk;
          double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     double **out;
      for(i=1;i<=nlstate*2;i++)    double lli; /* Individual log likelihood */
       for(j=1;j<=nlstate*2;j++)    double llt;
         varhe[i][j][(int)age] =0.;    int s1, s2;
     double bbh, survp;
      printf("%d|",(int)age);fflush(stdout);    /*extern weight */
      for(h=0;h<=nhstepm-1;h++){    /* We are differentiating ll according to initial status */
       for(k=0;k<=nhstepm-1;k++){    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);    /*for(i=1;i<imx;i++) 
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      printf(" %d\n",s[4][i]);
         for(i=1;i<=nlstate*2;i++)    */
           for(j=1;j<=nlstate*2;j++)    cov[1]=1.;
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;  
       }    for(k=1; k<=nlstate; k++) ll[k]=0.;
     }  
     /* Computing expectancies */    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(i=1; i<=nlstate;i++)      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1; j<=nlstate;j++)      for(mi=1; mi<= wav[i]-1; mi++){
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){        for (ii=1;ii<=nlstate+ndeath;ii++)
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          for (j=1;j<=nlstate+ndeath;j++){
                      oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 /* 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]);*/            savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }
         }        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
     fprintf(ficreseij,"%3.0f",age );          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     cptj=0;          for (kk=1; kk<=cptcovage;kk++) {
     for(i=1; i<=nlstate;i++)            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for(j=1; j<=nlstate;j++){          }
         cptj++;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       }          savm=oldm;
     fprintf(ficreseij,"\n");          oldm=newm;
            } /* end mult */
     free_matrix(gm,0,nhstepm,1,nlstate*2);        
     free_matrix(gp,0,nhstepm,1,nlstate*2);        s1=s[mw[mi][i]][i];
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);        s2=s[mw[mi+1][i]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);        bbh=(double)bh[mi][i]/(double)stepm; 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        /* bias is positive if real duration
   }         * is higher than the multiple of stepm and negative otherwise.
   printf("\n");         */
         if( s2 > nlstate && (mle <5) ){  /* Jackson */
   free_vector(xp,1,npar);          lli=log(out[s1][s2] - savm[s1][s2]);
   free_matrix(dnewm,1,nlstate*2,1,npar);        } else if  (s2==-2) {
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);          for (j=1,survp=0. ; j<=nlstate; j++) 
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
 }          lli= log(survp);
         }else if (mle==1){
 /************ Variance ******************/          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 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)        } 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 */
   /* Variance of health expectancies */        } else if(mle==3){  /* exponential inter-extrapolation */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          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 */
   double **newm;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   double **dnewm,**doldm;          lli=log(out[s1][s2]); /* Original formula */
   int i, j, nhstepm, hstepm, h, nstepm ;        } else{  /* mle=0 back to 1 */
   int k, cptcode;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   double *xp;          /*lli=log(out[s1][s2]); */ /* Original formula */
   double **gp, **gm;        } /* End of if */
   double ***gradg, ***trgradg;        ipmx +=1;
   double ***p3mat;        sw += weight[i];
   double age,agelim, hf;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int theta;        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         if(globpr){
   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");          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   fprintf(ficresvij,"# Age");   %11.6f %11.6f %11.6f ", \
   for(i=1; i<=nlstate;i++)                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     for(j=1; j<=nlstate;j++)                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   fprintf(ficresvij,"\n");            llt +=ll[k]*gipmx/gsw;
             fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   xp=vector(1,npar);          }
   dnewm=matrix(1,nlstate,1,npar);          fprintf(ficresilk," %10.6f\n", -llt);
   doldm=matrix(1,nlstate,1,nlstate);        }
        } /* end of wave */
   if(estepm < stepm){    } /* end of individual */
     printf ("Problem %d lower than %d\n",estepm, stepm);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   else  hstepm=estepm;      l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   /* For example we decided to compute the life expectancy with the smallest unit */    if(globpr==0){ /* First time we count the contributions and weights */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.      gipmx=ipmx;
      nhstepm is the number of hstepm from age to agelim      gsw=sw;
      nstepm is the number of stepm from age to agelin.    }
      Look at hpijx to understand the reason of that which relies in memory size    return -l;
      and note for a fixed period like k years */  }
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the  
      survival function given by stepm (the optimization length). Unfortunately it  
      means that if the survival funtion is printed only each two years of age and if  /*************** function likelione ***********/
      you sum them up and add 1 year (area under the trapezoids) you won't get the same  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
      results. So we changed our mind and took the option of the best precision.  {
   */    /* This routine should help understanding what is done with 
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */       the selection of individuals/waves and
   agelim = AGESUP;       to check the exact contribution to the likelihood.
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */       Plotting could be done.
     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 */    int k;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    if(*globpri !=0){ /* Just counts and sums, no printings */
     gp=matrix(0,nhstepm,1,nlstate);      strcpy(fileresilk,"ilk"); 
     gm=matrix(0,nhstepm,1,nlstate);      strcat(fileresilk,fileres);
       if((ficresilk=fopen(fileresilk,"w"))==NULL) {
     for(theta=1; theta <=npar; theta++){        printf("Problem with resultfile: %s\n", fileresilk);
       for(i=1; i<=npar; i++){ /* Computes gradient */        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      }
       }      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");
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
       for(k=1; k<=nlstate; k++) 
       if (popbased==1) {        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
         for(i=1; i<=nlstate;i++)      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
           prlim[i][i]=probs[(int)age][i][ij];    }
       }  
      *fretone=(*funcone)(p);
       for(j=1; j<= nlstate; j++){    if(*globpri !=0){
         for(h=0; h<=nhstepm; h++){      fclose(ficresilk);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      fflush(fichtm); 
         }    } 
       }    return;
      }
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    /*********** Maximum Likelihood Estimation ***************/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
    void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       if (popbased==1) {  {
         for(i=1; i<=nlstate;i++)    int i,j, iter;
           prlim[i][i]=probs[(int)age][i][ij];    double **xi;
       }    double fret;
     double fretone; /* Only one call to likelihood */
       for(j=1; j<= nlstate; j++){    /*  char filerespow[FILENAMELENGTH];*/
         for(h=0; h<=nhstepm; h++){    xi=matrix(1,npar,1,npar);
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    for (i=1;i<=npar;i++)
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];      for (j=1;j<=npar;j++)
         }        xi[i][j]=(i==j ? 1.0 : 0.0);
       }    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow"); 
       for(j=1; j<= nlstate; j++)    strcat(filerespow,fileres);
         for(h=0; h<=nhstepm; h++){    if((ficrespow=fopen(filerespow,"w"))==NULL) {
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      printf("Problem with resultfile: %s\n", filerespow);
         }      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     } /* End theta */    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate+ndeath;j++)
     for(h=0; h<=nhstepm; h++)        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       for(j=1; j<=nlstate;j++)    fprintf(ficrespow,"\n");
         for(theta=1; theta <=npar; theta++)  
           trgradg[h][j][theta]=gradg[h][theta][j];    powell(p,xi,npar,ftol,&iter,&fret,func);
   
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    free_matrix(xi,1,npar,1,npar);
     for(i=1;i<=nlstate;i++)    fclose(ficrespow);
       for(j=1;j<=nlstate;j++)    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         vareij[i][j][(int)age] =0.;    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     for(h=0;h<=nhstepm;h++){  
       for(k=0;k<=nhstepm;k++){  }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);  
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  /**** Computes Hessian and covariance matrix ***/
         for(i=1;i<=nlstate;i++)  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
           for(j=1;j<=nlstate;j++)  {
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    double  **a,**y,*x,pd;
       }    double **hess;
     }    int i, j,jk;
     int *indx;
     fprintf(ficresvij,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(j=1; j<=nlstate;j++){    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    void lubksb(double **a, int npar, int *indx, double b[]) ;
       }    void ludcmp(double **a, int npar, int *indx, double *d) ;
     fprintf(ficresvij,"\n");    double gompertz(double p[]);
     free_matrix(gp,0,nhstepm,1,nlstate);    hess=matrix(1,npar,1,npar);
     free_matrix(gm,0,nhstepm,1,nlstate);  
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    printf("\nCalculation of the hessian matrix. Wait...\n");
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for (i=1;i<=npar;i++){
   } /* End age */      printf("%d",i);fflush(stdout);
        fprintf(ficlog,"%d",i);fflush(ficlog);
   free_vector(xp,1,npar);     
   free_matrix(doldm,1,nlstate,1,npar);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   free_matrix(dnewm,1,nlstate,1,nlstate);      
       /*  printf(" %f ",p[i]);
 }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     }
 /************ Variance of 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)    for (i=1;i<=npar;i++) {
 {      for (j=1;j<=npar;j++)  {
   /* Variance of prevalence limit */        if (j>i) { 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          printf(".%d%d",i,j);fflush(stdout);
   double **newm;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double **dnewm,**doldm;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   int i, j, nhstepm, hstepm;          
   int k, cptcode;          hess[j][i]=hess[i][j];    
   double *xp;          /*printf(" %lf ",hess[i][j]);*/
   double *gp, *gm;        }
   double **gradg, **trgradg;      }
   double age,agelim;    }
   int theta;    printf("\n");
        fprintf(ficlog,"\n");
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");  
   fprintf(ficresvpl,"# Age");    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   for(i=1; i<=nlstate;i++)    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
       fprintf(ficresvpl," %1d-%1d",i,i);    
   fprintf(ficresvpl,"\n");    a=matrix(1,npar,1,npar);
     y=matrix(1,npar,1,npar);
   xp=vector(1,npar);    x=vector(1,npar);
   dnewm=matrix(1,nlstate,1,npar);    indx=ivector(1,npar);
   doldm=matrix(1,nlstate,1,nlstate);    for (i=1;i<=npar;i++)
        for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   hstepm=1*YEARM; /* Every year of age */    ludcmp(a,npar,indx,&pd);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;    for (j=1;j<=npar;j++) {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (i=1;i<=npar;i++) x[i]=0;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      x[j]=1;
     if (stepm >= YEARM) hstepm=1;      lubksb(a,npar,indx,x);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for (i=1;i<=npar;i++){ 
     gradg=matrix(1,npar,1,nlstate);        matcov[i][j]=x[i];
     gp=vector(1,nlstate);      }
     gm=vector(1,nlstate);    }
   
     for(theta=1; theta <=npar; theta++){    printf("\n#Hessian matrix#\n");
       for(i=1; i<=npar; i++){ /* Computes gradient */    fprintf(ficlog,"\n#Hessian matrix#\n");
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    for (i=1;i<=npar;i++) { 
       }      for (j=1;j<=npar;j++) { 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        printf("%.3e ",hess[i][j]);
       for(i=1;i<=nlstate;i++)        fprintf(ficlog,"%.3e ",hess[i][j]);
         gp[i] = prlim[i][i];      }
          printf("\n");
       for(i=1; i<=npar; i++) /* Computes gradient */      fprintf(ficlog,"\n");
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)    /* Recompute Inverse */
         gm[i] = prlim[i][i];    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
       for(i=1;i<=nlstate;i++)    ludcmp(a,npar,indx,&pd);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */    /*  printf("\n#Hessian matrix recomputed#\n");
   
     trgradg =matrix(1,nlstate,1,npar);    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
     for(j=1; j<=nlstate;j++)      x[j]=1;
       for(theta=1; theta <=npar; theta++)      lubksb(a,npar,indx,x);
         trgradg[j][theta]=gradg[theta][j];      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
     for(i=1;i<=nlstate;i++)        printf("%.3e ",y[i][j]);
       varpl[i][(int)age] =0.;        fprintf(ficlog,"%.3e ",y[i][j]);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      }
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);      printf("\n");
     for(i=1;i<=nlstate;i++)      fprintf(ficlog,"\n");
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    }
     */
     fprintf(ficresvpl,"%.0f ",age );  
     for(i=1; i<=nlstate;i++)    free_matrix(a,1,npar,1,npar);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    free_matrix(y,1,npar,1,npar);
     fprintf(ficresvpl,"\n");    free_vector(x,1,npar);
     free_vector(gp,1,nlstate);    free_ivector(indx,1,npar);
     free_vector(gm,1,nlstate);    free_matrix(hess,1,npar,1,npar);
     free_matrix(gradg,1,npar,1,nlstate);  
     free_matrix(trgradg,1,nlstate,1,npar);  
   } /* End age */  }
   
   free_vector(xp,1,npar);  /*************** hessian matrix ****************/
   free_matrix(doldm,1,nlstate,1,npar);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   free_matrix(dnewm,1,nlstate,1,nlstate);  {
     int i;
 }    int l=1, lmax=20;
     double k1,k2;
 /************ Variance of one-step probabilities  ******************/    double p2[MAXPARM+1]; /* identical to x */
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    double res;
 {    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   int i, j,  i1, k1, l1;    double fx;
   int k2, l2, j1,  z1;    int k=0,kmax=10;
   int k=0,l, cptcode;    double l1;
   int first=1;  
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2;    fx=func(x);
   double **dnewm,**doldm;    for (i=1;i<=npar;i++) p2[i]=x[i];
   double *xp;    for(l=0 ; l <=lmax; l++){
   double *gp, *gm;      l1=pow(10,l);
   double **gradg, **trgradg;      delts=delt;
   double **mu;      for(k=1 ; k <kmax; k=k+1){
   double age,agelim, cov[NCOVMAX];        delt = delta*(l1*k);
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */        p2[theta]=x[theta] +delt;
   int theta;        k1=func(p2)-fx;
   char fileresprob[FILENAMELENGTH];        p2[theta]=x[theta]-delt;
   char fileresprobcov[FILENAMELENGTH];        k2=func(p2)-fx;
   char fileresprobcor[FILENAMELENGTH];        /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   double ***varpij;        
   #ifdef DEBUGHESS
   strcpy(fileresprob,"prob");        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);
   strcat(fileresprob,fileres);        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);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  #endif
     printf("Problem with resultfile: %s\n", fileresprob);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   strcpy(fileresprobcov,"probcov");          k=kmax;
   strcat(fileresprobcov,fileres);        }
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     printf("Problem with resultfile: %s\n", fileresprobcov);          k=kmax; l=lmax*10.;
   }        }
   strcpy(fileresprobcor,"probcor");        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   strcat(fileresprobcor,fileres);          delts=delt;
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {        }
     printf("Problem with resultfile: %s\n", fileresprobcor);      }
   }    }
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    delti[theta]=delts;
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    return res; 
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);    
    }
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");  
   fprintf(ficresprob,"# Age");  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");  {
   fprintf(ficresprobcov,"# Age");    int i;
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    int l=1, l1, lmax=20;
   fprintf(ficresprobcov,"# Age");    double k1,k2,k3,k4,res,fx;
     double p2[MAXPARM+1];
     int k;
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=(nlstate+ndeath);j++){    fx=func(x);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    for (k=1; k<=2; k++) {
       fprintf(ficresprobcov," p%1d-%1d ",i,j);      for (i=1;i<=npar;i++) p2[i]=x[i];
       fprintf(ficresprobcor," p%1d-%1d ",i,j);      p2[thetai]=x[thetai]+delti[thetai]/k;
     }        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   fprintf(ficresprob,"\n");      k1=func(p2)-fx;
   fprintf(ficresprobcov,"\n");    
   fprintf(ficresprobcor,"\n");      p2[thetai]=x[thetai]+delti[thetai]/k;
   xp=vector(1,npar);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);      k2=func(p2)-fx;
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));    
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);      p2[thetai]=x[thetai]-delti[thetai]/k;
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   first=1;      k3=func(p2)-fx;
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);      p2[thetai]=x[thetai]-delti[thetai]/k;
     exit(0);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   }      k4=func(p2)-fx;
   else{      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     fprintf(ficgp,"\n# Routine varprob");  #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);
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {      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);
     printf("Problem with html file: %s\n", optionfilehtm);  #endif
     exit(0);    }
   }    return res;
   else{  }
     fprintf(fichtm,"\n<H2> Computing matrix of variance-covariance of step probabilities</h2>\n");  
     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");  /************** Inverse of matrix **************/
     fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");  void ludcmp(double **a, int n, int *indx, double *d) 
   { 
   }    int i,imax,j,k; 
   cov[1]=1;    double big,dum,sum,temp; 
   j=cptcoveff;    double *vv; 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}   
   j1=0;    vv=vector(1,n); 
   for(k1=1; k1<=1;k1++){    *d=1.0; 
     for(i1=1; i1<=ncodemax[k1];i1++){    for (i=1;i<=n;i++) { 
     j1++;      big=0.0; 
       for (j=1;j<=n;j++) 
     if  (cptcovn>0) {        if ((temp=fabs(a[i][j])) > big) big=temp; 
       fprintf(ficresprob, "\n#********** Variable ");      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       fprintf(ficresprobcov, "\n#********** Variable ");      vv[i]=1.0/big; 
       fprintf(ficgp, "\n#********** Variable ");    } 
       fprintf(fichtm, "\n<h4>********** Variable</h4>\n ");    for (j=1;j<=n;j++) { 
       fprintf(ficresprobcor, "\n#********** Variable ");      for (i=1;i<j;i++) { 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        sum=a[i][j]; 
       fprintf(ficresprob, "**********\n#");        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        a[i][j]=sum; 
       fprintf(ficresprobcov, "**********\n#");      } 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      big=0.0; 
       fprintf(ficgp, "**********\n#");      for (i=j;i<=n;i++) { 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        sum=a[i][j]; 
       fprintf(ficgp, "**********\n#");        for (k=1;k<j;k++) 
       for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          sum -= a[i][k]*a[k][j]; 
       fprintf(fichtm, "**********\n#");        a[i][j]=sum; 
     }        if ( (dum=vv[i]*fabs(sum)) >= big) { 
              big=dum; 
       for (age=bage; age<=fage; age ++){          imax=i; 
         cov[2]=age;        } 
         for (k=1; k<=cptcovn;k++) {      } 
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];      if (j != imax) { 
         }        for (k=1;k<=n;k++) { 
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          dum=a[imax][k]; 
         for (k=1; k<=cptcovprod;k++)          a[imax][k]=a[j][k]; 
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];          a[j][k]=dum; 
                } 
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));        *d = -(*d); 
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);        vv[imax]=vv[j]; 
         gp=vector(1,(nlstate)*(nlstate+ndeath));      } 
         gm=vector(1,(nlstate)*(nlstate+ndeath));      indx[j]=imax; 
          if (a[j][j] == 0.0) a[j][j]=TINY; 
         for(theta=1; theta <=npar; theta++){      if (j != n) { 
           for(i=1; i<=npar; i++)        dum=1.0/(a[j][j]); 
             xp[i] = x[i] + (i==theta ?delti[theta]:0);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
                } 
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    } 
              free_vector(vv,1,n);  /* Doesn't work */
           k=0;  ;
           for(i=1; i<= (nlstate); i++){  } 
             for(j=1; j<=(nlstate+ndeath);j++){  
               k=k+1;  void lubksb(double **a, int n, int *indx, double b[]) 
               gp[k]=pmmij[i][j];  { 
             }    int i,ii=0,ip,j; 
           }    double sum; 
             
           for(i=1; i<=npar; i++)    for (i=1;i<=n;i++) { 
             xp[i] = x[i] - (i==theta ?delti[theta]:0);      ip=indx[i]; 
          sum=b[ip]; 
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      b[ip]=b[i]; 
           k=0;      if (ii) 
           for(i=1; i<=(nlstate); i++){        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
             for(j=1; j<=(nlstate+ndeath);j++){      else if (sum) ii=i; 
               k=k+1;      b[i]=sum; 
               gm[k]=pmmij[i][j];    } 
             }    for (i=n;i>=1;i--) { 
           }      sum=b[i]; 
            for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)      b[i]=sum/a[i][i]; 
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      } 
         }  } 
   
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)  void pstamp(FILE *fichier)
           for(theta=1; theta <=npar; theta++)  {
             trgradg[j][theta]=gradg[theta][j];    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
          }
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);  
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);  /************ Frequencies ********************/
          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[])
         pmij(pmmij,cov,ncovmodel,x,nlstate);  {  /* Some frequencies */
            
         k=0;    int i, m, jk, k1,i1, j1, bool, z1,j;
         for(i=1; i<=(nlstate); i++){    int first;
           for(j=1; j<=(nlstate+ndeath);j++){    double ***freq; /* Frequencies */
             k=k+1;    double *pp, **prop;
             mu[k][(int) age]=pmmij[i][j];    double pos,posprop, k2, dateintsum=0,k2cpt=0;
           }    char fileresp[FILENAMELENGTH];
         }    
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)    pp=vector(1,nlstate);
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)    prop=matrix(1,nlstate,iagemin,iagemax+3);
             varpij[i][j][(int)age] = doldm[i][j];    strcpy(fileresp,"p");
     strcat(fileresp,fileres);
         /*printf("\n%d ",(int)age);    if((ficresp=fopen(fileresp,"w"))==NULL) {
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){      printf("Problem with prevalence resultfile: %s\n", fileresp);
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
      }*/      exit(0);
     }
         fprintf(ficresprob,"\n%d ",(int)age);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
         fprintf(ficresprobcov,"\n%d ",(int)age);    j1=0;
         fprintf(ficresprobcor,"\n%d ",(int)age);    
     j=cptcoveff;
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));  
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){    first=1;
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);  
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);    for(k1=1; k1<=j;k1++){
         }      for(i1=1; i1<=ncodemax[k1];i1++){
         i=0;        j1++;
         for (k=1; k<=(nlstate);k++){        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           for (l=1; l<=(nlstate+ndeath);l++){          scanf("%d", i);*/
             i=i++;        for (i=-5; i<=nlstate+ndeath; i++)  
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);            for(m=iagemin; m <= iagemax+3; m++)
             for (j=1; j<=i;j++){              freq[i][jk][m]=0;
               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]));      for (i=1; i<=nlstate; i++)  
             }        for(m=iagemin; m <= iagemax+3; m++)
           }          prop[i][m]=0;
         }/* end of loop for state */        
       } /* end of loop for age */        dateintsum=0;
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/        k2cpt=0;
       for (k1=1; k1<=(nlstate);k1++){        for (i=1; i<=imx; i++) {
         for (l1=1; l1<=(nlstate+ndeath);l1++){          bool=1;
           if(l1==k1) continue;          if  (cptcovn>0) {
           i=(k1-1)*(nlstate+ndeath)+l1;            for (z1=1; z1<=cptcoveff; z1++) 
           for (k2=1; k2<=(nlstate);k2++){              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
             for (l2=1; l2<=(nlstate+ndeath);l2++){                bool=0;
               if(l2==k2) continue;          }
               j=(k2-1)*(nlstate+ndeath)+l2;          if (bool==1){
               if(j<=i) continue;            for(m=firstpass; m<=lastpass; m++){
               for (age=bage; age<=fage; age ++){              k2=anint[m][i]+(mint[m][i]/12.);
                 if ((int)age %5==0){              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                   mu1=mu[i][(int) age]/stepm*YEARM ;                if (m<lastpass) {
                   mu2=mu[j][(int) age]/stepm*YEARM;                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   /* Computing eigen value of matrix of covariance */                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                   lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));                }
                   lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12));                
                   printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                   /* Eigen vectors */                  dateintsum=dateintsum+k2;
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));                  k2cpt++;
                   v21=sqrt(1.-v11*v11);                }
                   v12=-v21;                /*}*/
                   v22=v11;            }
                   /*printf(fignu*/          }
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */        }
                   /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */         
                   if(first==1){        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
                     first=0;        pstamp(ficresp);
                     fprintf(ficgp,"\nset parametric;set nolabel");        if  (cptcovn>0) {
                     fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1);          fprintf(ficresp, "\n#********** Variable "); 
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
                     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(ficresp, "**********\n#");
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%1d%1d-%1d%1d.png\">, ",optionfilefiname,k2,l2,k1,l1);        }
                     fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\"",optionfilefiname,k2,l2,k1,l1);        for(i=1; i<=nlstate;i++) 
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);        fprintf(ficresp, "\n");
                     fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(-%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) t \"%d\"",\        
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \        for(i=iagemin; i <= iagemax+3; i++){
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);          if(i==iagemax+3){
                   }else{            fprintf(ficlog,"Total");
                     first=0;          }else{
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1);            if(first==1){
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1);              first=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\"",\              printf("See log file for details...\n");
                             mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \            }
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age);            fprintf(ficlog,"Age %d", i);
                   }/* if first */          }
                 } /* age mod 5 */          for(jk=1; jk <=nlstate ; jk++){
               } /* end loop age */            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               fprintf(ficgp,"\nset out \"varpijgr%s%1d%1d-%1d%1d.png\";replot;",optionfilefiname,k2,l2,k1,l1);              pp[jk] += freq[jk][m][i]; 
               first=1;          }
             } /*l12 */          for(jk=1; jk <=nlstate ; jk++){
           } /* k12 */            for(m=-1, pos=0; m <=0 ; m++)
         } /*l1 */              pos += freq[jk][m][i];
       }/* k1 */            if(pp[jk]>=1.e-10){
     } /* loop covariates */              if(first==1){
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));              }
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);            }else{
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);              if(first==1)
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   free_vector(xp,1,npar);            }
   fclose(ficresprob);          }
   fclose(ficresprobcov);  
   fclose(ficresprobcor);          for(jk=1; jk <=nlstate ; jk++){
   fclose(ficgp);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   fclose(fichtm);              pp[jk] += freq[jk][m][i];
 }          }       
           for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
             pos += pp[jk];
 /******************* Printing html file ***********/            posprop += prop[jk][i];
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \          }
                   int lastpass, int stepm, int weightopt, char model[],\          for(jk=1; jk <=nlstate ; jk++){
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\            if(pos>=1.e-5){
                   int popforecast, int estepm ,\              if(first==1)
                   double jprev1, double mprev1,double anprev1, \                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                   double jprev2, double mprev2,double anprev2){              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   int jj1, k1, i1, cpt;            }else{
   /*char optionfilehtm[FILENAMELENGTH];*/              if(first==1)
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     printf("Problem with %s \n",optionfilehtm), exit(0);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   }            }
             if( i <= iagemax){
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n              if(pos>=1.e-5){
  - 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                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n                /*probs[i][jk][j1]= pp[jk]/pos;*/
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
  - Life expectancies by age and initial health status (estepm=%2d months):              }
    <a href=\"e%s\">e%s</a> <br>\n</li>", \              else
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             }
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n          }
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n          for(jk=-1; jk <=nlstate+ndeath; jk++)
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n            for(m=-1; m <=nlstate+ndeath; m++)
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n              if(freq[jk][m][i] !=0 ) {
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n              if(first==1)
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
  - 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);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
  if(popforecast==1) fprintf(fichtm,"\n          if(i <= iagemax)
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n            fprintf(ficresp,"\n");
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n          if(first==1)
         <br>",fileres,fileres,fileres,fileres);            printf("Others in log...\n");
  else          fprintf(ficlog,"\n");
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);        }
 fprintf(fichtm," <li>Graphs</li><p>");      }
     }
  m=cptcoveff;    dateintmean=dateintsum/k2cpt; 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}   
     fclose(ficresp);
  jj1=0;    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
  for(k1=1; k1<=m;k1++){    free_vector(pp,1,nlstate);
    for(i1=1; i1<=ncodemax[k1];i1++){    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
      jj1++;    /* End of Freq */
      if (cptcovn > 0) {  }
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");  
        for (cpt=1; cpt<=cptcoveff;cpt++)  /************ Prevalence ********************/
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);  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)
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");  {  
      }    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
      /* Pij */       in each health status at the date of interview (if between dateprev1 and dateprev2).
      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>       We still use firstpass and lastpass as another selection.
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        */
      /* Quasi-incidences */   
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>    int i, m, jk, k1, i1, j1, bool, z1,j;
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);    double ***freq; /* Frequencies */
        /* Stable prevalence in each health state */    double *pp, **prop;
        for(cpt=1; cpt<nlstate;cpt++){    double pos,posprop; 
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>    double  y2; /* in fractional years */
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    int iagemin, iagemax;
        }  
     for(cpt=1; cpt<=nlstate;cpt++) {    iagemin= (int) agemin;
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    iagemax= (int) agemax;
 interval) in state (%d): v%s%d%d.png <br>    /*pp=vector(1,nlstate);*/
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      prop=matrix(1,nlstate,iagemin,iagemax+3); 
      }    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
      for(cpt=1; cpt<=nlstate;cpt++) {    j1=0;
         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);    j=cptcoveff;
      }    if (cptcovn<1) {j=1;ncodemax[1]=1;}
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    
 health expectancies in states (1) and (2): e%s%d.png<br>    for(k1=1; k1<=j;k1++){
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      for(i1=1; i1<=ncodemax[k1];i1++){
    }        j1++;
  }        
 fclose(fichtm);        for (i=1; i<=nlstate; i++)  
 }          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
 /******************* Gnuplot file **************/       
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){        for (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;          if  (cptcovn>0) {
   int ng;            for (z1=1; z1<=cptcoveff; z1++) 
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     printf("Problem with file %s",optionfilegnuplot);                bool=0;
   }          } 
           if (bool==1) { 
 #ifdef windows            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     fprintf(ficgp,"cd \"%s\" \n",pathc);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
 #endif              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
 m=pow(2,cptcoveff);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                  if(agev[m][i]==1) agev[m][i]=iagemax+2;
  /* 1eme*/                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
   for (cpt=1; cpt<= nlstate ; cpt ++) {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
    for (k1=1; k1<= m ; 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]]);*/
                   prop[s[m][i]][(int)agev[m][i]] += weight[i];
 #ifdef windows                  prop[s[m][i]][iagemax+3] += weight[i]; 
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);                } 
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);              }
 #endif            } /* end selection of waves */
 #ifdef unix          }
 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);        for(i=iagemin; i <= iagemax+3; i++){  
 #endif          
           for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
 for (i=1; i<= nlstate ; i ++) {            posprop += prop[jk][i]; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }          for(jk=1; jk <=nlstate ; jk++){     
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            if( i <=  iagemax){ 
     for (i=1; i<= nlstate ; i ++) {              if(posprop>=1.e-5){ 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");                probs[i][jk][j1]= prop[jk][i]/posprop;
   else fprintf(ficgp," \%%*lf (\%%*lf)");              } else
 }                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            } 
      for (i=1; i<= nlstate ; i ++) {          }/* end jk */ 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        }/* end i */ 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      } /* end i1 */
 }      } /* end k1 */
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    
 #ifdef unix    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");    /*free_vector(pp,1,nlstate);*/
 #endif    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
    }  }  /* End of prevalence */
   }  
   /*2 eme*/  /************* Waves Concatenation ***************/
   
   for (k1=1; k1<= m ; k1 ++) {  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,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);  {
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           Death is a valid wave (if date is known).
     for (i=1; i<= nlstate+1 ; i ++) {       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       k=2*i;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);       and mw[mi+1][i]. dh depends on stepm.
       for (j=1; j<= nlstate+1 ; j ++) {       */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    int i, mi, m;
 }      /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");       double sum=0., jmean=0.;*/
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    int first;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    int j, k=0,jk, ju, jl;
       for (j=1; j<= nlstate+1 ; j ++) {    double sum=0.;
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    first=0;
         else fprintf(ficgp," \%%*lf (\%%*lf)");    jmin=1e+5;
 }      jmax=-1;
       fprintf(ficgp,"\" t\"\" w l 0,");    jmean=0.;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    for(i=1; i<=imx; i++){
       for (j=1; j<= nlstate+1 ; j ++) {      mi=0;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      m=firstpass;
   else fprintf(ficgp," \%%*lf (\%%*lf)");      while(s[m][i] <= nlstate){
 }          if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");          mw[++mi][i]=m;
       else fprintf(ficgp,"\" t\"\" w l 0,");        if(m >=lastpass)
     }          break;
   }        else
            m++;
   /*3eme*/      }/* end while */
       if (s[m][i] > nlstate){
   for (k1=1; k1<= m ; k1 ++) {        mi++;     /* Death is another wave */
     for (cpt=1; cpt<= nlstate ; cpt ++) {        /* if(mi==0)  never been interviewed correctly before death */
       k=2+nlstate*(2*cpt-2);           /* Only death is a correct wave */
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);        mw[mi][i]=m;
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);      }
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);  
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");      wav[i]=mi;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);      if(mi==0){
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);        nbwarn++;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");        if(first==0){
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
           first=1;
 */        }
       for (i=1; i< nlstate ; i ++) {        if(first==1){
         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);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
         }
       }      } /* end mi==0 */
     }    } /* End individuals */
   }  
      for(i=1; i<=imx; i++){
   /* CV preval stat */      for(mi=1; mi<wav[i];mi++){
     for (k1=1; k1<= m ; k1 ++) {        if (stepm <=0)
     for (cpt=1; cpt<nlstate ; cpt ++) {          dh[mi][i]=1;
       k=3;        else{
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
       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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);            if (agedc[i] < 2*AGESUP) {
               j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       for (i=1; i< nlstate ; i ++)              if(j==0) j=1;  /* Survives at least one month after exam */
         fprintf(ficgp,"+$%d",k+i+1);              else if(j<0){
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);                nberr++;
                      printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       l=3+(nlstate+ndeath)*cpt;                j=1; /* Temporary Dangerous patch */
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
       for (i=1; i< nlstate ; i ++) {                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
         l=3+(nlstate+ndeath)*cpt;                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
         fprintf(ficgp,"+$%d",l+i+1);              }
       }              k=k+1;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                if (j >= jmax){
     }                jmax=j;
   }                  ijmax=i;
                }
   /* proba elementaires */              if (j <= jmin){
    for(i=1,jk=1; i <=nlstate; i++){                jmin=j;
     for(k=1; k <=(nlstate+ndeath); k++){                ijmin=i;
       if (k != i) {              }
         for(j=1; j <=ncovmodel; j++){              sum=sum+j;
                      /*if (j<0) printf("j=%d num=%d \n",j,i);*/
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
           jk++;            }
           fprintf(ficgp,"\n");          }
         }          else{
       }            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     }  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
    }  
             k=k+1;
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/            if (j >= jmax) {
      for(jk=1; jk <=m; jk++) {              jmax=j;
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);              ijmax=i;
        if (ng==2)            }
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");            else if (j <= jmin){
        else              jmin=j;
          fprintf(ficgp,"\nset title \"Probability\"\n");              ijmin=i;
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);            }
        i=1;            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
        for(k2=1; k2<=nlstate; k2++) {            /*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]);*/
          k3=i;            if(j<0){
          for(k=1; k<=(nlstate+ndeath); k++) {              nberr++;
            if (k != k2){              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
              if(ng==2)              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]);
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);            }
              else            sum=sum+j;
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          }
              ij=1;          jk= j/stepm;
              for(j=3; j <=ncovmodel; j++) {          jl= j -jk*stepm;
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          ju= j -(jk+1)*stepm;
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
                  ij++;            if(jl==0){
                }              dh[mi][i]=jk;
                else              bh[mi][i]=0;
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);            }else{ /* We want a negative bias in order to only have interpolation ie
              }                    * to avoid the price of an extra matrix product in likelihood */
              fprintf(ficgp,")/(1");              dh[mi][i]=jk+1;
                            bh[mi][i]=ju;
              for(k1=1; k1 <=nlstate; k1++){              }
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);          }else{
                ij=1;            if(jl <= -ju){
                for(j=3; j <=ncovmodel; j++){              dh[mi][i]=jk;
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {              bh[mi][i]=jl;       /* bias is positive if real duration
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                                   * is higher than the multiple of stepm and negative otherwise.
                    ij++;                                   */
                  }            }
                  else            else{
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);              dh[mi][i]=jk+1;
                }              bh[mi][i]=ju;
                fprintf(ficgp,")");            }
              }            if(dh[mi][i]==0){
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);              dh[mi][i]=1; /* At least one step */
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");              bh[mi][i]=ju; /* At least one step */
              i=i+ncovmodel;              /*  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);*/
            }            }
          }          } /* end if mle */
        }        }
      }      } /* end wave */
    }    }
    fclose(ficgp);    jmean=sum/k;
 }  /* end gnuplot */    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
     fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
    }
 /*************** Moving average **************/  
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){  /*********** Tricode ****************************/
   void tricode(int *Tvar, int **nbcode, int imx)
   int i, cpt, cptcod;  {
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)    /* Uses cptcovn+2*cptcovprod as the number of covariates */
       for (i=1; i<=nlstate;i++)    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)  
           mobaverage[(int)agedeb][i][cptcod]=0.;    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
        int modmaxcovj=0; /* Modality max of covariates j */
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){    cptcoveff=0; 
       for (i=1; i<=nlstate;i++){   
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    for (k=0; k<maxncov; k++) Ndum[k]=0;
           for (cpt=0;cpt<=4;cpt++){    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];  
           }    for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
         }                                 modality of this covariate Vj*/ 
       }        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
     }                                        modality of the nth covariate of individual i. */
            Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
 }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         if (ij > modmaxcovj) modmaxcovj=ij; 
         /* getting the maximum value of the modality of the covariate
 /************** Forecasting ******************/           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
 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){           female is 1, then modmaxcovj=1.*/
        }
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;  
   int *popage;      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*/
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;        if( Ndum[i] != 0 )
   double *popeffectif,*popcount;          ncodemax[j]++; 
   double ***p3mat;        /* Number of modalities of the j th covariate. In fact
   char fileresf[FILENAMELENGTH];           ncodemax[j]=2 (dichotom. variables only) but it could be more for
            historical reasons */
  agelim=AGESUP;      } /* Ndum[-1] number of undefined modalities */
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;  
       /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      ij=1; 
        for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
          for (k=0; k<= maxncov; k++) { /* k=-1 ? NCOVMAX*/
   strcpy(fileresf,"f");          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
   strcat(fileresf,fileres);            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
   if((ficresf=fopen(fileresf,"w"))==NULL) {                                       k is a modality. If we have model=V1+V1*sex 
     printf("Problem with forecast resultfile: %s\n", fileresf);                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   }            ij++;
   printf("Computing forecasting: result on file '%s' \n", fileresf);          }
           if (ij > ncodemax[j]) break; 
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        }  
       } 
   if (mobilav==1) {    }  
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
     movingaverage(agedeb, fage, ageminpar, mobaverage);   for (k=0; k< maxncov; k++) Ndum[k]=0;
   }  
    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
   stepsize=(int) (stepm+YEARM-1)/YEARM;     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
   if (stepm<=12) stepsize=1;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
       Ndum[ij]++;
   agelim=AGESUP;   }
    
   hstepm=1;   ij=1;
   hstepm=hstepm/stepm;   for (i=1; i<= maxncov; i++) {
   yp1=modf(dateintmean,&yp);     if((Ndum[i]!=0) && (i<=ncovcol)){
   anprojmean=yp;       Tvaraff[ij]=i; /*For printing */
   yp2=modf((yp1*12),&yp);       ij++;
   mprojmean=yp;     }
   yp1=modf((yp2*30.5),&yp);   }
   jprojmean=yp;   ij--;
   if(jprojmean==0) jprojmean=1;   cptcoveff=ij; /*Number of simple covariates*/
   if(mprojmean==0) jprojmean=1;  }
    
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  /*********** Health Expectancies ****************/
    
   for(cptcov=1;cptcov<=i2;cptcov++){  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
       k=k+1;  {
       fprintf(ficresf,"\n#******");    /* Health expectancies, no variances */
       for(j=1;j<=cptcoveff;j++) {    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    int nhstepma, nstepma; /* Decreasing with age */
       }    double age, agelim, hf;
       fprintf(ficresf,"******\n");    double ***p3mat;
       fprintf(ficresf,"# StartingAge FinalAge");    double eip;
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  
          pstamp(ficreseij);
          fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {    fprintf(ficreseij,"# Age");
         fprintf(ficresf,"\n");    for(i=1; i<=nlstate;i++){
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);        for(j=1; j<=nlstate;j++){
         fprintf(ficreseij," e%1d%1d ",i,j);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      }
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      fprintf(ficreseij," e%1d. ",i);
           nhstepm = nhstepm/hstepm;    }
              fprintf(ficreseij,"\n");
           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);      if(estepm < stepm){
              printf ("Problem %d lower than %d\n",estepm, stepm);
           for (h=0; h<=nhstepm; h++){    }
             if (h==(int) (calagedate+YEARM*cpt)) {    else  hstepm=estepm;   
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    /* We compute the life expectancy from trapezoids spaced every estepm months
             }     * This is mainly to measure the difference between two models: for example
             for(j=1; j<=nlstate+ndeath;j++) {     * if stepm=24 months pijx are given only every 2 years and by summing them
               kk1=0.;kk2=0;     * we are calculating an estimate of the Life Expectancy assuming a linear 
               for(i=1; i<=nlstate;i++) {                   * progression in between and thus overestimating or underestimating according
                 if (mobilav==1)     * to the curvature of the survival function. If, for the same date, we 
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];     * estimate the model with stepm=1 month, we can keep estepm to 24 months
                 else {     * to compare the new estimate of Life expectancy with the same linear 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];     * hypothesis. A more precise result, taking into account a more precise
                 }     * curvature will be obtained if estepm is as small as stepm. */
                  
               }    /* For example we decided to compute the life expectancy with the smallest unit */
               if (h==(int)(calagedate+12*cpt)){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
                 fprintf(ficresf," %.3f", kk1);       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
             }       and note for a fixed period like estepm months */
           }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       survival function given by stepm (the optimization length). Unfortunately it
         }       means that if the survival funtion is printed only each two years of age and if
       }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     }       results. So we changed our mind and took the option of the best precision.
   }    */
            hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
     agelim=AGESUP;
   fclose(ficresf);    /* If stepm=6 months */
 }      /* Computed by stepm unit matrices, product of hstepm matrices, stored
 /************** Forecasting ******************/         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
 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){      
    /* nhstepm age range expressed in number of stepm */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   int *popage;    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    /* if (stepm >= YEARM) hstepm=1;*/
   double *popeffectif,*popcount;    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   double ***p3mat,***tabpop,***tabpopprev;    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   char filerespop[FILENAMELENGTH];  
     for (age=bage; age<=fage; age ++){ 
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   agelim=AGESUP;      /* if (stepm >= YEARM) hstepm=1;*/
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
    
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      /* If stepm=6 months */
        /* Computed by stepm unit matrices, product of hstepma matrices, stored
           in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   strcpy(filerespop,"pop");      
   strcat(filerespop,fileres);      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   if((ficrespop=fopen(filerespop,"w"))==NULL) {      
     printf("Problem with forecast resultfile: %s\n", filerespop);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   }      
   printf("Computing forecasting: result on file '%s' \n", filerespop);      printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      
       /* Computing expectancies */
   if (mobilav==1) {      for(i=1; i<=nlstate;i++)
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(j=1; j<=nlstate;j++)
     movingaverage(agedeb, fage, ageminpar, mobaverage);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   }            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
   stepsize=(int) (stepm+YEARM-1)/YEARM;            /* 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]);*/
   if (stepm<=12) stepsize=1;  
            }
   agelim=AGESUP;  
        fprintf(ficreseij,"%3.0f",age );
   hstepm=1;      for(i=1; i<=nlstate;i++){
   hstepm=hstepm/stepm;        eip=0;
          for(j=1; j<=nlstate;j++){
   if (popforecast==1) {          eip +=eij[i][j][(int)age];
     if((ficpop=fopen(popfile,"r"))==NULL) {          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
       printf("Problem with population file : %s\n",popfile);exit(0);        }
     }        fprintf(ficreseij,"%9.4f", eip );
     popage=ivector(0,AGESUP);      }
     popeffectif=vector(0,AGESUP);      fprintf(ficreseij,"\n");
     popcount=vector(0,AGESUP);      
        }
     i=1;      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    printf("\n");
        fprintf(ficlog,"\n");
     imx=i;    
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];  }
   }  
   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[] )
   for(cptcov=1;cptcov<=i2;cptcov++){  
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  {
       k=k+1;    /* Covariances of health expectancies eij and of total life expectancies according
       fprintf(ficrespop,"\n#******");     to initial status i, ei. .
       for(j=1;j<=cptcoveff;j++) {    */
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
       }    int nhstepma, nstepma; /* Decreasing with age */
       fprintf(ficrespop,"******\n");    double age, agelim, hf;
       fprintf(ficrespop,"# Age");    double ***p3matp, ***p3matm, ***varhe;
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    double **dnewm,**doldm;
       if (popforecast==1)  fprintf(ficrespop," [Population]");    double *xp, *xm;
          double **gp, **gm;
       for (cpt=0; cpt<=0;cpt++) {    double ***gradg, ***trgradg;
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      int theta;
          
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    double eip, vip;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
           nhstepm = nhstepm/hstepm;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
              xp=vector(1,npar);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    xm=vector(1,npar);
           oldm=oldms;savm=savms;    dnewm=matrix(1,nlstate*nlstate,1,npar);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
            
           for (h=0; h<=nhstepm; h++){    pstamp(ficresstdeij);
             if (h==(int) (calagedate+YEARM*cpt)) {    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    fprintf(ficresstdeij,"# Age");
             }    for(i=1; i<=nlstate;i++){
             for(j=1; j<=nlstate+ndeath;j++) {      for(j=1; j<=nlstate;j++)
               kk1=0.;kk2=0;        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
               for(i=1; i<=nlstate;i++) {                    fprintf(ficresstdeij," e%1d. ",i);
                 if (mobilav==1)    }
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    fprintf(ficresstdeij,"\n");
                 else {  
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    pstamp(ficrescveij);
                 }    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
               }    fprintf(ficrescveij,"# Age");
               if (h==(int)(calagedate+12*cpt)){    for(i=1; i<=nlstate;i++)
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;      for(j=1; j<=nlstate;j++){
                   /*fprintf(ficrespop," %.3f", kk1);        cptj= (j-1)*nlstate+i;
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/        for(i2=1; i2<=nlstate;i2++)
               }          for(j2=1; j2<=nlstate;j2++){
             }            cptj2= (j2-1)*nlstate+i2;
             for(i=1; i<=nlstate;i++){            if(cptj2 <= cptj)
               kk1=0.;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
                 for(j=1; j<=nlstate;j++){          }
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];      }
                 }    fprintf(ficrescveij,"\n");
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];    
             }    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    }
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);    else  hstepm=estepm;   
           }    /* We compute the life expectancy from trapezoids spaced every estepm months
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     * This is mainly to measure the difference between two models: for example
         }     * if stepm=24 months pijx are given only every 2 years and by summing them
       }     * we are calculating an estimate of the Life Expectancy assuming a linear 
       * progression in between and thus overestimating or underestimating according
   /******/     * to the curvature of the survival function. If, for the same date, we 
      * estimate the model with stepm=1 month, we can keep estepm to 24 months
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {     * to compare the new estimate of Life expectancy with the same linear 
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);       * hypothesis. A more precise result, taking into account a more precise
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     * curvature will be obtained if estepm is as small as stepm. */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
           nhstepm = nhstepm/hstepm;    /* 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. 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       nhstepm is the number of hstepm from age to agelim 
           oldm=oldms;savm=savms;       nstepm is the number of stepm from age to agelin. 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);         Look at hpijx to understand the reason of that which relies in memory size
           for (h=0; h<=nhstepm; h++){       and note for a fixed period like estepm months */
             if (h==(int) (calagedate+YEARM*cpt)) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);       survival function given by stepm (the optimization length). Unfortunately it
             }       means that if the survival funtion is printed only each two years of age and if
             for(j=1; j<=nlstate+ndeath;j++) {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
               kk1=0.;kk2=0;       results. So we changed our mind and took the option of the best precision.
               for(i=1; i<=nlstate;i++) {                  */
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
               }  
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    /* If stepm=6 months */
             }    /* nhstepm age range expressed in number of stepm */
           }    agelim=AGESUP;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
         }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       }    /* if (stepm >= YEARM) hstepm=1;*/
    }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   }    
      p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   if (popforecast==1) {    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ivector(popage,0,AGESUP);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     free_vector(popeffectif,0,AGESUP);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
     free_vector(popcount,0,AGESUP);  
   }    for (age=bage; age<=fage; age ++){ 
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   fclose(ficrespop);      /* if (stepm >= YEARM) hstepm=1;*/
 }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
 /***********************************************/      /* If stepm=6 months */
 /**************** Main Program *****************/      /* Computed by stepm unit matrices, product of hstepma matrices, stored
 /***********************************************/         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
 int main(int argc, char *argv[])      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 {  
       /* Computing  Variances of health expectancies */
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   double agedeb, agefin,hf;         decrease memory allocation */
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
   double fret;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   double **xi,tmp,delta;          xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
   double dum; /* Dummy variable */        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   double ***p3mat;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   int *indx;    
   char line[MAXLINE], linepar[MAXLINE];        for(j=1; j<= nlstate; j++){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];          for(i=1; i<=nlstate; i++){
   int firstobs=1, lastobs=10;            for(h=0; h<=nhstepm-1; h++){
   int sdeb, sfin; /* Status at beginning and end */              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   int c,  h , cpt,l;              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   int ju,jl, mi;            }
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;          }
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;        }
   int mobilav=0,popforecast=0;       
   int hstepm, nhstepm;        for(ij=1; ij<= nlstate*nlstate; ij++)
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   double bage, fage, age, agelim, agebase;          }
   double ftolpl=FTOL;      }/* End theta */
   double **prlim;      
   double *severity;      
   double ***param; /* Matrix of parameters */      for(h=0; h<=nhstepm-1; h++)
   double  *p;        for(j=1; j<=nlstate*nlstate;j++)
   double **matcov; /* Matrix of covariance */          for(theta=1; theta <=npar; theta++)
   double ***delti3; /* Scale */            trgradg[h][j][theta]=gradg[h][theta][j];
   double *delti; /* Scale */      
   double ***eij, ***vareij;  
   double **varpl; /* Variances of prevalence limits by age */       for(ij=1;ij<=nlstate*nlstate;ij++)
   double *epj, vepp;        for(ji=1;ji<=nlstate*nlstate;ji++)
   double kk1, kk2;          varhe[ij][ji][(int)age] =0.;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;  
         printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   char *alph[]={"a","a","b","c","d","e"}, str[4];       for(h=0;h<=nhstepm-1;h++){
         for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   char z[1]="c", occ;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
 #include <sys/time.h>          for(ij=1;ij<=nlstate*nlstate;ij++)
 #include <time.h>            for(ji=1;ji<=nlstate*nlstate;ji++)
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
          }
   /* long total_usecs;      }
   struct timeval start_time, end_time;  
        /* Computing expectancies */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   getcwd(pathcd, size);      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   printf("\n%s",version);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   if(argc <=1){            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     printf("\nEnter the parameter file name: ");            
     scanf("%s",pathtot);            /* 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]);*/
   }  
   else{          }
     strcpy(pathtot,argv[1]);  
   }      fprintf(ficresstdeij,"%3.0f",age );
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      for(i=1; i<=nlstate;i++){
   /*cygwin_split_path(pathtot,path,optionfile);        eip=0.;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/        vip=0.;
   /* cutv(path,optionfile,pathtot,'\\');*/        for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
   chdir(path);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
   replace(pathc,path);        }
         fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
 /*-------- arguments in the command line --------*/      }
       fprintf(ficresstdeij,"\n");
   strcpy(fileres,"r");  
   strcat(fileres, optionfilefiname);      fprintf(ficrescveij,"%3.0f",age );
   strcat(fileres,".txt");    /* Other files have txt extension */      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
   /*---------arguments file --------*/          cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
   if((ficpar=fopen(optionfile,"r"))==NULL)    {            for(j2=1; j2<=nlstate;j2++){
     printf("Problem with optionfile %s\n",optionfile);              cptj2= (j2-1)*nlstate+i2;
     goto end;              if(cptj2 <= cptj)
   }                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
   strcpy(filereso,"o");        }
   strcat(filereso,fileres);      fprintf(ficrescveij,"\n");
   if((ficparo=fopen(filereso,"w"))==NULL) {     
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    }
   }    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   /* Reads comments: lines beginning with '#' */    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     ungetc(c,ficpar);    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     fgets(line, MAXLINE, ficpar);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     puts(line);    printf("\n");
     fputs(line,ficparo);    fprintf(ficlog,"\n");
   }  
   ungetc(c,ficpar);    free_vector(xm,1,npar);
     free_vector(xp,1,npar);
   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);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   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);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   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);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
 while((c=getc(ficpar))=='#' && c!= EOF){  }
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);  /************ Variance ******************/
     puts(line);  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[])
     fputs(line,ficparo);  {
   }    /* Variance of health expectancies */
   ungetc(c,ficpar);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
      /* double **newm;*/
        double **dnewm,**doldm;
   covar=matrix(0,NCOVMAX,1,n);    double **dnewmp,**doldmp;
   cptcovn=0;    int i, j, nhstepm, hstepm, h, nstepm ;
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    int k, cptcode;
     double *xp;
   ncovmodel=2+cptcovn;    double **gp, **gm;  /* for var eij */
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    double ***gradg, ***trgradg; /*for var eij */
      double **gradgp, **trgradgp; /* for var p point j */
   /* Read guess parameters */    double *gpp, *gmp; /* for var p point j */
   /* Reads comments: lines beginning with '#' */    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   while((c=getc(ficpar))=='#' && c!= EOF){    double ***p3mat;
     ungetc(c,ficpar);    double age,agelim, hf;
     fgets(line, MAXLINE, ficpar);    double ***mobaverage;
     puts(line);    int theta;
     fputs(line,ficparo);    char digit[4];
   }    char digitp[25];
   ungetc(c,ficpar);  
      char fileresprobmorprev[FILENAMELENGTH];
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)    if(popbased==1){
     for(j=1; j <=nlstate+ndeath-1; j++){      if(mobilav!=0)
       fscanf(ficpar,"%1d%1d",&i1,&j1);        strcpy(digitp,"-populbased-mobilav-");
       fprintf(ficparo,"%1d%1d",i1,j1);      else strcpy(digitp,"-populbased-nomobil-");
       printf("%1d%1d",i,j);    }
       for(k=1; k<=ncovmodel;k++){    else 
         fscanf(ficpar," %lf",&param[i][j][k]);      strcpy(digitp,"-stablbased-");
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);    if (mobilav!=0) {
       }      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       fscanf(ficpar,"\n");      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
       printf("\n");        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
       fprintf(ficparo,"\n");        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     }      }
      }
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  
     strcpy(fileresprobmorprev,"prmorprev"); 
   p=param[1][1];    sprintf(digit,"%-d",ij);
      /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   /* Reads comments: lines beginning with '#' */    strcat(fileresprobmorprev,digit); /* Tvar to be done */
   while((c=getc(ficpar))=='#' && c!= EOF){    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     ungetc(c,ficpar);    strcat(fileresprobmorprev,fileres);
     fgets(line, MAXLINE, ficpar);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     puts(line);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     fputs(line,ficparo);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   }    }
   ungetc(c,ficpar);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    pstamp(ficresprobmorprev);
   for(i=1; i <=nlstate; i++){    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     for(j=1; j <=nlstate+ndeath-1; j++){    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       printf("%1d%1d",i,j);      fprintf(ficresprobmorprev," p.%-d SE",j);
       fprintf(ficparo,"%1d%1d",i1,j1);      for(i=1; i<=nlstate;i++)
       for(k=1; k<=ncovmodel;k++){        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
         fscanf(ficpar,"%le",&delti3[i][j][k]);    }  
         printf(" %le",delti3[i][j][k]);    fprintf(ficresprobmorprev,"\n");
         fprintf(ficparo," %le",delti3[i][j][k]);    fprintf(ficgp,"\n# Routine varevsij");
       }    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
       fscanf(ficpar,"\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");
       printf("\n");    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       fprintf(ficparo,"\n");  /*   } */
     }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   }    pstamp(ficresvij);
   delti=delti3[1][1];    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
      if(popbased==1)
   /* Reads comments: lines beginning with '#' */      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);
   while((c=getc(ficpar))=='#' && c!= EOF){    else
     ungetc(c,ficpar);      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fgets(line, MAXLINE, ficpar);    fprintf(ficresvij,"# Age");
     puts(line);    for(i=1; i<=nlstate;i++)
     fputs(line,ficparo);      for(j=1; j<=nlstate;j++)
   }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
   ungetc(c,ficpar);    fprintf(ficresvij,"\n");
    
   matcov=matrix(1,npar,1,npar);    xp=vector(1,npar);
   for(i=1; i <=npar; i++){    dnewm=matrix(1,nlstate,1,npar);
     fscanf(ficpar,"%s",&str);    doldm=matrix(1,nlstate,1,nlstate);
     printf("%s",str);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     fprintf(ficparo,"%s",str);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     for(j=1; j <=i; j++){  
       fscanf(ficpar," %le",&matcov[i][j]);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       printf(" %.5le",matcov[i][j]);    gpp=vector(nlstate+1,nlstate+ndeath);
       fprintf(ficparo," %.5le",matcov[i][j]);    gmp=vector(nlstate+1,nlstate+ndeath);
     }    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fscanf(ficpar,"\n");    
     printf("\n");    if(estepm < stepm){
     fprintf(ficparo,"\n");      printf ("Problem %d lower than %d\n",estepm, stepm);
   }    }
   for(i=1; i <=npar; i++)    else  hstepm=estepm;   
     for(j=i+1;j<=npar;j++)    /* For example we decided to compute the life expectancy with the smallest unit */
       matcov[i][j]=matcov[j][i];    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           nhstepm is the number of hstepm from age to agelim 
   printf("\n");       nstepm is the number of stepm from age to agelin. 
        Look at function hpijx to understand why (it is linked to memory size questions) */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     /*-------- Rewriting paramater file ----------*/       survival function given by stepm (the optimization length). Unfortunately it
      strcpy(rfileres,"r");    /* "Rparameterfile */       means that if the survival funtion is printed every two years of age and if
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
      strcat(rfileres,".");    /* */       results. So we changed our mind and took the option of the best precision.
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    */
     if((ficres =fopen(rfileres,"w"))==NULL) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    agelim = AGESUP;
     }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     fprintf(ficres,"#%s\n",version);      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 */
     /*-------- data file ----------*/      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     if((fic=fopen(datafile,"r"))==NULL)    {      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       printf("Problem with datafile: %s\n", datafile);goto end;      gp=matrix(0,nhstepm,1,nlstate);
     }      gm=matrix(0,nhstepm,1,nlstate);
   
     n= lastobs;  
     severity = vector(1,maxwav);      for(theta=1; theta <=npar; theta++){
     outcome=imatrix(1,maxwav+1,1,n);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     num=ivector(1,n);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     moisnais=vector(1,n);        }
     annais=vector(1,n);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     moisdc=vector(1,n);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     andc=vector(1,n);  
     agedc=vector(1,n);        if (popbased==1) {
     cod=ivector(1,n);          if(mobilav ==0){
     weight=vector(1,n);            for(i=1; i<=nlstate;i++)
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */              prlim[i][i]=probs[(int)age][i][ij];
     mint=matrix(1,maxwav,1,n);          }else{ /* mobilav */ 
     anint=matrix(1,maxwav,1,n);            for(i=1; i<=nlstate;i++)
     s=imatrix(1,maxwav+1,1,n);              prlim[i][i]=mobaverage[(int)age][i][ij];
     adl=imatrix(1,maxwav+1,1,n);              }
     tab=ivector(1,NCOVMAX);        }
     ncodemax=ivector(1,8);    
         for(j=1; j<= nlstate; j++){
     i=1;          for(h=0; h<=nhstepm; h++){
     while (fgets(line, MAXLINE, fic) != NULL)    {            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       if ((i >= firstobs) && (i <=lastobs)) {              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
                  }
         for (j=maxwav;j>=1;j--){        }
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        /* This for computing probability of death (h=1 means
           strcpy(line,stra);           computed over hstepm matrices product = hstepm*stepm months) 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);           as a weighted average of prlim.
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        */
         }        for(j=nlstate+1;j<=nlstate+ndeath;j++){
                  for(i=1,gpp[j]=0.; i<= nlstate; i++)
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        }    
         /* end probability of death */
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         for (j=ncovcol;j>=1;j--){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);   
         }        if (popbased==1) {
         num[i]=atol(stra);          if(mobilav ==0){
                    for(i=1; i<=nlstate;i++)
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){              prlim[i][i]=probs[(int)age][i][ij];
           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;}*/          }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
         i=i+1;              prlim[i][i]=mobaverage[(int)age][i][ij];
       }          }
     }        }
     /* printf("ii=%d", ij);  
        scanf("%d",i);*/        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
   imx=i-1; /* Number of individuals */          for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   /* for (i=1; i<=imx; i++){              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;          }
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;        }
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;        /* This for computing probability of death (h=1 means
     }*/           computed over hstepm matrices product = hstepm*stepm months) 
    /*  for (i=1; i<=imx; i++){           as a weighted average of prlim.
      if (s[4][i]==9)  s[4][i]=-1;        */
      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(j=nlstate+1;j<=nlstate+ndeath;j++){
            for(i=1,gmp[j]=0.; i<= nlstate; i++)
             gmp[j] += prlim[i][i]*p3mat[i][j][1];
   /* Calculation of the number of parameter from char model*/        }    
   Tvar=ivector(1,15);        /* end probability of death */
   Tprod=ivector(1,15);  
   Tvaraff=ivector(1,15);        for(j=1; j<= nlstate; j++) /* vareij */
   Tvard=imatrix(1,15,1,2);          for(h=0; h<=nhstepm; h++){
   Tage=ivector(1,15);                  gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
              }
   if (strlen(model) >1){  
     j=0, j1=0, k1=1, k2=1;        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     j=nbocc(model,'+');          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     j1=nbocc(model,'*');        }
     cptcovn=j+1;  
     cptcovprod=j1;      } /* End theta */
      
     strcpy(modelsav,model);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);      for(h=0; h<=nhstepm; h++) /* veij */
       goto end;        for(j=1; j<=nlstate;j++)
     }          for(theta=1; theta <=npar; theta++)
                trgradg[h][j][theta]=gradg[h][theta][j];
     for(i=(j+1); i>=1;i--){  
       cutv(stra,strb,modelsav,'+');      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);        for(theta=1; theta <=npar; theta++)
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          trgradgp[j][theta]=gradgp[theta][j];
       /*scanf("%d",i);*/    
       if (strchr(strb,'*')) {  
         cutv(strd,strc,strb,'*');      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         if (strcmp(strc,"age")==0) {      for(i=1;i<=nlstate;i++)
           cptcovprod--;        for(j=1;j<=nlstate;j++)
           cutv(strb,stre,strd,'V');          vareij[i][j][(int)age] =0.;
           Tvar[i]=atoi(stre);  
           cptcovage++;      for(h=0;h<=nhstepm;h++){
             Tage[cptcovage]=i;        for(k=0;k<=nhstepm;k++){
             /*printf("stre=%s ", stre);*/          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
         }          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
         else if (strcmp(strd,"age")==0) {          for(i=1;i<=nlstate;i++)
           cptcovprod--;            for(j=1;j<=nlstate;j++)
           cutv(strb,stre,strc,'V');              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
           Tvar[i]=atoi(stre);        }
           cptcovage++;      }
           Tage[cptcovage]=i;    
         }      /* pptj */
         else {      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
           cutv(strb,stre,strc,'V');      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
           Tvar[i]=ncovcol+k1;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
           cutv(strb,strc,strd,'V');        for(i=nlstate+1;i<=nlstate+ndeath;i++)
           Tprod[k1]=i;          varppt[j][i]=doldmp[j][i];
           Tvard[k1][1]=atoi(strc);      /* end ppptj */
           Tvard[k1][2]=atoi(stre);      /*  x centered again */
           Tvar[cptcovn+k2]=Tvard[k1][1];      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
           Tvar[cptcovn+k2+1]=Tvard[k1][2];      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
           for (k=1; k<=lastobs;k++)   
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];      if (popbased==1) {
           k1++;        if(mobilav ==0){
           k2=k2+2;          for(i=1; i<=nlstate;i++)
         }            prlim[i][i]=probs[(int)age][i][ij];
       }        }else{ /* mobilav */ 
       else {          for(i=1; i<=nlstate;i++)
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/            prlim[i][i]=mobaverage[(int)age][i][ij];
        /*  scanf("%d",i);*/        }
       cutv(strd,strc,strb,'V');      }
       Tvar[i]=atoi(strc);               
       }      /* This for computing probability of death (h=1 means
       strcpy(modelsav,stra);           computed over hstepm (estepm) matrices product = hstepm*stepm months) 
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);         as a weighted average of prlim.
         scanf("%d",i);*/      */
     }      for(j=nlstate+1;j<=nlstate+ndeath;j++){
 }        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
            gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);      }    
   printf("cptcovprod=%d ", cptcovprod);      /* end probability of death */
   scanf("%d ",i);*/  
     fclose(fic);      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     /*  if(mle==1){*/        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
     if (weightopt != 1) { /* Maximisation without weights*/        for(i=1; i<=nlstate;i++){
       for(i=1;i<=n;i++) weight[i]=1.0;          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     }        }
     /*-calculation of age at interview from date of interview and age at death -*/      } 
     agev=matrix(1,maxwav,1,imx);      fprintf(ficresprobmorprev,"\n");
   
     for (i=1; i<=imx; i++) {      fprintf(ficresvij,"%.0f ",age );
       for(m=2; (m<= maxwav); m++) {      for(i=1; i<=nlstate;i++)
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){        for(j=1; j<=nlstate;j++){
          anint[m][i]=9999;          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
          s[m][i]=-1;        }
        }      fprintf(ficresvij,"\n");
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;      free_matrix(gp,0,nhstepm,1,nlstate);
       }      free_matrix(gm,0,nhstepm,1,nlstate);
     }      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
     for (i=1; i<=imx; i++)  {      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    } /* End age */
       for(m=1; (m<= maxwav); m++){    free_vector(gpp,nlstate+1,nlstate+ndeath);
         if(s[m][i] >0){    free_vector(gmp,nlstate+1,nlstate+ndeath);
           if (s[m][i] >= nlstate+1) {    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
             if(agedc[i]>0)    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
               if(moisdc[i]!=99 && andc[i]!=9999)    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
                 agev[m][i]=agedc[i];    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
            else {  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
               if (andc[i]!=9999){  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
               printf("Warning negative age at death: %d line:%d\n",num[i],i);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
               agev[m][i]=-1;    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
               }    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
             }    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
           }    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
           else if(s[m][i] !=9){ /* Should no more exist */    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);
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
             if(mint[m][i]==99 || anint[m][i]==9999)  */
               agev[m][i]=1;  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
             else if(agev[m][i] <agemin){    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
               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);*/    free_vector(xp,1,npar);
             }    free_matrix(doldm,1,nlstate,1,nlstate);
             else if(agev[m][i] >agemax){    free_matrix(dnewm,1,nlstate,1,npar);
               agemax=agev[m][i];    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
             }    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
             /*agev[m][i]=anint[m][i]-annais[i];*/    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
             /*   agev[m][i] = age[i]+2*m;*/    fclose(ficresprobmorprev);
           }    fflush(ficgp);
           else { /* =9 */    fflush(fichtm); 
             agev[m][i]=1;  }  /* end varevsij */
             s[m][i]=-1;  
           }  /************ 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[])
         else /*= 0 Unknown */  {
           agev[m][i]=1;    /* Variance of prevalence limit */
       }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
        double **newm;
     }    double **dnewm,**doldm;
     for (i=1; i<=imx; i++)  {    int i, j, nhstepm, hstepm;
       for(m=1; (m<= maxwav); m++){    int k, cptcode;
         if (s[m][i] > (nlstate+ndeath)) {    double *xp;
           printf("Error: Wrong value in nlstate or ndeath\n");      double *gp, *gm;
           goto end;    double **gradg, **trgradg;
         }    double age,agelim;
       }    int theta;
     }    
     pstamp(ficresvpl);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     free_vector(severity,1,maxwav);    for(i=1; i<=nlstate;i++)
     free_imatrix(outcome,1,maxwav+1,1,n);        fprintf(ficresvpl," %1d-%1d",i,i);
     free_vector(moisnais,1,n);    fprintf(ficresvpl,"\n");
     free_vector(annais,1,n);  
     /* free_matrix(mint,1,maxwav,1,n);    xp=vector(1,npar);
        free_matrix(anint,1,maxwav,1,n);*/    dnewm=matrix(1,nlstate,1,npar);
     free_vector(moisdc,1,n);    doldm=matrix(1,nlstate,1,nlstate);
     free_vector(andc,1,n);    
     hstepm=1*YEARM; /* Every year of age */
        hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     wav=ivector(1,imx);    agelim = AGESUP;
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
          if (stepm >= YEARM) hstepm=1;
     /* Concatenates waves */      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
       Tcode=ivector(1,100);  
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);      for(theta=1; theta <=npar; theta++){
       ncodemax[1]=1;        for(i=1; i<=npar; i++){ /* Computes gradient */
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
              }
    codtab=imatrix(1,100,1,10);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    h=0;        for(i=1;i<=nlstate;i++)
    m=pow(2,cptcoveff);          gp[i] = prlim[i][i];
        
    for(k=1;k<=cptcoveff; k++){        for(i=1; i<=npar; i++) /* Computes gradient */
      for(i=1; i <=(m/pow(2,k));i++){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
        for(j=1; j <= ncodemax[k]; j++){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){        for(i=1;i<=nlstate;i++)
            h++;          gm[i] = prlim[i][i];
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;  
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/        for(i=1;i<=nlstate;i++)
          }          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
        }      } /* End theta */
      }  
    }      trgradg =matrix(1,nlstate,1,npar);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);  
       codtab[1][2]=1;codtab[2][2]=2; */      for(j=1; j<=nlstate;j++)
    /* for(i=1; i <=m ;i++){        for(theta=1; theta <=npar; theta++)
       for(k=1; k <=cptcovn; k++){          trgradg[j][theta]=gradg[theta][j];
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);  
       }      for(i=1;i<=nlstate;i++)
       printf("\n");        varpl[i][(int)age] =0.;
       }      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       scanf("%d",i);*/      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
          for(i=1;i<=nlstate;i++)
    /* Calculates basic frequencies. Computes observed prevalence at single age        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
        and prints on file fileres'p'. */  
       fprintf(ficresvpl,"%.0f ",age );
          for(i=1; i<=nlstate;i++)
            fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresvpl,"\n");
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_vector(gp,1,nlstate);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_vector(gm,1,nlstate);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      free_matrix(gradg,1,npar,1,nlstate);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      free_matrix(trgradg,1,nlstate,1,npar);
          } /* End age */
     /* 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] */    free_vector(xp,1,npar);
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
     if(mle==1){  
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);  }
     }  
      /************ Variance of one-step probabilities  ******************/
     /*--------- results files --------------*/  void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);  {
      int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
    jk=1;    int k=0,l, cptcode;
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    int first=1, first1;
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
    for(i=1,jk=1; i <=nlstate; i++){    double **dnewm,**doldm;
      for(k=1; k <=(nlstate+ndeath); k++){    double *xp;
        if (k != i)    double *gp, *gm;
          {    double **gradg, **trgradg;
            printf("%d%d ",i,k);    double **mu;
            fprintf(ficres,"%1d%1d ",i,k);    double age,agelim, cov[NCOVMAX];
            for(j=1; j <=ncovmodel; j++){    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
              printf("%f ",p[jk]);    int theta;
              fprintf(ficres,"%f ",p[jk]);    char fileresprob[FILENAMELENGTH];
              jk++;    char fileresprobcov[FILENAMELENGTH];
            }    char fileresprobcor[FILENAMELENGTH];
            printf("\n");  
            fprintf(ficres,"\n");    double ***varpij;
          }  
      }    strcpy(fileresprob,"prob"); 
    }    strcat(fileresprob,fileres);
  if(mle==1){    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
     /* Computing hessian and covariance matrix */      printf("Problem with resultfile: %s\n", fileresprob);
     ftolhess=ftol; /* Usually correct */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     hesscov(matcov, p, npar, delti, ftolhess, func);    }
  }    strcpy(fileresprobcov,"probcov"); 
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");    strcat(fileresprobcov,fileres);
     printf("# Scales (for hessian or gradient estimation)\n");    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
      for(i=1,jk=1; i <=nlstate; i++){      printf("Problem with resultfile: %s\n", fileresprobcov);
       for(j=1; j <=nlstate+ndeath; j++){      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
         if (j!=i) {    }
           fprintf(ficres,"%1d%1d",i,j);    strcpy(fileresprobcor,"probcor"); 
           printf("%1d%1d",i,j);    strcat(fileresprobcor,fileres);
           for(k=1; k<=ncovmodel;k++){    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
             printf(" %.5e",delti[jk]);      printf("Problem with resultfile: %s\n", fileresprobcor);
             fprintf(ficres," %.5e",delti[jk]);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
             jk++;    }
           }    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           printf("\n");    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
           fprintf(ficres,"\n");    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
         }    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
       }    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);
        pstamp(ficresprob);
     k=1;    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\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");    fprintf(ficresprob,"# Age");
     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");    pstamp(ficresprobcov);
     for(i=1;i<=npar;i++){    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
       /*  if (k>nlstate) k=1;    fprintf(ficresprobcov,"# Age");
       i1=(i-1)/(ncovmodel*nlstate)+1;    pstamp(ficresprobcor);
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
       printf("%s%d%d",alph[k],i1,tab[i]);*/    fprintf(ficresprobcor,"# Age");
       fprintf(ficres,"%3d",i);  
       printf("%3d",i);  
       for(j=1; j<=i;j++){    for(i=1; i<=nlstate;i++)
         fprintf(ficres," %.5e",matcov[i][j]);      for(j=1; j<=(nlstate+ndeath);j++){
         printf(" %.5e",matcov[i][j]);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
       }        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       fprintf(ficres,"\n");        fprintf(ficresprobcor," p%1d-%1d ",i,j);
       printf("\n");      }  
       k++;   /* fprintf(ficresprob,"\n");
     }    fprintf(ficresprobcov,"\n");
        fprintf(ficresprobcor,"\n");
     while((c=getc(ficpar))=='#' && c!= EOF){   */
       ungetc(c,ficpar);    xp=vector(1,npar);
       fgets(line, MAXLINE, ficpar);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
       puts(line);    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
       fputs(line,ficparo);    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     }    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     ungetc(c,ficpar);    first=1;
     estepm=0;    fprintf(ficgp,"\n# Routine varprob");
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     if (estepm==0 || estepm < stepm) estepm=stepm;    fprintf(fichtm,"\n");
     if (fage <= 2) {  
       bage = ageminpar;    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
       fage = agemaxpar;    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     }    file %s<br>\n",optionfilehtmcov);
        fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");  and drawn. It helps understanding how is the covariance between two incidences.\
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
    It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
     while((c=getc(ficpar))=='#' && c!= EOF){  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
     ungetc(c,ficpar);  standard deviations wide on each axis. <br>\
     fgets(line, MAXLINE, ficpar);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
     puts(line);   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
     fputs(line,ficparo);  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   }  
   ungetc(c,ficpar);    cov[1]=1;
      tj=cptcoveff;
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    j1=0;
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    for(t=1; t<=tj;t++){
            for(i1=1; i1<=ncodemax[t];i1++){ 
   while((c=getc(ficpar))=='#' && c!= EOF){        j1++;
     ungetc(c,ficpar);        if  (cptcovn>0) {
     fgets(line, MAXLINE, ficpar);          fprintf(ficresprob, "\n#********** Variable "); 
     puts(line);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     fputs(line,ficparo);          fprintf(ficresprob, "**********\n#\n");
   }          fprintf(ficresprobcov, "\n#********** Variable "); 
   ungetc(c,ficpar);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficresprobcov, "**********\n#\n");
           
    dateprev1=anprev1+mprev1/12.+jprev1/365.;          fprintf(ficgp, "\n#********** Variable "); 
    dateprev2=anprev2+mprev2/12.+jprev2/365.;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
   fscanf(ficpar,"pop_based=%d\n",&popbased);          
   fprintf(ficparo,"pop_based=%d\n",popbased);            
   fprintf(ficres,"pop_based=%d\n",popbased);            fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
            for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   while((c=getc(ficpar))=='#' && c!= EOF){          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
     ungetc(c,ficpar);          
     fgets(line, MAXLINE, ficpar);          fprintf(ficresprobcor, "\n#********** Variable ");    
     puts(line);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     fputs(line,ficparo);          fprintf(ficresprobcor, "**********\n#");    
   }        }
   ungetc(c,ficpar);        
         for (age=bage; age<=fage; age ++){ 
   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);          cov[2]=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);          for (k=1; k<=cptcovn;k++) {
 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);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 while((c=getc(ficpar))=='#' && c!= EOF){          for (k=1; k<=cptcovprod;k++)
     ungetc(c,ficpar);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     fgets(line, MAXLINE, ficpar);          
     puts(line);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
     fputs(line,ficparo);          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   }          gp=vector(1,(nlstate)*(nlstate+ndeath));
   ungetc(c,ficpar);          gm=vector(1,(nlstate)*(nlstate+ndeath));
       
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);          for(theta=1; theta <=npar; theta++){
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);            for(i=1; i<=npar; i++)
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
 /*------------ gnuplot -------------*/            k=0;
   strcpy(optionfilegnuplot,optionfilefiname);            for(i=1; i<= (nlstate); i++){
   strcat(optionfilegnuplot,".gp");              for(j=1; j<=(nlstate+ndeath);j++){
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {                k=k+1;
     printf("Problem with file %s",optionfilegnuplot);                gp[k]=pmmij[i][j];
   }              }
   fclose(ficgp);            }
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);            
 /*--------- index.htm --------*/            for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
   strcpy(optionfilehtm,optionfile);      
   strcat(optionfilehtm,".htm");            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {            k=0;
     printf("Problem with %s \n",optionfilehtm), exit(0);            for(i=1; i<=(nlstate); i++){
   }              for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n                gm[k]=pmmij[i][j];
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n              }
 \n            }
 Total number of observations=%d <br>\n       
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
 <hr  size=\"2\" color=\"#EC5E5E\">              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
  <ul><li>Parameter files<br>\n          }
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n  
  - 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);          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   fclose(fichtm);            for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);          
            matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
 /*------------ free_vector  -------------*/          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
  chdir(path);          free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
            free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
  free_ivector(wav,1,imx);          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);    
  free_ivector(num,1,n);          pmij(pmmij,cov,ncovmodel,x,nlstate);
  free_vector(agedc,1,n);          
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          k=0;
  fclose(ficparo);          for(i=1; i<=(nlstate); i++){
  fclose(ficres);            for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
   /*--------------- Prevalence limit --------------*/            }
            }
   strcpy(filerespl,"pl");          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
   strcat(filerespl,fileres);            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
   if((ficrespl=fopen(filerespl,"w"))==NULL) {              varpij[i][j][(int)age] = doldm[i][j];
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;  
   }          /*printf("\n%d ",(int)age);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   fprintf(ficrespl,"#Prevalence limit\n");            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   fprintf(ficrespl,"#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++) fprintf(ficrespl,"%d-%d ",i,i);            }*/
   fprintf(ficrespl,"\n");  
            fprintf(ficresprob,"\n%d ",(int)age);
   prlim=matrix(1,nlstate,1,nlstate);          fprintf(ficresprobcov,"\n%d ",(int)age);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          fprintf(ficresprobcor,"\n%d ",(int)age);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
   k=0;            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
   agebase=ageminpar;            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   agelim=agemaxpar;          }
   ftolpl=1.e-10;          i=0;
   i1=cptcoveff;          for (k=1; k<=(nlstate);k++){
   if (cptcovn < 1){i1=1;}            for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
   for(cptcov=1;cptcov<=i1;cptcov++){              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
         k=k+1;              for (j=1; j<=i;j++){
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
         fprintf(ficrespl,"\n#******");                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
         for(j=1;j<=cptcoveff;j++)              }
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            }
         fprintf(ficrespl,"******\n");          }/* end of loop for state */
                } /* end of loop for age */
         for (age=agebase; age<=agelim; age++){  
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        /* Confidence intervalle of pij  */
           fprintf(ficrespl,"%.0f",age );        /*
           for(i=1; i<=nlstate;i++)          fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficrespl," %.5f", prlim[i][i]);          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficrespl,"\n");          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
         }          fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
       }          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
     }          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
   fclose(ficrespl);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   /*------------- h Pij x at various ages ------------*/  
          /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        first1=1;
   if((ficrespij=fopen(filerespij,"w"))==NULL) {        for (k2=1; k2<=(nlstate);k2++){
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
   }            if(l2==k2) continue;
   printf("Computing pij: result on file '%s' \n", filerespij);            j=(k2-1)*(nlstate+ndeath)+l2;
              for (k1=1; k1<=(nlstate);k1++){
   stepsize=(int) (stepm+YEARM-1)/YEARM;              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   /*if (stepm<=24) stepsize=2;*/                if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
   agelim=AGESUP;                if(i<=j) continue;
   hstepm=stepsize*YEARM; /* Every year of age */                for (age=bage; age<=fage; age ++){ 
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */                  if ((int)age %5==0){
                      v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
   k=0;                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
   for(cptcov=1;cptcov<=i1;cptcov++){                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                    mu1=mu[i][(int) age]/stepm*YEARM ;
       k=k+1;                    mu2=mu[j][(int) age]/stepm*YEARM;
         fprintf(ficrespij,"\n#****** ");                    c12=cv12/sqrt(v1*v2);
         for(j=1;j<=cptcoveff;j++)                    /* Computing eigen value of matrix of covariance */
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
         fprintf(ficrespij,"******\n");                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                            if ((lc2 <0) || (lc1 <0) ){
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */                      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);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */                      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);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */                      lc1=fabs(lc1);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                      lc2=fabs(lc2);
           oldm=oldms;savm=savms;                    }
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);    
           fprintf(ficrespij,"# Age");                    /* Eigen vectors */
           for(i=1; i<=nlstate;i++)                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
             for(j=1; j<=nlstate+ndeath;j++)                    /*v21=sqrt(1.-v11*v11); *//* error */
               fprintf(ficrespij," %1d-%1d",i,j);                    v21=(lc1-v1)/cv12*v11;
           fprintf(ficrespij,"\n");                    v12=-v21;
            for (h=0; h<=nhstepm; h++){                    v22=v11;
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );                    tnalp=v21/v11;
             for(i=1; i<=nlstate;i++)                    if(first1==1){
               for(j=1; j<=nlstate+ndeath;j++)                      first1=0;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);                      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(ficrespij,"\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);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                    /*printf(fignu*/
           fprintf(ficrespij,"\n");                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
         }                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
     }                    if(first==1){
   }                      first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);                      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");
   fclose(ficrespij);                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
   /*---------- Forecasting ------------------*/                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
   if((stepm == 1) && (strcmp(model,".")==0)){                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
   }                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   else{                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
     erreur=108;                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
     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,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
   }                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                                mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
   /*---------- Health expectancies and variances ------------*/                      first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
   strcpy(filerest,"t");                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
   strcat(filerest,fileres);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
   if((ficrest=fopen(filerest,"w"))==NULL) {                      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",\
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
   }                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
   printf("Computing Total LEs with variances: file '%s' \n", filerest);                    }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
   strcpy(filerese,"e");                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   strcat(filerese,fileres);                first=1;
   if((ficreseij=fopen(filerese,"w"))==NULL) {              } /*l12 */
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);            } /* k12 */
   }          } /*l1 */
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);        }/* k1 */
       } /* loop covariates */
  strcpy(fileresv,"v");    }
   strcat(fileresv,fileres);    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   }    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    free_vector(xp,1,npar);
   calagedate=-1;    fclose(ficresprob);
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    fclose(ficresprobcov);
     fclose(ficresprobcor);
   k=0;    fflush(ficgp);
   for(cptcov=1;cptcov<=i1;cptcov++){    fflush(fichtmcov);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  }
       k=k+1;  
       fprintf(ficrest,"\n#****** ");  
       for(j=1;j<=cptcoveff;j++)  /******************* Printing html file ***********/
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
       fprintf(ficrest,"******\n");                    int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
       fprintf(ficreseij,"\n#****** ");                    int popforecast, int estepm ,\
       for(j=1;j<=cptcoveff;j++)                    double jprev1, double mprev1,double anprev1, \
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    double jprev2, double mprev2,double anprev2){
       fprintf(ficreseij,"******\n");    int jj1, k1, i1, cpt;
   
       fprintf(ficresvij,"\n#****** ");     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
       for(j=1;j<=cptcoveff;j++)     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  </ul>");
       fprintf(ficresvij,"******\n");     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
       oldm=oldms;savm=savms;     fprintf(fichtm,"\
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);     - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
               stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);     fprintf(fichtm,"\
       oldm=oldms;savm=savms;   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
         fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
       <a href=\"%s\">%s</a> <br>\n",
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);     fprintf(fichtm,"\
       fprintf(ficrest,"\n");   - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
       epj=vector(1,nlstate+1);  
       for(age=bage; age <=fage ;age++){  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  
         if (popbased==1) {   m=cptcoveff;
           for(i=1; i<=nlstate;i++)   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
             prlim[i][i]=probs[(int)age][i][k];  
         }   jj1=0;
           for(k1=1; k1<=m;k1++){
         fprintf(ficrest," %4.0f",age);     for(i1=1; i1<=ncodemax[k1];i1++){
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){       jj1++;
           for(i=1, epj[j]=0.;i <=nlstate;i++) {       if (cptcovn > 0) {
             epj[j] += prlim[i][i]*eij[i][j][(int)age];         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/         for (cpt=1; cpt<=cptcoveff;cpt++) 
           }           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
           epj[nlstate+1] +=epj[j];         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
         }       }
        /* Pij */
         for(i=1, vepp=0.;i <=nlstate;i++)       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> \
           for(j=1;j <=nlstate;j++)  <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
             vepp += vareij[i][j][(int)age];       /* Quasi-incidences */
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
         for(j=1;j <=nlstate;j++){   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> \
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));  <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 */
         fprintf(ficrest,"\n");         for(cpt=1; cpt<nlstate;cpt++){
       }           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
     }  <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
   }         }
 free_matrix(mint,1,maxwav,1,n);       for(cpt=1; cpt<=nlstate;cpt++) {
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);          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> \
     free_vector(weight,1,n);  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
   fclose(ficreseij);       }
   fclose(ficresvij);     } /* end i1 */
   fclose(ficrest);   }/* End k1 */
   fclose(ficpar);   fprintf(fichtm,"</ul>");
   free_vector(epj,1,nlstate+1);  
    
   /*------- Variance limit prevalence------*/     fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
   strcpy(fileresvpl,"vpl");   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   strcat(fileresvpl,fileres);  
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
     exit(0);   fprintf(fichtm,"\
   }   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
   k=0;   fprintf(fichtm,"\
   for(cptcov=1;cptcov<=i1;cptcov++){   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
       k=k+1;   fprintf(fichtm,"\
       fprintf(ficresvpl,"\n#****** ");   - 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): \
       for(j=1;j<=cptcoveff;j++)     <a href=\"%s\">%s</a> <br>\n</li>",
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
       fprintf(ficresvpl,"******\n");   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): \
       varpl=matrix(1,nlstate,(int) bage, (int) fage);     <a href=\"%s\">%s</a> <br>\n</li>",
       oldm=oldms;savm=savms;             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);   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,"\
   fclose(ficresvpl);   - 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"));
   /*---------- End : free ----------------*/   fprintf(fichtm,"\
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);   - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
             subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);  /*  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 */
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  /*      <br>",fileres,fileres,fileres,fileres); */
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);  /*  else  */
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);  /*    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); */
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);   fflush(fichtm);
     fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   free_matrix(matcov,1,npar,1,npar);  
   free_vector(delti,1,npar);   m=cptcoveff;
   free_matrix(agev,1,maxwav,1,imx);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);  
    jj1=0;
   fprintf(fichtm,"\n</body>");   for(k1=1; k1<=m;k1++){
   fclose(fichtm);     for(i1=1; i1<=ncodemax[k1];i1++){
   fclose(ficgp);       jj1++;
         if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
   if(erreur >0)         for (cpt=1; cpt<=cptcoveff;cpt++) 
     printf("End of Imach with error or warning %d\n",erreur);           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
   else   printf("End of Imach\n");         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */       }
         for(cpt=1; cpt<=nlstate;cpt++) {
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/         fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   /*printf("Total time was %d uSec.\n", total_usecs);*/  prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   /*------ End -----------*/  <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 \
  end:  health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
 #ifdef windows  true period expectancies (those weighted with period prevalences are also\
   /* chdir(pathcd);*/   drawn in addition to the population based expectancies computed using\
 #endif   observed and cahotic prevalences: %s%d.png<br>\
  /*system("wgnuplot graph.plt");*/  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
  /*system("../gp37mgw/wgnuplot graph.plt");*/     } /* end i1 */
  /*system("cd ../gp37mgw");*/   }/* End k1 */
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/   fprintf(fichtm,"</ul>");
  strcpy(plotcmd,GNUPLOTPROGRAM);   fflush(fichtm);
  strcat(plotcmd," ");  }
  strcat(plotcmd,optionfilegnuplot);  
  system(plotcmd);  /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
 #ifdef windows  
   while (z[0] != 'q') {    char dirfileres[132],optfileres[132];
     /* chdir(path); */    int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");    int ng=0;
     scanf("%s",z);  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
     if (z[0] == 'c') system("./imach");  /*     printf("Problem with file %s",optionfilegnuplot); */
     else if (z[0] == 'e') system(optionfilehtm);  /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
     else if (z[0] == 'g') system(plotcmd);  /*   } */
     else if (z[0] == 'q') exit(0);  
   }    /*#ifdef windows */
 #endif    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 ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option 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=V3*age+V2+V1+V4 strb=V3*age stra=V2+V1+V4 
           i=1 Tvar[1]=3 Tage[1]=1  
           i=2 Tvar[2]=2
           i=3 Tvar[3]=1
           i=4 Tvar[4]= 4
           i=5 Tvar[5]
         for (k=1; k<=cptcovn;k++) {
           cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
        */
       for(k=1; k<=(j+1);k++){
         cutv(strb,stra,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav=V3*age+V2+V1+V4 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 V3*age+V2+V1+V4 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);  /* V1+V3*age+V2 Tvar[2]=3, and Tvar[3]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] =2 */
             /*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 V1+V3*V2+V2  strb=V3*V2*/
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* find 'n' in Vn and stores in Tvar. 
                                     If already ncovcol=2 and model=V2*V1 Tvar[1]=2+1 and Tvar[2]=2+2 etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]  */
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (i=1; i<=lastobs;i++) /* Computes the new covariate which is a product of covar[n][i]* covar[m][i]
                                        and is stored at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V3*age+V1+V4 strb=V3*age+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);
     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(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     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);
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. Stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
   
       /*-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.1.136


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