Diff for /imach/src/imach.c between versions 1.52 and 1.153

version 1.52, 2002/07/19 18:49:30 version 1.153, 2014/06/20 16:45:46
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.153  2014/06/20 16:45:46  brouard
      Summary: If 3 live state, convergence to period prevalence on same graph
   This program computes Healthy Life Expectancies from    Author: Brouard
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a  
   first survey ("cross") where individuals from different ages are    Revision 1.152  2014/06/18 17:54:09  brouard
   interviewed on their health status or degree of disability (in the    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.151  2014/06/18 16:43:30  brouard
   (if any) in individual health status.  Health expectancies are    *** empty log message ***
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.150  2014/06/18 16:42:35  brouard
   Maximum Likelihood of the parameters involved in the model.  The    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
   simplest model is the multinomial logistic model where pij is the    Author: brouard
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.149  2014/06/18 15:51:14  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Summary: Some fixes in parameter files errors
   'age' is age and 'sex' is a covariate. If you want to have a more    Author: Nicolas Brouard
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.148  2014/06/17 17:38:48  brouard
   you to do it.  More covariates you add, slower the    Summary: Nothing new
   convergence.    Author: Brouard
   
   The advantage of this computer programme, compared to a simple    Just a new packaging for OS/X version 0.98nS
   multinomial logistic model, is clear when the delay between waves is not  
   identical for each individual. Also, if a individual missed an    Revision 1.147  2014/06/16 10:33:11  brouard
   intermediate interview, the information is lost, but taken into    *** empty log message ***
   account using an interpolation or extrapolation.    
     Revision 1.146  2014/06/16 10:20:28  brouard
   hPijx is the probability to be observed in state i at age x+h    Summary: Merge
   conditional to the observed state i at age x. The delay 'h' can be    Author: Brouard
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Merge, before building revised version.
   semester or year) is model as a multinomial logistic.  The hPx  
   matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.145  2014/06/10 21:23:15  brouard
   and the contribution of each individual to the likelihood is simply    Summary: Debugging with valgrind
   hPijx.    Author: Nicolas Brouard
   
   Also this programme outputs the covariance matrix of the parameters but also    Lot of changes in order to output the results with some covariates
   of the life expectancies. It also computes the prevalence limits.    After the Edimburgh REVES conference 2014, it seems mandatory to
      improve the code.
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    No more memory valgrind error but a lot has to be done in order to
            Institut national d'études démographiques, Paris.    continue the work of splitting the code into subroutines.
   This software have been partly granted by Euro-REVES, a concerted action    Also, decodemodel has been improved. Tricode is still not
   from the European Union.    optimal. nbcode should be improved. Documentation has been added in
   It is copyrighted identically to a GNU software product, ie programme and    the source code.
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.143  2014/01/26 09:45:38  brouard
   **********************************************************************/    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
    
 #include <math.h>    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #include <stdio.h>    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 #include <stdlib.h>  
 #include <unistd.h>    Revision 1.142  2014/01/26 03:57:36  brouard
     Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define MAXLINE 256  
 #define GNUPLOTPROGRAM "gnuplot"    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/  
 #define FILENAMELENGTH 80    Revision 1.141  2014/01/26 02:42:01  brouard
 /*#define DEBUG*/    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Revision 1.140  2011/09/02 10:37:54  brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    Summary: times.h is ok with mingw32 now.
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.139  2010/06/14 07:50:17  brouard
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
     I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.138  2010/04/30 18:19:40  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    *** empty log message ***
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.137  2010/04/29 18:11:38  brouard
 #define YEARM 12. /* Number of months per year */    (Module): Checking covariates for more complex models
 #define AGESUP 130    than V1+V2. A lot of change to be done. Unstable.
 #define AGEBASE 40  
 #ifdef windows    Revision 1.136  2010/04/26 20:30:53  brouard
 #define DIRSEPARATOR '\\'    (Module): merging some libgsl code. Fixing computation
 #define ODIRSEPARATOR '/'    of likelione (using inter/intrapolation if mle = 0) in order to
 #else    get same likelihood as if mle=1.
 #define DIRSEPARATOR '/'    Some cleaning of code and comments added.
 #define ODIRSEPARATOR '\\'  
 #endif    Revision 1.135  2009/10/29 15:33:14  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 char version[80]="Imach version 0.8i, June 2002, INED-EUROREVES ";  
 int erreur; /* Error number */    Revision 1.134  2009/10/29 13:18:53  brouard
 int nvar;    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.133  2009/07/06 10:21:25  brouard
 int nlstate=2; /* Number of live states */    just nforces
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.132  2009/07/06 08:22:05  brouard
 int popbased=0;    Many tings
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.131  2009/06/20 16:22:47  brouard
 int maxwav; /* Maxim number of waves */    Some dimensions resccaled
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.130  2009/05/26 06:44:34  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): Max Covariate is now set to 20 instead of 8. A
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    lot of cleaning with variables initialized to 0. Trying to make
 double jmean; /* Mean space between 2 waves */    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Revision 1.129  2007/08/31 13:49:27  lievre
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 FILE *ficlog;  
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    Revision 1.128  2006/06/30 13:02:05  brouard
 FILE *ficresprobmorprev;    (Module): Clarifications on computing e.j
 FILE *fichtm; /* Html File */  
 FILE *ficreseij;    Revision 1.127  2006/04/28 18:11:50  brouard
 char filerese[FILENAMELENGTH];    (Module): Yes the sum of survivors was wrong since
 FILE  *ficresvij;    imach-114 because nhstepm was no more computed in the age
 char fileresv[FILENAMELENGTH];    loop. Now we define nhstepma in the age loop.
 FILE  *ficresvpl;    (Module): In order to speed up (in case of numerous covariates) we
 char fileresvpl[FILENAMELENGTH];    compute health expectancies (without variances) in a first step
 char title[MAXLINE];    and then all the health expectancies with variances or standard
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    deviation (needs data from the Hessian matrices) which slows the
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    computation.
     In the future we should be able to stop the program is only health
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    expectancies and graph are needed without standard deviations.
 char filelog[FILENAMELENGTH]; /* Log file */  
 char filerest[FILENAMELENGTH];    Revision 1.126  2006/04/28 17:23:28  brouard
 char fileregp[FILENAMELENGTH];    (Module): Yes the sum of survivors was wrong since
 char popfile[FILENAMELENGTH];    imach-114 because nhstepm was no more computed in the age
     loop. Now we define nhstepma in the age loop.
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    Version 0.98h
   
 #define NR_END 1    Revision 1.125  2006/04/04 15:20:31  lievre
 #define FREE_ARG char*    Errors in calculation of health expectancies. Age was not initialized.
 #define FTOL 1.0e-10    Forecasting file added.
   
 #define NRANSI    Revision 1.124  2006/03/22 17:13:53  lievre
 #define ITMAX 200    Parameters are printed with %lf instead of %f (more numbers after the comma).
     The log-likelihood is printed in the log file
 #define TOL 2.0e-4  
     Revision 1.123  2006/03/20 10:52:43  brouard
 #define CGOLD 0.3819660    * imach.c (Module): <title> changed, corresponds to .htm file
 #define ZEPS 1.0e-10    name. <head> headers where missing.
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     * imach.c (Module): Weights can have a decimal point as for
 #define GOLD 1.618034    English (a comma might work with a correct LC_NUMERIC environment,
 #define GLIMIT 100.0    otherwise the weight is truncated).
 #define TINY 1.0e-20    Modification of warning when the covariates values are not 0 or
     1.
 static double maxarg1,maxarg2;    Version 0.98g
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.122  2006/03/20 09:45:41  brouard
      (Module): Weights can have a decimal point as for
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    English (a comma might work with a correct LC_NUMERIC environment,
 #define rint(a) floor(a+0.5)    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
 static double sqrarg;    1.
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Version 0.98g
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     Revision 1.121  2006/03/16 17:45:01  lievre
 int imx;    * imach.c (Module): Comments concerning covariates added
 int stepm;  
 /* Stepm, step in month: minimum step interpolation*/    * imach.c (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
 int estepm;    not 1 month. Version 0.98f
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
     Revision 1.120  2006/03/16 15:10:38  lievre
 int m,nb;    (Module): refinements in the computation of lli if
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    status=-2 in order to have more reliable computation if stepm is
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    not 1 month. Version 0.98f
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.119  2006/03/15 17:42:26  brouard
     (Module): Bug if status = -2, the loglikelihood was
 double *weight;    computed as likelihood omitting the logarithm. Version O.98e
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.118  2006/03/14 18:20:07  brouard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 double ftolhess; /* Tolerance for computing hessian */    (Module): Function pstamp added
     (Module): Version 0.98d
 /**************** split *************************/  
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    Revision 1.117  2006/03/14 17:16:22  brouard
 {    (Module): varevsij Comments added explaining the second
    char *s;                             /* pointer */    table of variances if popbased=1 .
    int  l1, l2;                         /* length counters */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
    l1 = strlen( path );                 /* length of path */    (Module): Version 0.98d
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );  
    s= strrchr( path, DIRSEPARATOR );            /* find last / */    Revision 1.116  2006/03/06 10:29:27  brouard
    if ( s == NULL ) {                   /* no directory, so use current */    (Module): Variance-covariance wrong links and
      /*if(strrchr(path, ODIRSEPARATOR )==NULL)    varian-covariance of ej. is needed (Saito).
        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.115  2006/02/27 12:17:45  brouard
       extern char       *getwd( );    (Module): One freematrix added in mlikeli! 0.98c
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.114  2006/02/26 12:57:58  brouard
 #else    (Module): Some improvements in processing parameter
       extern char       *getcwd( );    filename with strsep.
   
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Revision 1.113  2006/02/24 14:20:24  brouard
 #endif    (Module): Memory leaks checks with valgrind and:
          return( GLOCK_ERROR_GETCWD );    datafile was not closed, some imatrix were not freed and on matrix
       }    allocation too.
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Revision 1.112  2006/01/30 09:55:26  brouard
       s++;                              /* after this, the filename */    (Module): Back to gnuplot.exe instead of wgnuplot.exe
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.111  2006/01/25 20:38:18  brouard
       strcpy( name, s );                /* save file name */    (Module): Lots of cleaning and bugs added (Gompertz)
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    (Module): Comments can be added in data file. Missing date values
       dirc[l1-l2] = 0;                  /* add zero */    can be a simple dot '.'.
    }  
    l1 = strlen( dirc );                 /* length of directory */    Revision 1.110  2006/01/25 00:51:50  brouard
 #ifdef windows    (Module): Lots of cleaning and bugs added (Gompertz)
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Revision 1.109  2006/01/24 19:37:15  brouard
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    (Module): Comments (lines starting with a #) are allowed in data.
 #endif  
    s = strrchr( name, '.' );            /* find last / */    Revision 1.108  2006/01/19 18:05:42  lievre
    s++;    Gnuplot problem appeared...
    strcpy(ext,s);                       /* save extension */    To be fixed
    l1= strlen( name);  
    l2= strlen( s)+1;    Revision 1.107  2006/01/19 16:20:37  brouard
    strncpy( finame, name, l1-l2);    Test existence of gnuplot in imach path
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    Revision 1.106  2006/01/19 13:24:36  brouard
 }    Some cleaning and links added in html output
   
     Revision 1.105  2006/01/05 20:23:19  lievre
 /******************************************/    *** empty log message ***
   
 void replace(char *s, char*t)    Revision 1.104  2005/09/30 16:11:43  lievre
 {    (Module): sump fixed, loop imx fixed, and simplifications.
   int i;    (Module): If the status is missing at the last wave but we know
   int lg=20;    that the person is alive, then we can code his/her status as -2
   i=0;    (instead of missing=-1 in earlier versions) and his/her
   lg=strlen(t);    contributions to the likelihood is 1 - Prob of dying from last
   for(i=0; i<= lg; i++) {    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     (s[i] = t[i]);    the healthy state at last known wave). Version is 0.98
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.103  2005/09/30 15:54:49  lievre
 }    (Module): sump fixed, loop imx fixed, and simplifications.
   
 int nbocc(char *s, char occ)    Revision 1.102  2004/09/15 17:31:30  brouard
 {    Add the possibility to read data file including tab characters.
   int i,j=0;  
   int lg=20;    Revision 1.101  2004/09/15 10:38:38  brouard
   i=0;    Fix on curr_time
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {    Revision 1.100  2004/07/12 18:29:06  brouard
   if  (s[i] == occ ) j++;    Add version for Mac OS X. Just define UNIX in Makefile
   }  
   return j;    Revision 1.99  2004/06/05 08:57:40  brouard
 }    *** empty log message ***
   
 void cutv(char *u,char *v, char*t, char occ)    Revision 1.98  2004/05/16 15:05:56  brouard
 {    New version 0.97 . First attempt to estimate force of mortality
   /* cuts string t into u and v where u is ended by char occ excluding it    directly from the data i.e. without the need of knowing the health
      and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)    state at each age, but using a Gompertz model: log u =a + b*age .
      gives u="abcedf" and v="ghi2j" */    This is the basic analysis of mortality and should be done before any
   int i,lg,j,p=0;    other analysis, in order to test if the mortality estimated from the
   i=0;    cross-longitudinal survey is different from the mortality estimated
   for(j=0; j<=strlen(t)-1; j++) {    from other sources like vital statistic data.
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  
   }    The same imach parameter file can be used but the option for mle should be -3.
   
   lg=strlen(t);    Agnès, who wrote this part of the code, tried to keep most of the
   for(j=0; j<p; j++) {    former routines in order to include the new code within the former code.
     (u[j] = t[j]);  
   }    The output is very simple: only an estimate of the intercept and of
      u[p]='\0';    the slope with 95% confident intervals.
   
    for(j=0; j<= lg; j++) {    Current limitations:
     if (j>=(p+1))(v[j-p-1] = t[j]);    A) Even if you enter covariates, i.e. with the
   }    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 }    B) There is no computation of Life Expectancy nor Life Table.
   
 /********************** nrerror ********************/    Revision 1.97  2004/02/20 13:25:42  lievre
     Version 0.96d. Population forecasting command line is (temporarily)
 void nrerror(char error_text[])    suppressed.
 {  
   fprintf(stderr,"ERREUR ...\n");    Revision 1.96  2003/07/15 15:38:55  brouard
   fprintf(stderr,"%s\n",error_text);    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   exit(1);    rewritten within the same printf. Workaround: many printfs.
 }  
 /*********************** vector *******************/    Revision 1.95  2003/07/08 07:54:34  brouard
 double *vector(int nl, int nh)    * imach.c (Repository):
 {    (Repository): Using imachwizard code to output a more meaningful covariance
   double *v;    matrix (cov(a12,c31) instead of numbers.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Revision 1.94  2003/06/27 13:00:02  brouard
   return v-nl+NR_END;    Just cleaning
 }  
     Revision 1.93  2003/06/25 16:33:55  brouard
 /************************ free vector ******************/    (Module): On windows (cygwin) function asctime_r doesn't
 void free_vector(double*v, int nl, int nh)    exist so I changed back to asctime which exists.
 {    (Module): Version 0.96b
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.92  2003/06/25 16:30:45  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 /************************ivector *******************************/    exist so I changed back to asctime which exists.
 int *ivector(long nl,long nh)  
 {    Revision 1.91  2003/06/25 15:30:29  brouard
   int *v;    * imach.c (Repository): Duplicated warning errors corrected.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    (Repository): Elapsed time after each iteration is now output. It
   if (!v) nrerror("allocation failure in ivector");    helps to forecast when convergence will be reached. Elapsed time
   return v-nl+NR_END;    is stamped in powell.  We created a new html file for the graphs
 }    concerning matrix of covariance. It has extension -cov.htm.
   
 /******************free ivector **************************/    Revision 1.90  2003/06/24 12:34:15  brouard
 void free_ivector(int *v, long nl, long nh)    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   free((FREE_ARG)(v+nl-NR_END));    of the covariance matrix to be input.
 }  
     Revision 1.89  2003/06/24 12:30:52  brouard
 /******************* imatrix *******************************/    (Module): Some bugs corrected for windows. Also, when
 int **imatrix(long nrl, long nrh, long ncl, long nch)    mle=-1 a template is output in file "or"mypar.txt with the design
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    of the covariance matrix to be input.
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Revision 1.88  2003/06/23 17:54:56  brouard
   int **m;    * 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.
    
   /* allocate pointers to rows */    Revision 1.87  2003/06/18 12:26:01  brouard
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    Version 0.96
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.86  2003/06/17 20:04:08  brouard
   m -= nrl;    (Module): Change position of html and gnuplot routines and added
      routine fileappend.
    
   /* allocate rows and set pointers to them */    Revision 1.85  2003/06/17 13:12:43  brouard
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    * imach.c (Repository): Check when date of death was earlier that
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    current date of interview. It may happen when the death was just
   m[nrl] += NR_END;    prior to the death. In this case, dh was negative and likelihood
   m[nrl] -= ncl;    was wrong (infinity). We still send an "Error" but patch by
      assuming that the date of death was just one stepm after the
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    interview.
      (Repository): Because some people have very long ID (first column)
   /* return pointer to array of pointers to rows */    we changed int to long in num[] and we added a new lvector for
   return m;    memory allocation. But we also truncated to 8 characters (left
 }    truncation)
     (Repository): No more line truncation errors.
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Revision 1.84  2003/06/13 21:44:43  brouard
       int **m;    * imach.c (Repository): Replace "freqsummary" at a correct
       long nch,ncl,nrh,nrl;    place. It differs from routine "prevalence" which may be called
      /* free an int matrix allocated by imatrix() */    many times. Probs is memory consuming and must be used with
 {    parcimony.
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
 /******************* matrix *******************************/  
 double **matrix(long nrl, long nrh, long ncl, long nch)    Revision 1.82  2003/06/05 15:57:20  brouard
 {    Add log in  imach.c and  fullversion number is now printed.
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  
   double **m;  */
   /*
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));     Interpolated Markov Chain
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Short summary of the programme:
   m -= nrl;    
     This program computes Healthy Life Expectancies from
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    first survey ("cross") where individuals from different ages are
   m[nrl] += NR_END;    interviewed on their health status or degree of disability (in the
   m[nrl] -= ncl;    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    (if any) in individual health status.  Health expectancies are
   return m;    computed from the time spent in each health state according to a
 }    model. More health states you consider, more time is necessary to reach the
     Maximum Likelihood of the parameters involved in the model.  The
 /*************************free matrix ************************/    simplest model is the multinomial logistic model where pij is the
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    probability to be observed in state j at the second wave
 {    conditional to be observed in state i at the first wave. Therefore
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   free((FREE_ARG)(m+nrl-NR_END));    '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
     where the markup *Covariates have to be included here again* invites
 /******************* ma3x *******************************/    you to do it.  More covariates you add, slower the
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    convergence.
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    The advantage of this computer programme, compared to a simple
   double ***m;    multinomial logistic model, is clear when the delay between waves is not
     identical for each individual. Also, if a individual missed an
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    intermediate interview, the information is lost, but taken into
   if (!m) nrerror("allocation failure 1 in matrix()");    account using an interpolation or extrapolation.  
   m += NR_END;  
   m -= nrl;    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
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    split into an exact number (nh*stepm) of unobserved intermediate
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    states. This elementary transition (by month, quarter,
   m[nrl] += NR_END;    semester or year) is modelled as a multinomial logistic.  The hPx
   m[nrl] -= ncl;    matrix is simply the matrix product of nh*stepm elementary matrices
     and the contribution of each individual to the likelihood is simply
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    hPijx.
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    Also this programme outputs the covariance matrix of the parameters but also
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    of the life expectancies. It also computes the period (stable) prevalence. 
   m[nrl][ncl] += NR_END;    
   m[nrl][ncl] -= nll;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   for (j=ncl+1; j<=nch; j++)             Institut national d'études démographiques, Paris.
     m[nrl][j]=m[nrl][j-1]+nlay;    This software have been partly granted by Euro-REVES, a concerted action
      from the European Union.
   for (i=nrl+1; i<=nrh; i++) {    It is copyrighted identically to a GNU software product, ie programme and
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    software can be distributed freely for non commercial use. Latest version
     for (j=ncl+1; j<=nch; j++)    can be accessed at http://euroreves.ined.fr/imach .
       m[i][j]=m[i][j-1]+nlay;  
   }    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   return m;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
 }    
     **********************************************************************/
 /*************************free ma3x ************************/  /*
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    main
 {    read parameterfile
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    read datafile
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    concatwav
   free((FREE_ARG)(m+nrl-NR_END));    freqsummary
 }    if (mle >= 1)
       mlikeli
 /***************** f1dim *************************/    print results files
 extern int ncom;    if mle==1 
 extern double *pcom,*xicom;       computes hessian
 extern double (*nrfunc)(double []);    read end of parameter file: agemin, agemax, bage, fage, estepm
          begin-prev-date,...
 double f1dim(double x)    open gnuplot file
 {    open html file
   int j;    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
   double f;     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
   double *xt;                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
        freexexit2 possible for memory heap.
   xt=vector(1,ncom);  
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    h Pij x                         | pij_nom  ficrestpij
   f=(*nrfunc)(xt);     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
   free_vector(xt,1,ncom);         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
   return f;         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
 }  
          1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
 /*****************brent *************************/         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
 {     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
   int iter;     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
   double a,b,d,etemp;  
   double fu,fv,fw,fx;    forecasting if prevfcast==1 prevforecast call prevalence()
   double ftemp;    health expectancies
   double p,q,r,tol1,tol2,u,v,w,x,xm;    Variance-covariance of DFLE
   double e=0.0;    prevalence()
       movingaverage()
   a=(ax < cx ? ax : cx);    varevsij() 
   b=(ax > cx ? ax : cx);    if popbased==1 varevsij(,popbased)
   x=w=v=bx;    total life expectancies
   fw=fv=fx=(*f)(x);    Variance of period (stable) prevalence
   for (iter=1;iter<=ITMAX;iter++) {   end
     xm=0.5*(a+b);  */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  
     printf(".");fflush(stdout);  
     fprintf(ficlog,".");fflush(ficlog);   
 #ifdef DEBUG  #include <math.h>
     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);  #include <stdio.h>
     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);  #include <stdlib.h>
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  #include <string.h>
 #endif  #include <unistd.h>
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;  #include <limits.h>
       return fx;  #include <sys/types.h>
     }  #include <sys/stat.h>
     ftemp=fu;  #include <errno.h>
     if (fabs(e) > tol1) {  extern int errno;
       r=(x-w)*(fx-fv);  
       q=(x-v)*(fx-fw);  #ifdef LINUX
       p=(x-v)*q-(x-w)*r;  #include <time.h>
       q=2.0*(q-r);  #include "timeval.h"
       if (q > 0.0) p = -p;  #else
       q=fabs(q);  #include <sys/time.h>
       etemp=e;  #endif
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #ifdef GSL
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #include <gsl/gsl_errno.h>
       else {  #include <gsl/gsl_multimin.h>
         d=p/q;  #endif
         u=x+d;  
         if (u-a < tol2 || b-u < tol2)  /* #include <libintl.h> */
           d=SIGN(tol1,xm-x);  /* #define _(String) gettext (String) */
       }  
     } else {  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  
     }  #define GNUPLOTPROGRAM "gnuplot"
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
     fu=(*f)(u);  #define FILENAMELENGTH 132
     if (fu <= fx) {  
       if (u >= x) a=x; else b=x;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
       SHFT(v,w,x,u)  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
         SHFT(fv,fw,fx,fu)  
         } else {  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
           if (u < x) a=u; else b=u;  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
           if (fu <= fw || w == x) {  
             v=w;  #define NINTERVMAX 8
             w=u;  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
             fv=fw;  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
             fw=fu;  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
           } else if (fu <= fv || v == x || v == w) {  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
             v=u;  #define MAXN 20000
             fv=fu;  #define YEARM 12. /**< Number of months per year */
           }  #define AGESUP 130
         }  #define AGEBASE 40
   }  #define AGEGOMP 10. /**< Minimal age for Gompertz adjustment */
   nrerror("Too many iterations in brent");  #ifdef UNIX
   *xmin=x;  #define DIRSEPARATOR '/'
   return fx;  #define CHARSEPARATOR "/"
 }  #define ODIRSEPARATOR '\\'
   #else
 /****************** mnbrak ***********************/  #define DIRSEPARATOR '\\'
   #define CHARSEPARATOR "\\"
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  #define ODIRSEPARATOR '/'
             double (*func)(double))  #endif
 {  
   double ulim,u,r,q, dum;  /* $Id$ */
   double fu;  /* $State$ */
    
   *fa=(*func)(*ax);  char version[]="Imach version 0.98nT, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
   *fb=(*func)(*bx);  char fullversion[]="$Revision$ $Date$"; 
   if (*fb > *fa) {  char strstart[80];
     SHFT(dum,*ax,*bx,dum)  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       SHFT(dum,*fb,*fa,dum)  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       }  int nvar=0, nforce=0; /* Number of variables, number of forces */
   *cx=(*bx)+GOLD*(*bx-*ax);  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
   *fc=(*func)(*cx);  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
   while (*fb > *fc) {  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
     r=(*bx-*ax)*(*fb-*fc);  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
     q=(*bx-*cx)*(*fb-*fa);  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  int cptcovprodnoage=0; /**< Number of covariate products without age */   
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  int cptcoveff=0; /* Total number of covariates to vary for printing results */
     ulim=(*bx)+GLIMIT*(*cx-*bx);  int cptcov=0; /* Working variable */
     if ((*bx-u)*(u-*cx) > 0.0) {  int npar=NPARMAX;
       fu=(*func)(u);  int nlstate=2; /* Number of live states */
     } else if ((*cx-u)*(u-ulim) > 0.0) {  int ndeath=1; /* Number of dead states */
       fu=(*func)(u);  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       if (fu < *fc) {  int popbased=0;
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))  int *wav; /* Number of waves for this individuual 0 is possible */
           }  int maxwav=0; /* Maxim number of waves */
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       u=ulim;  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       fu=(*func)(u);  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
     } else {                     to the likelihood and the sum of weights (done by funcone)*/
       u=(*cx)+GOLD*(*cx-*bx);  int mle=1, weightopt=0;
       fu=(*func)(u);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
     }  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     SHFT(*ax,*bx,*cx,u)  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       SHFT(*fa,*fb,*fc,fu)             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       }  double jmean=1; /* Mean space between 2 waves */
 }  double **matprod2(); /* test */
   double **oldm, **newm, **savm; /* Working pointers to matrices */
 /*************** linmin ************************/  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   /*FILE *fic ; */ /* Used in readdata only */
 int ncom;  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
 double *pcom,*xicom;  FILE *ficlog, *ficrespow;
 double (*nrfunc)(double []);  int globpr=0; /* Global variable for printing or not */
    double fretone; /* Only one call to likelihood */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  long ipmx=0; /* Number of contributions */
 {  double sw; /* Sum of weights */
   double brent(double ax, double bx, double cx,  char filerespow[FILENAMELENGTH];
                double (*f)(double), double tol, double *xmin);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   double f1dim(double x);  FILE *ficresilk;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
               double *fc, double (*func)(double));  FILE *ficresprobmorprev;
   int j;  FILE *fichtm, *fichtmcov; /* Html File */
   double xx,xmin,bx,ax;  FILE *ficreseij;
   double fx,fb,fa;  char filerese[FILENAMELENGTH];
    FILE *ficresstdeij;
   ncom=n;  char fileresstde[FILENAMELENGTH];
   pcom=vector(1,n);  FILE *ficrescveij;
   xicom=vector(1,n);  char filerescve[FILENAMELENGTH];
   nrfunc=func;  FILE  *ficresvij;
   for (j=1;j<=n;j++) {  char fileresv[FILENAMELENGTH];
     pcom[j]=p[j];  FILE  *ficresvpl;
     xicom[j]=xi[j];  char fileresvpl[FILENAMELENGTH];
   }  char title[MAXLINE];
   ax=0.0;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   xx=1.0;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  char command[FILENAMELENGTH];
 #ifdef DEBUG  int  outcmd=0;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
   fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 #endif  
   for (j=1;j<=n;j++) {  char filelog[FILENAMELENGTH]; /* Log file */
     xi[j] *= xmin;  char filerest[FILENAMELENGTH];
     p[j] += xi[j];  char fileregp[FILENAMELENGTH];
   }  char popfile[FILENAMELENGTH];
   free_vector(xicom,1,n);  
   free_vector(pcom,1,n);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
 }  
   struct timeval start_time, end_time, curr_time, last_time, forecast_time;
 /*************** powell ************************/  struct timezone tzp;
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  extern int gettimeofday();
             double (*func)(double []))  struct tm tmg, tm, tmf, *gmtime(), *localtime();
 {  long time_value;
   void linmin(double p[], double xi[], int n, double *fret,  extern long time();
               double (*func)(double []));  char strcurr[80], strfor[80];
   int i,ibig,j;  
   double del,t,*pt,*ptt,*xit;  char *endptr;
   double fp,fptt;  long lval;
   double *xits;  double dval;
   pt=vector(1,n);  
   ptt=vector(1,n);  #define NR_END 1
   xit=vector(1,n);  #define FREE_ARG char*
   xits=vector(1,n);  #define FTOL 1.0e-10
   *fret=(*func)(p);  
   for (j=1;j<=n;j++) pt[j]=p[j];  #define NRANSI 
   for (*iter=1;;++(*iter)) {  #define ITMAX 200 
     fp=(*fret);  
     ibig=0;  #define TOL 2.0e-4 
     del=0.0;  
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #define CGOLD 0.3819660 
     fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #define ZEPS 1.0e-10 
     for (i=1;i<=n;i++)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       printf(" %d %.12f",i, p[i]);  
     fprintf(ficlog," %d %.12f",i, p[i]);  #define GOLD 1.618034 
     printf("\n");  #define GLIMIT 100.0 
     fprintf(ficlog,"\n");  #define TINY 1.0e-20 
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  static double maxarg1,maxarg2;
       fptt=(*fret);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 #ifdef DEBUG  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
       printf("fret=%lf \n",*fret);    
       fprintf(ficlog,"fret=%lf \n",*fret);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 #endif  #define rint(a) floor(a+0.5)
       printf("%d",i);fflush(stdout);  
       fprintf(ficlog,"%d",i);fflush(ficlog);  static double sqrarg;
       linmin(p,xit,n,fret,func);  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       if (fabs(fptt-(*fret)) > del) {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
         del=fabs(fptt-(*fret));  int agegomp= AGEGOMP;
         ibig=i;  
       }  int imx; 
 #ifdef DEBUG  int stepm=1;
       printf("%d %.12e",i,(*fret));  /* Stepm, step in month: minimum step interpolation*/
       fprintf(ficlog,"%d %.12e",i,(*fret));  
       for (j=1;j<=n;j++) {  int estepm;
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
         printf(" x(%d)=%.12e",j,xit[j]);  
         fprintf(ficlog," x(%d)=%.12e",j,xit[j]);  int m,nb;
       }  long *num;
       for(j=1;j<=n;j++) {  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
         printf(" p=%.12e",p[j]);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
         fprintf(ficlog," p=%.12e",p[j]);  double **pmmij, ***probs;
       }  double *ageexmed,*agecens;
       printf("\n");  double dateintmean=0;
       fprintf(ficlog,"\n");  
 #endif  double *weight;
     }  int **s; /* Status */
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  double *agedc;
 #ifdef DEBUG  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
       int k[2],l;                    * covar=matrix(0,NCOVMAX,1,n); 
       k[0]=1;                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
       k[1]=-1;  double  idx; 
       printf("Max: %.12e",(*func)(p));  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
       fprintf(ficlog,"Max: %.12e",(*func)(p));  int *Ndum; /** Freq of modality (tricode */
       for (j=1;j<=n;j++) {  int **codtab; /**< codtab=imatrix(1,100,1,10); */
         printf(" %.12e",p[j]);  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
         fprintf(ficlog," %.12e",p[j]);  double *lsurv, *lpop, *tpop;
       }  
       printf("\n");  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
       fprintf(ficlog,"\n");  double ftolhess; /**< Tolerance for computing hessian */
       for(l=0;l<=1;l++) {  
         for (j=1;j<=n;j++) {  /**************** split *************************/
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
           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]);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
         }       the name of the file (name), its extension only (ext) and its first part of the name (finame)
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    */ 
         fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    char  *ss;                            /* pointer */
       }    int   l1, l2;                         /* length counters */
 #endif  
     l1 = strlen(path );                   /* length of path */
     if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       free_vector(xit,1,n);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       free_vector(xits,1,n);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       free_vector(ptt,1,n);      strcpy( name, path );               /* we got the fullname name because no directory */
       free_vector(pt,1,n);      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
       return;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     }      /* get current working directory */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");      /*    extern  char* getcwd ( char *buf , int len);*/
     for (j=1;j<=n;j++) {      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       ptt[j]=2.0*p[j]-pt[j];        return( GLOCK_ERROR_GETCWD );
       xit[j]=p[j]-pt[j];      }
       pt[j]=p[j];      /* got dirc from getcwd*/
     }      printf(" DIRC = %s \n",dirc);
     fptt=(*func)(ptt);    } else {                              /* strip direcotry from path */
     if (fptt < fp) {      ss++;                               /* after this, the filename */
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);      l2 = strlen( ss );                  /* length of filename */
       if (t < 0.0) {      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
         linmin(p,xit,n,fret,func);      strcpy( name, ss );         /* save file name */
         for (j=1;j<=n;j++) {      strncpy( dirc, path, l1 - l2 );     /* now the directory */
           xi[j][ibig]=xi[j][n];      dirc[l1-l2] = 0;                    /* add zero */
           xi[j][n]=xit[j];      printf(" DIRC2 = %s \n",dirc);
         }    }
 #ifdef DEBUG    /* We add a separator at the end of dirc if not exists */
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    l1 = strlen( dirc );                  /* length of directory */
         fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    if( dirc[l1-1] != DIRSEPARATOR ){
         for(j=1;j<=n;j++){      dirc[l1] =  DIRSEPARATOR;
           printf(" %.12e",xit[j]);      dirc[l1+1] = 0; 
           fprintf(ficlog," %.12e",xit[j]);      printf(" DIRC3 = %s \n",dirc);
         }    }
         printf("\n");    ss = strrchr( name, '.' );            /* find last / */
         fprintf(ficlog,"\n");    if (ss >0){
 #endif      ss++;
       }      strcpy(ext,ss);                     /* save extension */
     }      l1= strlen( name);
   }      l2= strlen(ss)+1;
 }      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
 /**** Prevalence limit ****************/    }
   
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    return( 0 );                          /* we're done */
 {  }
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  
      matrix by transitions matrix until convergence is reached */  
   /******************************************/
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  void replace_back_to_slash(char *s, char*t)
   double **matprod2();  {
   double **out, cov[NCOVMAX], **pmij();    int i;
   double **newm;    int lg=0;
   double agefin, delaymax=50 ; /* Max number of years to converge */    i=0;
     lg=strlen(t);
   for (ii=1;ii<=nlstate+ndeath;ii++)    for(i=0; i<= lg; i++) {
     for (j=1;j<=nlstate+ndeath;j++){      (s[i] = t[i]);
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);      if (t[i]== '\\') s[i]='/';
     }    }
   }
    cov[1]=1.;  
    char *trimbb(char *out, char *in)
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    char *s;
     newm=savm;    s=out;
     /* Covariates have to be included here again */    while (*in != '\0'){
      cov[2]=agefin;      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
          in++;
       for (k=1; k<=cptcovn;k++) {      }
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      *out++ = *in++;
         /*      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]]);*/    }
       }    *out='\0';
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    return s;
       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]]];  
   char *cutl(char *blocc, char *alocc, char *in, char occ)
       /*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]);*/    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);       gives blocc="abcdef2ghi" and alocc="j".
        If occ is not found blocc is null and alocc is equal to in. Returns blocc
     savm=oldm;    */
     oldm=newm;    char *s, *t, *bl;
     maxmax=0.;    t=in;s=in;
     for(j=1;j<=nlstate;j++){    while ((*in != occ) && (*in != '\0')){
       min=1.;      *alocc++ = *in++;
       max=0.;    }
       for(i=1; i<=nlstate; i++) {    if( *in == occ){
         sumnew=0;      *(alocc)='\0';
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];      s=++in;
         prlim[i][j]= newm[i][j]/(1-sumnew);    }
         max=FMAX(max,prlim[i][j]);   
         min=FMIN(min,prlim[i][j]);    if (s == t) {/* occ not found */
       }      *(alocc-(in-s))='\0';
       maxmin=max-min;      in=s;
       maxmax=FMAX(maxmax,maxmin);    }
     }    while ( *in != '\0'){
     if(maxmax < ftolpl){      *blocc++ = *in++;
       return prlim;    }
     }  
   }    *blocc='\0';
 }    return t;
   }
 /*************** transition probabilities ***************/  char *cutv(char *blocc, char *alocc, char *in, char occ)
   {
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
 {       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
   double s1, s2;       gives blocc="abcdef2ghi" and alocc="j".
   /*double t34;*/       If occ is not found blocc is null and alocc is equal to in. Returns alocc
   int i,j,j1, nc, ii, jj;    */
     char *s, *t;
     for(i=1; i<= nlstate; i++){    t=in;s=in;
     for(j=1; j<i;j++){    while (*in != '\0'){
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      while( *in == occ){
         /*s2 += param[i][j][nc]*cov[nc];*/        *blocc++ = *in++;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];        s=in;
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/      }
       }      *blocc++ = *in++;
       ps[i][j]=s2;    }
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    if (s == t) /* occ not found */
     }      *(blocc-(in-s))='\0';
     for(j=i+1; j<=nlstate+ndeath;j++){    else
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      *(blocc-(in-s)-1)='\0';
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    in=s;
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    while ( *in != '\0'){
       }      *alocc++ = *in++;
       ps[i][j]=s2;    }
     }  
   }    *alocc='\0';
     /*ps[3][2]=1;*/    return s;
   }
   for(i=1; i<= nlstate; i++){  
      s1=0;  int nbocc(char *s, char occ)
     for(j=1; j<i; j++)  {
       s1+=exp(ps[i][j]);    int i,j=0;
     for(j=i+1; j<=nlstate+ndeath; j++)    int lg=20;
       s1+=exp(ps[i][j]);    i=0;
     ps[i][i]=1./(s1+1.);    lg=strlen(s);
     for(j=1; j<i; j++)    for(i=0; i<= lg; i++) {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    if  (s[i] == occ ) j++;
     for(j=i+1; j<=nlstate+ndeath; j++)    }
       ps[i][j]= exp(ps[i][j])*ps[i][i];    return j;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  }
   } /* end i */  
   /* void cutv(char *u,char *v, char*t, char occ) */
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  /* { */
     for(jj=1; jj<= nlstate+ndeath; jj++){  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       ps[ii][jj]=0;  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       ps[ii][ii]=1;  /*      gives u="abcdef2ghi" and v="j" *\/ */
     }  /*   int i,lg,j,p=0; */
   }  /*   i=0; */
   /*   lg=strlen(t); */
   /*   for(j=0; j<=lg-1; j++) { */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
     for(jj=1; jj<= nlstate+ndeath; jj++){  /*   } */
      printf("%lf ",ps[ii][jj]);  
    }  /*   for(j=0; j<p; j++) { */
     printf("\n ");  /*     (u[j] = t[j]); */
     }  /*   } */
     printf("\n ");printf("%lf ",cov[2]);*/  /*      u[p]='\0'; */
 /*  
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  /*    for(j=0; j<= lg; j++) { */
   goto end;*/  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
     return ps;  /*   } */
 }  /* } */
   
 /**************** Product of 2 matrices ******************/  /********************** nrerror ********************/
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  void nrerror(char error_text[])
 {  {
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    fprintf(stderr,"ERREUR ...\n");
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    fprintf(stderr,"%s\n",error_text);
   /* in, b, out are matrice of pointers which should have been initialized    exit(EXIT_FAILURE);
      before: only the contents of out is modified. The function returns  }
      a pointer to pointers identical to out */  /*********************** vector *******************/
   long i, j, k;  double *vector(int nl, int nh)
   for(i=nrl; i<= nrh; i++)  {
     for(k=ncolol; k<=ncoloh; k++)    double *v;
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
         out[i][k] +=in[i][j]*b[j][k];    if (!v) nrerror("allocation failure in vector");
     return v-nl+NR_END;
   return out;  }
 }  
   /************************ free vector ******************/
   void free_vector(double*v, int nl, int nh)
 /************* Higher Matrix Product ***************/  {
     free((FREE_ARG)(v+nl-NR_END));
 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  /************************ivector *******************************/
      duration (i.e. until  int *ivector(long nl,long nh)
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  {
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    int *v;
      (typically every 2 years instead of every month which is too big).    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
      Model is determined by parameters x and covariates have to be    if (!v) nrerror("allocation failure in ivector");
      included manually here.    return v-nl+NR_END;
   }
      */  
   /******************free ivector **************************/
   int i, j, d, h, k;  void free_ivector(int *v, long nl, long nh)
   double **out, cov[NCOVMAX];  {
   double **newm;    free((FREE_ARG)(v+nl-NR_END));
   }
   /* Hstepm could be zero and should return the unit matrix */  
   for (i=1;i<=nlstate+ndeath;i++)  /************************lvector *******************************/
     for (j=1;j<=nlstate+ndeath;j++){  long *lvector(long nl,long nh)
       oldm[i][j]=(i==j ? 1.0 : 0.0);  {
       po[i][j][0]=(i==j ? 1.0 : 0.0);    long *v;
     }    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    if (!v) nrerror("allocation failure in ivector");
   for(h=1; h <=nhstepm; h++){    return v-nl+NR_END;
     for(d=1; d <=hstepm; d++){  }
       newm=savm;  
       /* Covariates have to be included here again */  /******************free lvector **************************/
       cov[1]=1.;  void free_lvector(long *v, long nl, long nh)
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  {
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    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++)  /******************* imatrix *******************************/
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  int **imatrix(long nrl, long nrh, long ncl, long nch) 
        /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   { 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    int **m; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    /* allocate pointers to rows */ 
       savm=oldm;    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       oldm=newm;    if (!m) nrerror("allocation failure 1 in matrix()"); 
     }    m += NR_END; 
     for(i=1; i<=nlstate+ndeath; i++)    m -= nrl; 
       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]);    /* allocate rows and set pointers to them */ 
          */    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
   } /* end h */    m[nrl] += NR_END; 
   return po;    m[nrl] -= ncl; 
 }    
     for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     
 /*************** log-likelihood *************/    /* return pointer to array of pointers to rows */ 
 double func( double *x)    return m; 
 {  } 
   int i, ii, j, k, mi, d, kk;  
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  /****************** free_imatrix *************************/
   double **out;  void free_imatrix(m,nrl,nrh,ncl,nch)
   double sw; /* Sum of weights */        int **m;
   double lli; /* Individual log likelihood */        long nch,ncl,nrh,nrl; 
   long ipmx;       /* free an int matrix allocated by imatrix() */ 
   /*extern weight */  { 
   /* We are differentiating ll according to initial status */    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    free((FREE_ARG) (m+nrl-NR_END)); 
   /*for(i=1;i<imx;i++)  } 
     printf(" %d\n",s[4][i]);  
   */  /******************* matrix *******************************/
   cov[1]=1.;  double **matrix(long nrl, long nrh, long ncl, long nch)
   {
   for(k=1; k<=nlstate; k++) ll[k]=0.;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    double **m;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  
     for(mi=1; mi<= wav[i]-1; mi++){    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       for (ii=1;ii<=nlstate+ndeath;ii++)    if (!m) nrerror("allocation failure 1 in matrix()");
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    m += NR_END;
       for(d=0; d<dh[mi][i]; d++){    m -= nrl;
         newm=savm;  
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         for (kk=1; kk<=cptcovage;kk++) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    m[nrl] += NR_END;
         }    m[nrl] -= ncl;
          
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    return m;
         savm=oldm;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
         oldm=newm;  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
          that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
             */
       } /* end mult */  }
        
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  /*************************free matrix ************************/
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       ipmx +=1;  {
       sw += weight[i];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    free((FREE_ARG)(m+nrl-NR_END));
     } /* end of wave */  }
   } /* end of individual */  
   /******************* ma3x *******************************/
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   /* 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 */    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   return -l;    double ***m;
 }  
     m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
 /*********** Maximum Likelihood Estimation ***************/    m += NR_END;
     m -= nrl;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  
 {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   int i,j, iter;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double **xi,*delti;    m[nrl] += NR_END;
   double fret;    m[nrl] -= ncl;
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   printf("Powell\n");  fprintf(ficlog,"Powell\n");    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   powell(p,xi,npar,ftol,&iter,&fret,func);    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    for (j=ncl+1; j<=nch; j++) 
   fprintf(ficlog,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));      m[nrl][j]=m[nrl][j-1]+nlay;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    
     for (i=nrl+1; i<=nrh; i++) {
 }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       for (j=ncl+1; j<=nch; j++) 
 /**** Computes Hessian and covariance matrix ***/        m[i][j]=m[i][j-1]+nlay;
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    }
 {    return m; 
   double  **a,**y,*x,pd;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   double **hess;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   int i, j,jk;    */
   int *indx;  }
   
   double hessii(double p[], double delta, int theta, double delti[]);  /*************************free ma3x ************************/
   double hessij(double p[], double delti[], int i, int j);  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   void lubksb(double **a, int npar, int *indx, double b[]) ;  {
   void ludcmp(double **a, int npar, int *indx, double *d) ;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     free((FREE_ARG)(m[nrl]+ncl-NR_END));
   hess=matrix(1,npar,1,npar);    free((FREE_ARG)(m+nrl-NR_END));
   }
   printf("\nCalculation of the hessian matrix. Wait...\n");  
   fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");  /*************** function subdirf ***********/
   for (i=1;i<=npar;i++){  char *subdirf(char fileres[])
     printf("%d",i);fflush(stdout);  {
     fprintf(ficlog,"%d",i);fflush(ficlog);    /* Caution optionfilefiname is hidden */
     hess[i][i]=hessii(p,ftolhess,i,delti);    strcpy(tmpout,optionfilefiname);
     /*printf(" %f ",p[i]);*/    strcat(tmpout,"/"); /* Add to the right */
     /*printf(" %lf ",hess[i][i]);*/    strcat(tmpout,fileres);
   }    return tmpout;
    }
   for (i=1;i<=npar;i++) {  
     for (j=1;j<=npar;j++)  {  /*************** function subdirf2 ***********/
       if (j>i) {  char *subdirf2(char fileres[], char *preop)
         printf(".%d%d",i,j);fflush(stdout);  {
         fprintf(ficlog,".%d%d",i,j);fflush(ficlog);    
         hess[i][j]=hessij(p,delti,i,j);    /* Caution optionfilefiname is hidden */
         hess[j][i]=hess[i][j];        strcpy(tmpout,optionfilefiname);
         /*printf(" %lf ",hess[i][j]);*/    strcat(tmpout,"/");
       }    strcat(tmpout,preop);
     }    strcat(tmpout,fileres);
   }    return tmpout;
   printf("\n");  }
   fprintf(ficlog,"\n");  
   /*************** function subdirf3 ***********/
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  char *subdirf3(char fileres[], char *preop, char *preop2)
   fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");  {
      
   a=matrix(1,npar,1,npar);    /* Caution optionfilefiname is hidden */
   y=matrix(1,npar,1,npar);    strcpy(tmpout,optionfilefiname);
   x=vector(1,npar);    strcat(tmpout,"/");
   indx=ivector(1,npar);    strcat(tmpout,preop);
   for (i=1;i<=npar;i++)    strcat(tmpout,preop2);
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    strcat(tmpout,fileres);
   ludcmp(a,npar,indx,&pd);    return tmpout;
   }
   for (j=1;j<=npar;j++) {  
     for (i=1;i<=npar;i++) x[i]=0;  /***************** f1dim *************************/
     x[j]=1;  extern int ncom; 
     lubksb(a,npar,indx,x);  extern double *pcom,*xicom;
     for (i=1;i<=npar;i++){  extern double (*nrfunc)(double []); 
       matcov[i][j]=x[i];   
     }  double f1dim(double x) 
   }  { 
     int j; 
   printf("\n#Hessian matrix#\n");    double f;
   fprintf(ficlog,"\n#Hessian matrix#\n");    double *xt; 
   for (i=1;i<=npar;i++) {   
     for (j=1;j<=npar;j++) {    xt=vector(1,ncom); 
       printf("%.3e ",hess[i][j]);    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
       fprintf(ficlog,"%.3e ",hess[i][j]);    f=(*nrfunc)(xt); 
     }    free_vector(xt,1,ncom); 
     printf("\n");    return f; 
     fprintf(ficlog,"\n");  } 
   }  
   /*****************brent *************************/
   /* Recompute Inverse */  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   for (i=1;i<=npar;i++)  { 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    int iter; 
   ludcmp(a,npar,indx,&pd);    double a,b,d,etemp;
     double fu,fv,fw,fx;
   /*  printf("\n#Hessian matrix recomputed#\n");    double ftemp;
     double p,q,r,tol1,tol2,u,v,w,x,xm; 
   for (j=1;j<=npar;j++) {    double e=0.0; 
     for (i=1;i<=npar;i++) x[i]=0;   
     x[j]=1;    a=(ax < cx ? ax : cx); 
     lubksb(a,npar,indx,x);    b=(ax > cx ? ax : cx); 
     for (i=1;i<=npar;i++){    x=w=v=bx; 
       y[i][j]=x[i];    fw=fv=fx=(*f)(x); 
       printf("%.3e ",y[i][j]);    for (iter=1;iter<=ITMAX;iter++) { 
       fprintf(ficlog,"%.3e ",y[i][j]);      xm=0.5*(a+b); 
     }      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
     printf("\n");      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     fprintf(ficlog,"\n");      printf(".");fflush(stdout);
   }      fprintf(ficlog,".");fflush(ficlog);
   */  #ifdef DEBUG
       printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   free_matrix(a,1,npar,1,npar);      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   free_matrix(y,1,npar,1,npar);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   free_vector(x,1,npar);  #endif
   free_ivector(indx,1,npar);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   free_matrix(hess,1,npar,1,npar);        *xmin=x; 
         return fx; 
       } 
 }      ftemp=fu;
       if (fabs(e) > tol1) { 
 /*************** hessian matrix ****************/        r=(x-w)*(fx-fv); 
 double hessii( double x[], double delta, int theta, double delti[])        q=(x-v)*(fx-fw); 
 {        p=(x-v)*q-(x-w)*r; 
   int i;        q=2.0*(q-r); 
   int l=1, lmax=20;        if (q > 0.0) p = -p; 
   double k1,k2;        q=fabs(q); 
   double p2[NPARMAX+1];        etemp=e; 
   double res;        e=d; 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   double fx;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   int k=0,kmax=10;        else { 
   double l1;          d=p/q; 
           u=x+d; 
   fx=func(x);          if (u-a < tol2 || b-u < tol2) 
   for (i=1;i<=npar;i++) p2[i]=x[i];            d=SIGN(tol1,xm-x); 
   for(l=0 ; l <=lmax; l++){        } 
     l1=pow(10,l);      } else { 
     delts=delt;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     for(k=1 ; k <kmax; k=k+1){      } 
       delt = delta*(l1*k);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       p2[theta]=x[theta] +delt;      fu=(*f)(u); 
       k1=func(p2)-fx;      if (fu <= fx) { 
       p2[theta]=x[theta]-delt;        if (u >= x) a=x; else b=x; 
       k2=func(p2)-fx;        SHFT(v,w,x,u) 
       /*res= (k1-2.0*fx+k2)/delt/delt; */          SHFT(fv,fw,fx,fu) 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */          } else { 
                  if (u < x) a=u; else b=u; 
 #ifdef DEBUG            if (fu <= fw || w == x) { 
       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);              v=w; 
       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);              w=u; 
 #endif              fv=fw; 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */              fw=fu; 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){            } else if (fu <= fv || v == x || v == w) { 
         k=kmax;              v=u; 
       }              fv=fu; 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */            } 
         k=kmax; l=lmax*10.;          } 
       }    } 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    nrerror("Too many iterations in brent"); 
         delts=delt;    *xmin=x; 
       }    return fx; 
     }  } 
   }  
   delti[theta]=delts;  /****************** mnbrak ***********************/
   return res;  
    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
 }              double (*func)(double)) 
   { 
 double hessij( double x[], double delti[], int thetai,int thetaj)    double ulim,u,r,q, dum;
 {    double fu; 
   int i;   
   int l=1, l1, lmax=20;    *fa=(*func)(*ax); 
   double k1,k2,k3,k4,res,fx;    *fb=(*func)(*bx); 
   double p2[NPARMAX+1];    if (*fb > *fa) { 
   int k;      SHFT(dum,*ax,*bx,dum) 
         SHFT(dum,*fb,*fa,dum) 
   fx=func(x);        } 
   for (k=1; k<=2; k++) {    *cx=(*bx)+GOLD*(*bx-*ax); 
     for (i=1;i<=npar;i++) p2[i]=x[i];    *fc=(*func)(*cx); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    while (*fb > *fc) { 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      r=(*bx-*ax)*(*fb-*fc); 
     k1=func(p2)-fx;      q=(*bx-*cx)*(*fb-*fa); 
        u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     p2[thetai]=x[thetai]+delti[thetai]/k;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
     k2=func(p2)-fx;      if ((*bx-u)*(u-*cx) > 0.0) { 
          fu=(*func)(u); 
     p2[thetai]=x[thetai]-delti[thetai]/k;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        fu=(*func)(u); 
     k3=func(p2)-fx;        if (fu < *fc) { 
            SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
     p2[thetai]=x[thetai]-delti[thetai]/k;            SHFT(*fb,*fc,fu,(*func)(u)) 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            } 
     k4=func(p2)-fx;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        u=ulim; 
 #ifdef DEBUG        fu=(*func)(u); 
     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);      } else { 
     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);        u=(*cx)+GOLD*(*cx-*bx); 
 #endif        fu=(*func)(u); 
   }      } 
   return res;      SHFT(*ax,*bx,*cx,u) 
 }        SHFT(*fa,*fb,*fc,fu) 
         } 
 /************** Inverse of matrix **************/  } 
 void ludcmp(double **a, int n, int *indx, double *d)  
 {  /*************** linmin ************************/
   int i,imax,j,k;  
   double big,dum,sum,temp;  int ncom; 
   double *vv;  double *pcom,*xicom;
    double (*nrfunc)(double []); 
   vv=vector(1,n);   
   *d=1.0;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for (i=1;i<=n;i++) {  { 
     big=0.0;    double brent(double ax, double bx, double cx, 
     for (j=1;j<=n;j++)                 double (*f)(double), double tol, double *xmin); 
       if ((temp=fabs(a[i][j])) > big) big=temp;    double f1dim(double x); 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     vv[i]=1.0/big;                double *fc, double (*func)(double)); 
   }    int j; 
   for (j=1;j<=n;j++) {    double xx,xmin,bx,ax; 
     for (i=1;i<j;i++) {    double fx,fb,fa;
       sum=a[i][j];   
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    ncom=n; 
       a[i][j]=sum;    pcom=vector(1,n); 
     }    xicom=vector(1,n); 
     big=0.0;    nrfunc=func; 
     for (i=j;i<=n;i++) {    for (j=1;j<=n;j++) { 
       sum=a[i][j];      pcom[j]=p[j]; 
       for (k=1;k<j;k++)      xicom[j]=xi[j]; 
         sum -= a[i][k]*a[k][j];    } 
       a[i][j]=sum;    ax=0.0; 
       if ( (dum=vv[i]*fabs(sum)) >= big) {    xx=1.0; 
         big=dum;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
         imax=i;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       }  #ifdef DEBUG
     }    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     if (j != imax) {    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       for (k=1;k<=n;k++) {  #endif
         dum=a[imax][k];    for (j=1;j<=n;j++) { 
         a[imax][k]=a[j][k];      xi[j] *= xmin; 
         a[j][k]=dum;      p[j] += xi[j]; 
       }    } 
       *d = -(*d);    free_vector(xicom,1,n); 
       vv[imax]=vv[j];    free_vector(pcom,1,n); 
     }  } 
     indx[j]=imax;  
     if (a[j][j] == 0.0) a[j][j]=TINY;  char *asc_diff_time(long time_sec, char ascdiff[])
     if (j != n) {  {
       dum=1.0/(a[j][j]);    long sec_left, days, hours, minutes;
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    days = (time_sec) / (60*60*24);
     }    sec_left = (time_sec) % (60*60*24);
   }    hours = (sec_left) / (60*60) ;
   free_vector(vv,1,n);  /* Doesn't work */    sec_left = (sec_left) %(60*60);
 ;    minutes = (sec_left) /60;
 }    sec_left = (sec_left) % (60);
     sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
 void lubksb(double **a, int n, int *indx, double b[])    return ascdiff;
 {  }
   int i,ii=0,ip,j;  
   double sum;  /*************** powell ************************/
    void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   for (i=1;i<=n;i++) {              double (*func)(double [])) 
     ip=indx[i];  { 
     sum=b[ip];    void linmin(double p[], double xi[], int n, double *fret, 
     b[ip]=b[i];                double (*func)(double [])); 
     if (ii)    int i,ibig,j; 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];    double del,t,*pt,*ptt,*xit;
     else if (sum) ii=i;    double fp,fptt;
     b[i]=sum;    double *xits;
   }    int niterf, itmp;
   for (i=n;i>=1;i--) {  
     sum=b[i];    pt=vector(1,n); 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    ptt=vector(1,n); 
     b[i]=sum/a[i][i];    xit=vector(1,n); 
   }    xits=vector(1,n); 
 }    *fret=(*func)(p); 
     for (j=1;j<=n;j++) pt[j]=p[j]; 
 /************ Frequencies ********************/    for (*iter=1;;++(*iter)) { 
 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)      fp=(*fret); 
 {  /* Some frequencies */      ibig=0; 
        del=0.0; 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;      last_time=curr_time;
   int first;      (void) gettimeofday(&curr_time,&tzp);
   double ***freq; /* Frequencies */      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);
   double *pp;      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);
   double pos, k2, dateintsum=0,k2cpt=0;  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   FILE *ficresp;     for (i=1;i<=n;i++) {
   char fileresp[FILENAMELENGTH];        printf(" %d %.12f",i, p[i]);
          fprintf(ficlog," %d %.12lf",i, p[i]);
   pp=vector(1,nlstate);        fprintf(ficrespow," %.12lf", p[i]);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      }
   strcpy(fileresp,"p");      printf("\n");
   strcat(fileresp,fileres);      fprintf(ficlog,"\n");
   if((ficresp=fopen(fileresp,"w"))==NULL) {      fprintf(ficrespow,"\n");fflush(ficrespow);
     printf("Problem with prevalence resultfile: %s\n", fileresp);      if(*iter <=3){
     fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);        tm = *localtime(&curr_time.tv_sec);
     exit(0);        strcpy(strcurr,asctime(&tm));
   }  /*       asctime_r(&tm,strcurr); */
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        forecast_time=curr_time; 
   j1=0;        itmp = strlen(strcurr);
          if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   j=cptcoveff;          strcurr[itmp-1]='\0';
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   first=1;        for(niterf=10;niterf<=30;niterf+=10){
           forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   for(k1=1; k1<=j;k1++){          tmf = *localtime(&forecast_time.tv_sec);
     for(i1=1; i1<=ncodemax[k1];i1++){  /*      asctime_r(&tmf,strfor); */
       j1++;          strcpy(strfor,asctime(&tmf));
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          itmp = strlen(strfor);
         scanf("%d", i);*/          if(strfor[itmp-1]=='\n')
       for (i=-1; i<=nlstate+ndeath; i++)            strfor[itmp-1]='\0';
         for (jk=-1; jk<=nlstate+ndeath; jk++)            printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
           for(m=agemin; m <= agemax+3; m++)          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);
             freq[i][jk][m]=0;        }
            }
       dateintsum=0;      for (i=1;i<=n;i++) { 
       k2cpt=0;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
       for (i=1; i<=imx; i++) {        fptt=(*fret); 
         bool=1;  #ifdef DEBUG
         if  (cptcovn>0) {        printf("fret=%lf \n",*fret);
           for (z1=1; z1<=cptcoveff; z1++)        fprintf(ficlog,"fret=%lf \n",*fret);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  #endif
               bool=0;        printf("%d",i);fflush(stdout);
         }        fprintf(ficlog,"%d",i);fflush(ficlog);
         if (bool==1) {        linmin(p,xit,n,fret,func); 
           for(m=firstpass; m<=lastpass; m++){        if (fabs(fptt-(*fret)) > del) { 
             k2=anint[m][i]+(mint[m][i]/12.);          del=fabs(fptt-(*fret)); 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          ibig=i; 
               if(agev[m][i]==0) agev[m][i]=agemax+1;        } 
               if(agev[m][i]==1) agev[m][i]=agemax+2;  #ifdef DEBUG
               if (m<lastpass) {        printf("%d %.12e",i,(*fret));
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        fprintf(ficlog,"%d %.12e",i,(*fret));
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        for (j=1;j<=n;j++) {
               }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
                        printf(" x(%d)=%.12e",j,xit[j]);
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
                 dateintsum=dateintsum+k2;        }
                 k2cpt++;        for(j=1;j<=n;j++) {
               }          printf(" p=%.12e",p[j]);
             }          fprintf(ficlog," p=%.12e",p[j]);
           }        }
         }        printf("\n");
       }        fprintf(ficlog,"\n");
          #endif
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       if  (cptcovn>0) {  #ifdef DEBUG
         fprintf(ficresp, "\n#********** Variable ");        int k[2],l;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        k[0]=1;
         fprintf(ficresp, "**********\n#");        k[1]=-1;
       }        printf("Max: %.12e",(*func)(p));
       for(i=1; i<=nlstate;i++)        fprintf(ficlog,"Max: %.12e",(*func)(p));
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        for (j=1;j<=n;j++) {
       fprintf(ficresp, "\n");          printf(" %.12e",p[j]);
                fprintf(ficlog," %.12e",p[j]);
       for(i=(int)agemin; i <= (int)agemax+3; i++){        }
         if(i==(int)agemax+3){        printf("\n");
           fprintf(ficlog,"Total");        fprintf(ficlog,"\n");
         }else{        for(l=0;l<=1;l++) {
           if(first==1){          for (j=1;j<=n;j++) {
             first=0;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
             printf("See log file for details...\n");            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]);
           fprintf(ficlog,"Age %d", i);          }
         }          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         for(jk=1; jk <=nlstate ; jk++){          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        }
             pp[jk] += freq[jk][m][i];  #endif
         }  
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pos=0; m <=0 ; m++)        free_vector(xit,1,n); 
             pos += freq[jk][m][i];        free_vector(xits,1,n); 
           if(pp[jk]>=1.e-10){        free_vector(ptt,1,n); 
             if(first==1){        free_vector(pt,1,n); 
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        return; 
             }      } 
             fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
           }else{      for (j=1;j<=n;j++) { 
             if(first==1)        ptt[j]=2.0*p[j]-pt[j]; 
               printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        xit[j]=p[j]-pt[j]; 
             fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        pt[j]=p[j]; 
           }      } 
         }      fptt=(*func)(ptt); 
       if (fptt < fp) { 
         for(jk=1; jk <=nlstate ; jk++){        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        if (t < 0.0) { 
             pp[jk] += freq[jk][m][i];          linmin(p,xit,n,fret,func); 
         }          for (j=1;j<=n;j++) { 
             xi[j][ibig]=xi[j][n]; 
         for(jk=1,pos=0; jk <=nlstate ; jk++)            xi[j][n]=xit[j]; 
           pos += pp[jk];          }
         for(jk=1; jk <=nlstate ; jk++){  #ifdef DEBUG
           if(pos>=1.e-5){          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
             if(first==1)          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
               printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          for(j=1;j<=n;j++){
             fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);            printf(" %.12e",xit[j]);
           }else{            fprintf(ficlog," %.12e",xit[j]);
             if(first==1)          }
               printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          printf("\n");
             fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          fprintf(ficlog,"\n");
           }  #endif
           if( i <= (int) agemax){        }
             if(pos>=1.e-5){      } 
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    } 
               probs[i][jk][j1]= pp[jk]/pos;  } 
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/  
             }  /**** Prevalence limit (stable or period prevalence)  ****************/
             else  
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
           }  {
         }    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
               matrix by transitions matrix until convergence is reached */
         for(jk=-1; jk <=nlstate+ndeath; jk++)  
           for(m=-1; m <=nlstate+ndeath; m++)    int i, ii,j,k;
             if(freq[jk][m][i] !=0 ) {    double min, max, maxmin, maxmax,sumnew=0.;
             if(first==1)    /* double **matprod2(); */ /* test */
               printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    double **out, cov[NCOVMAX+1], **pmij();
               fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);    double **newm;
             }    double agefin, delaymax=50 ; /* Max number of years to converge */
         if(i <= (int) agemax)  
           fprintf(ficresp,"\n");    for (ii=1;ii<=nlstate+ndeath;ii++)
         if(first==1)      for (j=1;j<=nlstate+ndeath;j++){
           printf("Others in log...\n");        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         fprintf(ficlog,"\n");      }
       }  
     }     cov[1]=1.;
   }   
   dateintmean=dateintsum/k2cpt;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
      for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   fclose(ficresp);      newm=savm;
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      /* Covariates have to be included here again */
   free_vector(pp,1,nlstate);      cov[2]=agefin;
        
   /* End of Freq */      for (k=1; k<=cptcovn;k++) {
 }        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         /*printf("prevalim ij=%d k=%d Tvar[%d]=%d nbcode=%d cov=%lf codtab[%d][Tvar[%d]]=%d \n",ij,k, k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], ij, k, codtab[ij][Tvar[k]]);*/
 /************ 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 (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
 {  /* Some frequencies */      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
        /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      
   double ***freq; /* Frequencies */      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   double *pp;      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   double pos, k2;      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   pp=vector(1,nlstate);      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
        
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      savm=oldm;
   j1=0;      oldm=newm;
        maxmax=0.;
   j=cptcoveff;      for(j=1;j<=nlstate;j++){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        min=1.;
          max=0.;
   for(k1=1; k1<=j;k1++){        for(i=1; i<=nlstate; i++) {
     for(i1=1; i1<=ncodemax[k1];i1++){          sumnew=0;
       j1++;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
                prlim[i][j]= newm[i][j]/(1-sumnew);
       for (i=-1; i<=nlstate+ndeath; i++)            /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
         for (jk=-1; jk<=nlstate+ndeath; jk++)            max=FMAX(max,prlim[i][j]);
           for(m=agemin; m <= agemax+3; m++)          min=FMIN(min,prlim[i][j]);
             freq[i][jk][m]=0;        }
              maxmin=max-min;
       for (i=1; i<=imx; i++) {        maxmax=FMAX(maxmax,maxmin);
         bool=1;      }
         if  (cptcovn>0) {      if(maxmax < ftolpl){
           for (z1=1; z1<=cptcoveff; z1++)        return prlim;
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      }
               bool=0;    }
         }  }
         if (bool==1) {  
           for(m=firstpass; m<=lastpass; m++){  /*************** transition probabilities ***************/ 
             k2=anint[m][i]+(mint[m][i]/12.);  
             if ((k2>=dateprev1) && (k2<=dateprev2)) {  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
               if(agev[m][i]==0) agev[m][i]=agemax+1;  {
               if(agev[m][i]==1) agev[m][i]=agemax+2;    /* According to parameters values stored in x and the covariate's values stored in cov,
               if (m<lastpass) {       computes the probability to be observed in state j being in state i by appying the
                 if (calagedate>0)       model to the ncovmodel covariates (including constant and age).
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
                 else       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];       ncth covariate in the global vector x is given by the formula:
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
               }       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
             }       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
           }       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
         }       Outputs ps[i][j] the probability to be observed in j being in j according to
       }       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
       for(i=(int)agemin; i <= (int)agemax+3; i++){    */
         for(jk=1; jk <=nlstate ; jk++){    double s1, lnpijopii;
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    /*double t34;*/
             pp[jk] += freq[jk][m][i];    int i,j,j1, nc, ii, jj;
         }  
         for(jk=1; jk <=nlstate ; jk++){      for(i=1; i<= nlstate; i++){
           for(m=-1, pos=0; m <=0 ; m++)        for(j=1; j<i;j++){
             pos += freq[jk][m][i];          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
         }            /*lnpijopii += param[i][j][nc]*cov[nc];*/
                    lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
         for(jk=1; jk <=nlstate ; jk++){  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          }
             pp[jk] += freq[jk][m][i];          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         }  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
                }
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        for(j=i+1; j<=nlstate+ndeath;j++){
                  for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
         for(jk=1; jk <=nlstate ; jk++){                /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
           if( i <= (int) agemax){            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
             if(pos>=1.e-5){  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
               probs[i][jk][j1]= pp[jk]/pos;          }
             }          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
           }        }
         }/* end jk */      }
       }/* end i */      
     } /* end i1 */      for(i=1; i<= nlstate; i++){
   } /* end k1 */        s1=0;
         for(j=1; j<i; j++){
            s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
   free_vector(pp,1,nlstate);        }
          for(j=i+1; j<=nlstate+ndeath; j++){
 }  /* End of Freq */          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
           /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
 /************* Waves Concatenation ***************/        }
         /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)        ps[i][i]=1./(s1+1.);
 {        /* Computing other pijs */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        for(j=1; j<i; j++)
      Death is a valid wave (if date is known).          ps[i][j]= exp(ps[i][j])*ps[i][i];
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        for(j=i+1; j<=nlstate+ndeath; j++)
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          ps[i][j]= exp(ps[i][j])*ps[i][i];
      and mw[mi+1][i]. dh depends on stepm.        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
      */      } /* end i */
       
   int i, mi, m;      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        for(jj=1; jj<= nlstate+ndeath; jj++){
      double sum=0., jmean=0.;*/          ps[ii][jj]=0;
   int first;          ps[ii][ii]=1;
   int j, k=0,jk, ju, jl;        }
   double sum=0.;      }
   first=0;      
   jmin=1e+5;      
   jmax=-1;      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
   jmean=0.;      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
   for(i=1; i<=imx; i++){      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
     mi=0;      /*   } */
     m=firstpass;      /*   printf("\n "); */
     while(s[m][i] <= nlstate){      /* } */
       if(s[m][i]>=1)      /* printf("\n ");printf("%lf ",cov[2]);*/
         mw[++mi][i]=m;      /*
       if(m >=lastpass)        for(i=1; i<= npar; i++) printf("%f ",x[i]);
         break;        goto end;*/
       else      return ps;
         m++;  }
     }/* end while */  
     if (s[m][i] > nlstate){  /**************** Product of 2 matrices ******************/
       mi++;     /* Death is another wave */  
       /* if(mi==0)  never been interviewed correctly before death */  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
          /* Only death is a correct wave */  {
       mw[mi][i]=m;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     }       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     /* in, b, out are matrice of pointers which should have been initialized 
     wav[i]=mi;       before: only the contents of out is modified. The function returns
     if(mi==0){       a pointer to pointers identical to out */
       if(first==0){    int i, j, k;
         printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);    for(i=nrl; i<= nrh; i++)
         first=1;      for(k=ncolol; k<=ncoloh; k++){
       }        out[i][k]=0.;
       if(first==1){        for(j=ncl; j<=nch; j++)
         fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);          out[i][k] +=in[i][j]*b[j][k];
       }      }
     } /* end mi==0 */    return out;
   }  }
   
   for(i=1; i<=imx; i++){  
     for(mi=1; mi<wav[i];mi++){  /************* Higher Matrix Product ***************/
       if (stepm <=0)  
         dh[mi][i]=1;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
       else{  {
         if (s[mw[mi+1][i]][i] > nlstate) {    /* Computes the transition matrix starting at age 'age' over 
           if (agedc[i] < 2*AGESUP) {       'nhstepm*hstepm*stepm' months (i.e. until
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
           if(j==0) j=1;  /* Survives at least one month after exam */       nhstepm*hstepm matrices. 
           k=k+1;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
           if (j >= jmax) jmax=j;       (typically every 2 years instead of every month which is too big 
           if (j <= jmin) jmin=j;       for the memory).
           sum=sum+j;       Model is determined by parameters x and covariates have to be 
           /*if (j<0) printf("j=%d num=%d \n",j,i); */       included manually here. 
           }  
         }       */
         else{  
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    int i, j, d, h, k;
           k=k+1;    double **out, cov[NCOVMAX+1];
           if (j >= jmax) jmax=j;    double **newm;
           else if (j <= jmin)jmin=j;  
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    /* Hstepm could be zero and should return the unit matrix */
           sum=sum+j;    for (i=1;i<=nlstate+ndeath;i++)
         }      for (j=1;j<=nlstate+ndeath;j++){
         jk= j/stepm;        oldm[i][j]=(i==j ? 1.0 : 0.0);
         jl= j -jk*stepm;        po[i][j][0]=(i==j ? 1.0 : 0.0);
         ju= j -(jk+1)*stepm;      }
         if(jl <= -ju)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           dh[mi][i]=jk;    for(h=1; h <=nhstepm; h++){
         else      for(d=1; d <=hstepm; d++){
           dh[mi][i]=jk+1;        newm=savm;
         if(dh[mi][i]==0)        /* Covariates have to be included here again */
           dh[mi][i]=1; /* At least one step */        cov[1]=1.;
       }        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
     }        for (k=1; k<=cptcovn;k++) 
   }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   jmean=sum/k;        for (k=1; k<=cptcovage;k++)
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
  }          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
 /*********** Tricode ****************************/  
 void tricode(int *Tvar, int **nbcode, int imx)        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
 {        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   int Ndum[20],ij=1, k, j, i;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
   int cptcode=0;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   cptcoveff=0;        savm=oldm;
          oldm=newm;
   for (k=0; k<19; k++) Ndum[k]=0;      }
   for (k=1; k<=7; k++) ncodemax[k]=0;      for(i=1; i<=nlstate+ndeath; i++)
         for(j=1;j<=nlstate+ndeath;j++) {
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          po[i][j][h]=newm[i][j];
     for (i=1; i<=imx; i++) {          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
       ij=(int)(covar[Tvar[j]][i]);        }
       Ndum[ij]++;      /*printf("h=%d ",h);*/
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    } /* end h */
       if (ij > cptcode) cptcode=ij;  /*     printf("\n H=%d \n",h); */
     }    return po;
   }
     for (i=0; i<=cptcode; i++) {  
       if(Ndum[i]!=0) ncodemax[j]++;  
     }  /*************** log-likelihood *************/
     ij=1;  double func( double *x)
   {
     int i, ii, j, k, mi, d, kk;
     for (i=1; i<=ncodemax[j]; i++) {    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
       for (k=0; k<=19; k++) {    double **out;
         if (Ndum[k] != 0) {    double sw; /* Sum of weights */
           nbcode[Tvar[j]][ij]=k;    double lli; /* Individual log likelihood */
              int s1, s2;
           ij++;    double bbh, survp;
         }    long ipmx;
         if (ij > ncodemax[j]) break;    /*extern weight */
       }      /* We are differentiating ll according to initial status */
     }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   }      /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
  for (k=0; k<19; k++) Ndum[k]=0;    */
     cov[1]=1.;
  for (i=1; i<=ncovmodel-2; i++) {  
    ij=Tvar[i];    for(k=1; k<=nlstate; k++) ll[k]=0.;
    Ndum[ij]++;  
  }    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
  ij=1;        /* Computes the values of the ncovmodel covariates of the model
  for (i=1; i<=10; i++) {           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
    if((Ndum[i]!=0) && (i<=ncovcol)){           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
      Tvaraff[ij]=i;           to be observed in j being in i according to the model.
      ij++;         */
    }        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
  }          cov[2+k]=covar[Tvar[k]][i];
          }
  cptcoveff=ij-1;        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
 }           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
            has been calculated etc */
 /*********** Health Expectancies ****************/        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
 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 )            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* Health expectancies */            }
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;          for(d=0; d<dh[mi][i]; d++){
   double age, agelim, hf;            newm=savm;
   double ***p3mat,***varhe;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double **dnewm,**doldm;            for (kk=1; kk<=cptcovage;kk++) {
   double *xp;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
   double **gp, **gm;            }
   double ***gradg, ***trgradg;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int theta;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);            oldm=newm;
   xp=vector(1,npar);          } /* end mult */
   dnewm=matrix(1,nlstate*2,1,npar);        
   doldm=matrix(1,nlstate*2,1,nlstate*2);          /*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.
   fprintf(ficreseij,"# Health expectancies\n");           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   fprintf(ficreseij,"# Age");           * (in months) between two waves is not a multiple of stepm, we rounded to 
   for(i=1; i<=nlstate;i++)           * the nearest (and in case of equal distance, to the lowest) interval but now
     for(j=1; j<=nlstate;j++)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       fprintf(ficreseij," %1d-%1d (SE)",i,j);           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
   fprintf(ficreseij,"\n");           * probability in order to take into account the bias as a fraction of the way
            * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   if(estepm < stepm){           * -stepm/2 to stepm/2 .
     printf ("Problem %d lower than %d\n",estepm, stepm);           * For stepm=1 the results are the same as for previous versions of Imach.
   }           * For stepm > 1 the results are less biased than in previous versions. 
   else  hstepm=estepm;             */
   /* We compute the life expectancy from trapezoids spaced every estepm months          s1=s[mw[mi][i]][i];
    * This is mainly to measure the difference between two models: for example          s2=s[mw[mi+1][i]][i];
    * if stepm=24 months pijx are given only every 2 years and by summing them          bbh=(double)bh[mi][i]/(double)stepm; 
    * we are calculating an estimate of the Life Expectancy assuming a linear          /* bias bh is positive if real duration
    * progression inbetween and thus overestimating or underestimating according           * is higher than the multiple of stepm and negative otherwise.
    * 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          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
    * to compare the new estimate of Life expectancy with the same linear          if( s2 > nlstate){ 
    * hypothesis. A more precise result, taking into account a more precise            /* i.e. if s2 is a death state and if the date of death is known 
    * curvature will be obtained if estepm is as small as stepm. */               then the contribution to the likelihood is the probability to 
                die between last step unit time and current  step unit time, 
   /* For example we decided to compute the life expectancy with the smallest unit */               which is also equal to probability to die before dh 
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.               minus probability to die before dh-stepm . 
      nhstepm is the number of hstepm from age to agelim               In version up to 0.92 likelihood was computed
      nstepm is the number of stepm from age to agelin.          as if date of death was unknown. Death was treated as any other
      Look at hpijx to understand the reason of that which relies in memory size          health state: the date of the interview describes the actual state
      and note for a fixed period like estepm months */          and not the date of a change in health state. The former idea was
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          to consider that at each interview the state was recorded
      survival function given by stepm (the optimization length). Unfortunately it          (healthy, disable or death) and IMaCh was corrected; but when we
      means that if the survival funtion is printed only each two years of age and if          introduced the exact date of death then we should have modified
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          the contribution of an exact death to the likelihood. This new
      results. So we changed our mind and took the option of the best precision.          contribution is smaller and very dependent of the step unit
   */          stepm. It is no more the probability to die between last interview
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          and month of death but the probability to survive from last
           interview up to one month before death multiplied by the
   agelim=AGESUP;          probability to die within a month. Thanks to Chris
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          Jackson for correcting this bug.  Former versions increased
     /* nhstepm age range expressed in number of stepm */          mortality artificially. The bad side is that we add another loop
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          which slows down the processing. The difference can be up to 10%
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */          lower mortality.
     /* if (stepm >= YEARM) hstepm=1;*/            */
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */            lli=log(out[s1][s2] - savm[s1][s2]);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);  
     gp=matrix(0,nhstepm,1,nlstate*2);          } else if  (s2==-2) {
     gm=matrix(0,nhstepm,1,nlstate*2);            for (j=1,survp=0. ; j<=nlstate; j++) 
               survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            /*survp += out[s1][j]; */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            lli= log(survp);
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);            }
            
           else if  (s2==-4) { 
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */            for (j=3,survp=0. ; j<=nlstate; j++)  
               survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     /* Computing Variances of health expectancies */            lli= log(survp); 
           } 
      for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){          else if  (s2==-5) { 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            for (j=1,survp=0. ; j<=2; j++)  
       }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              lli= log(survp); 
            } 
       cptj=0;          
       for(j=1; j<= nlstate; j++){          else{
         for(i=1; i<=nlstate; i++){            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           cptj=cptj+1;            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          } 
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
           }          /*if(lli ==000.0)*/
         }          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       }          ipmx +=1;
                sw += weight[i];
                ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1; i<=npar; i++)        } /* end of wave */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      } /* end of individual */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      }  else if(mle==2){
            for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       cptj=0;        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(i=1;i<=nlstate;i++){          for (ii=1;ii<=nlstate+ndeath;ii++)
           cptj=cptj+1;            for (j=1;j<=nlstate+ndeath;j++){
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }            }
         }          for(d=0; d<=dh[mi][i]; d++){
       }            newm=savm;
       for(j=1; j<= nlstate*2; j++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         for(h=0; h<=nhstepm-1; h++){            for (kk=1; kk<=cptcovage;kk++) {
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         }            }
      }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                             1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 /* End theta */            savm=oldm;
             oldm=newm;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          } /* end mult */
         
      for(h=0; h<=nhstepm-1; h++)          s1=s[mw[mi][i]][i];
       for(j=1; j<=nlstate*2;j++)          s2=s[mw[mi+1][i]][i];
         for(theta=1; theta <=npar; theta++)          bbh=(double)bh[mi][i]/(double)stepm; 
           trgradg[h][j][theta]=gradg[h][theta][j];          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
                ipmx +=1;
           sw += weight[i];
      for(i=1;i<=nlstate*2;i++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(j=1;j<=nlstate*2;j++)        } /* end of wave */
         varhe[i][j][(int)age] =0.;      } /* end of individual */
     }  else if(mle==3){  /* exponential inter-extrapolation */
      printf("%d|",(int)age);fflush(stdout);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      for(h=0;h<=nhstepm-1;h++){        for(mi=1; mi<= wav[i]-1; mi++){
       for(k=0;k<=nhstepm-1;k++){          for (ii=1;ii<=nlstate+ndeath;ii++)
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);            for (j=1;j<=nlstate+ndeath;j++){
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(i=1;i<=nlstate*2;i++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(j=1;j<=nlstate*2;j++)            }
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;          for(d=0; d<dh[mi][i]; d++){
       }            newm=savm;
     }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     /* Computing expectancies */            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++)            }
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                      savm=oldm;
 /* 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]);*/            oldm=newm;
           } /* end mult */
         }        
           s1=s[mw[mi][i]][i];
     fprintf(ficreseij,"%3.0f",age );          s2=s[mw[mi+1][i]][i];
     cptj=0;          bbh=(double)bh[mi][i]/(double)stepm; 
     for(i=1; i<=nlstate;i++)          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       for(j=1; j<=nlstate;j++){          ipmx +=1;
         cptj++;          sw += weight[i];
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        } /* end of wave */
     fprintf(ficreseij,"\n");      } /* end of individual */
        }else if (mle==4){  /* ml=4 no inter-extrapolation */
     free_matrix(gm,0,nhstepm,1,nlstate*2);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     free_matrix(gp,0,nhstepm,1,nlstate*2);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);        for(mi=1; mi<= wav[i]-1; mi++){
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for (j=1;j<=nlstate+ndeath;j++){
   }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   printf("\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficlog,"\n");            }
           for(d=0; d<dh[mi][i]; d++){
   free_vector(xp,1,npar);            newm=savm;
   free_matrix(dnewm,1,nlstate*2,1,npar);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);            for (kk=1; kk<=cptcovage;kk++) {
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 }            }
           
 /************ Variance ******************/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 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)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 {            savm=oldm;
   /* Variance of health expectancies */            oldm=newm;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          } /* end mult */
   /* double **newm;*/        
   double **dnewm,**doldm;          s1=s[mw[mi][i]][i];
   double **dnewmp,**doldmp;          s2=s[mw[mi+1][i]][i];
   int i, j, nhstepm, hstepm, h, nstepm ;          if( s2 > nlstate){ 
   int k, cptcode;            lli=log(out[s1][s2] - savm[s1][s2]);
   double *xp;          }else{
   double **gp, **gm;  /* for var eij */            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   double ***gradg, ***trgradg; /*for var eij */          }
   double **gradgp, **trgradgp; /* for var p point j */          ipmx +=1;
   double *gpp, *gmp; /* for var p point j */          sw += weight[i];
   double **varppt; /* for var p point j nlstate to nlstate+ndeath */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double ***p3mat;  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   double age,agelim, hf;        } /* end of wave */
   int theta;      } /* end of individual */
   char digit[4];    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   char digitp[16];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   char fileresprobmorprev[FILENAMELENGTH];        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
   if(popbased==1)            for (j=1;j<=nlstate+ndeath;j++){
     strcpy(digitp,"-populbased-");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   else              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     strcpy(digitp,"-stablbased-");            }
           for(d=0; d<dh[mi][i]; d++){
   strcpy(fileresprobmorprev,"prmorprev");            newm=savm;
   sprintf(digit,"%-d",ij);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/            for (kk=1; kk<=cptcovage;kk++) {
   strcat(fileresprobmorprev,digit); /* Tvar to be done */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   strcat(fileresprobmorprev,digitp); /* Popbased or not */            }
   strcat(fileresprobmorprev,fileres);          
   if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     printf("Problem with resultfile: %s\n", fileresprobmorprev);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);            savm=oldm;
   }            oldm=newm;
   printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);          } /* end mult */
   fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);        
   fprintf(ficresprobmorprev,"# probabilities of dying during a year and weighted mean w1*p1j+w2*p2j+... stand dev in()\n");          s1=s[mw[mi][i]][i];
   fprintf(ficresprobmorprev,"# Age cov=%-d",ij);          s2=s[mw[mi+1][i]][i];
   for(j=nlstate+1; j<=(nlstate+ndeath);j++){          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     fprintf(ficresprobmorprev," p.%-d SE",j);          ipmx +=1;
     for(i=1; i<=nlstate;i++)          sw += weight[i];
       fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   }            /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
   fprintf(ficresprobmorprev,"\n");        } /* end of wave */
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      } /* end of individual */
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    } /* End of if */
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     exit(0);    /* 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 */
   else{    return -l;
     fprintf(ficgp,"\n# Routine varevsij");  }
   }  
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {  /*************** log-likelihood *************/
     printf("Problem with html file: %s\n", optionfilehtm);  double funcone( double *x)
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);  {
     exit(0);    /* Same as likeli but slower because of a lot of printf and if */
   }    int i, ii, j, k, mi, d, kk;
   else{    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");    double **out;
   }    double lli; /* Individual log likelihood */
   varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    double llt;
     int s1, s2;
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");    double bbh, survp;
   fprintf(ficresvij,"# Age");    /*extern weight */
   for(i=1; i<=nlstate;i++)    /* We are differentiating ll according to initial status */
     for(j=1; j<=nlstate;j++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    /*for(i=1;i<imx;i++) 
   fprintf(ficresvij,"\n");      printf(" %d\n",s[4][i]);
     */
   xp=vector(1,npar);    cov[1]=1.;
   dnewm=matrix(1,nlstate,1,npar);  
   doldm=matrix(1,nlstate,1,nlstate);    for(k=1; k<=nlstate; k++) ll[k]=0.;
   dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);  
   doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);      for(mi=1; mi<= wav[i]-1; mi++){
   gpp=vector(nlstate+1,nlstate+ndeath);        for (ii=1;ii<=nlstate+ndeath;ii++)
   gmp=vector(nlstate+1,nlstate+ndeath);          for (j=1;j<=nlstate+ndeath;j++){
   trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   if(estepm < stepm){          }
     printf ("Problem %d lower than %d\n",estepm, stepm);        for(d=0; d<dh[mi][i]; d++){
   }          newm=savm;
   else  hstepm=estepm;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* For example we decided to compute the life expectancy with the smallest unit */          for (kk=1; kk<=cptcovage;kk++) {
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      nhstepm is the number of hstepm from age to agelim          }
      nstepm is the number of stepm from age to agelin.          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
      Look at hpijx to understand the reason of that which relies in memory size          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      and note for a fixed period like k years */                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
      survival function given by stepm (the optimization length). Unfortunately it          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
      means that if the survival funtion is printed only each two years of age and if          savm=oldm;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          oldm=newm;
      results. So we changed our mind and took the option of the best precision.        } /* end mult */
   */        
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        s1=s[mw[mi][i]][i];
   agelim = AGESUP;        s2=s[mw[mi+1][i]][i];
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        bbh=(double)bh[mi][i]/(double)stepm; 
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        /* bias is positive if real duration
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */         * is higher than the multiple of stepm and negative otherwise.
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     gp=matrix(0,nhstepm,1,nlstate);          lli=log(out[s1][s2] - savm[s1][s2]);
     gm=matrix(0,nhstepm,1,nlstate);        } else if  (s2==-2) {
           for (j=1,survp=0. ; j<=nlstate; j++) 
             survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     for(theta=1; theta <=npar; theta++){          lli= log(survp);
       for(i=1; i<=npar; i++){ /* Computes gradient */        }else if (mle==1){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       }        } else if(mle==2){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        } else if(mle==3){  /* exponential inter-extrapolation */
           lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       if (popbased==1) {        } else if (mle==4){  /* mle=4 no inter-extrapolation */
         for(i=1; i<=nlstate;i++)          lli=log(out[s1][s2]); /* Original formula */
           prlim[i][i]=probs[(int)age][i][ij];        } else{  /* mle=0 back to 1 */
       }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
            /*lli=log(out[s1][s2]); */ /* Original formula */
       for(j=1; j<= nlstate; j++){        } /* End of if */
         for(h=0; h<=nhstepm; h++){        ipmx +=1;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        sw += weight[i];
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
       }        if(globpr){
       /* This for computing forces of mortality (h=1)as a weighted average */          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
       for(j=nlstate+1,gpp[j]=0.;j<=nlstate+ndeath;j++){   %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],
           gpp[j] += prlim[i][i]*p3mat[i][j][1];                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
       }              for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       /* end force of mortality */            llt +=ll[k]*gipmx/gsw;
             fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
       for(i=1; i<=npar; i++) /* Computes gradient */          }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          fprintf(ficresilk," %10.6f\n", -llt);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      } /* end of wave */
      } /* end of individual */
       if (popbased==1) {    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         for(i=1; i<=nlstate;i++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
           prlim[i][i]=probs[(int)age][i][ij];    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       }    if(globpr==0){ /* First time we count the contributions and weights */
       gipmx=ipmx;
       for(j=1; j<= nlstate; j++){      gsw=sw;
         for(h=0; h<=nhstepm; h++){    }
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    return -l;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];  }
         }  
       }  
       /* This for computing force of mortality (h=1)as a weighted average */  /*************** function likelione ***********/
       for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
         for(i=1; i<= nlstate; i++)  {
           gmp[j] += prlim[i][i]*p3mat[i][j][1];    /* This routine should help understanding what is done with 
       }           the selection of individuals/waves and
       /* end force of mortality */       to check the exact contribution to the likelihood.
        Plotting could be done.
       for(j=1; j<= nlstate; j++) /* vareij */     */
         for(h=0; h<=nhstepm; h++){    int k;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  
         }    if(*globpri !=0){ /* Just counts and sums, no printings */
       for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */      strcpy(fileresilk,"ilk"); 
         gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];      strcat(fileresilk,fileres);
       }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", fileresilk);
     } /* End theta */        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
       fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
     for(h=0; h<=nhstepm; h++) /* veij */      /*  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(j=1; j<=nlstate;j++)      for(k=1; k<=nlstate; k++) 
         for(theta=1; theta <=npar; theta++)        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
           trgradg[h][j][theta]=gradg[h][theta][j];      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
     }
     for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */  
       for(theta=1; theta <=npar; theta++)    *fretone=(*funcone)(p);
         trgradgp[j][theta]=gradgp[theta][j];    if(*globpri !=0){
       fclose(ficresilk);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
     for(i=1;i<=nlstate;i++)      fflush(fichtm); 
       for(j=1;j<=nlstate;j++)    } 
         vareij[i][j][(int)age] =0.;    return;
   }
     for(h=0;h<=nhstepm;h++){  
       for(k=0;k<=nhstepm;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);  /*********** Maximum Likelihood Estimation ***************/
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  
         for(i=1;i<=nlstate;i++)  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
           for(j=1;j<=nlstate;j++)  {
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    int i,j, iter;
       }    double **xi;
     }    double fret;
     double fretone; /* Only one call to likelihood */
     /* pptj */    /*  char filerespow[FILENAMELENGTH];*/
     matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);    xi=matrix(1,npar,1,npar);
     matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);    for (i=1;i<=npar;i++)
     for(j=nlstate+1;j<=nlstate+ndeath;j++)      for (j=1;j<=npar;j++)
       for(i=nlstate+1;i<=nlstate+ndeath;i++)        xi[i][j]=(i==j ? 1.0 : 0.0);
         varppt[j][i]=doldmp[j][i];    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     /* end ppptj */    strcpy(filerespow,"pow"); 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);      strcat(filerespow,fileres);
     prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", filerespow);
     if (popbased==1) {      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       for(i=1; i<=nlstate;i++)    }
         prlim[i][i]=probs[(int)age][i][ij];    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     }    for (i=1;i<=nlstate;i++)
          for(j=1;j<=nlstate+ndeath;j++)
     /* This for computing force of mortality (h=1)as a weighted average */        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){    fprintf(ficrespow,"\n");
       for(i=1; i<= nlstate; i++)  
         gmp[j] += prlim[i][i]*p3mat[i][j][1];    powell(p,xi,npar,ftol,&iter,&fret,func);
     }      
     /* end force of mortality */    free_matrix(xi,1,npar,1,npar);
     fclose(ficrespow);
     fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       for(i=1; i<=nlstate;i++){  
         fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);  }
       }  
     }  /**** Computes Hessian and covariance matrix ***/
     fprintf(ficresprobmorprev,"\n");  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   {
     fprintf(ficresvij,"%.0f ",age );    double  **a,**y,*x,pd;
     for(i=1; i<=nlstate;i++)    double **hess;
       for(j=1; j<=nlstate;j++){    int i, j,jk;
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);    int *indx;
       }  
     fprintf(ficresvij,"\n");    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     free_matrix(gp,0,nhstepm,1,nlstate);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     free_matrix(gm,0,nhstepm,1,nlstate);    void lubksb(double **a, int npar, int *indx, double b[]) ;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    void ludcmp(double **a, int npar, int *indx, double *d) ;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    double gompertz(double p[]);
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    hess=matrix(1,npar,1,npar);
   } /* End age */  
   free_vector(gpp,nlstate+1,nlstate+ndeath);    printf("\nCalculation of the hessian matrix. Wait...\n");
   free_vector(gmp,nlstate+1,nlstate+ndeath);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);    for (i=1;i<=npar;i++){
   free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/      printf("%d",i);fflush(stdout);
   fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");      fprintf(ficlog,"%d",i);fflush(ficlog);
   /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */     
   fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm);      
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm);      /*  printf(" %f ",p[i]);
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);    }
   fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,digitp,digit);    
   /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);    for (i=1;i<=npar;i++) {
 */      for (j=1;j<=npar;j++)  {
   fprintf(ficgp,"\nset out \"varmuptjgr%s%s.png\";replot;",digitp,digit);        if (j>i) { 
           printf(".%d%d",i,j);fflush(stdout);
   free_vector(xp,1,npar);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   free_matrix(doldm,1,nlstate,1,nlstate);          hess[i][j]=hessij(p,delti,i,j,func,npar);
   free_matrix(dnewm,1,nlstate,1,npar);          
   free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);          hess[j][i]=hess[i][j];    
   free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);          /*printf(" %lf ",hess[i][j]);*/
   free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);        }
   fclose(ficresprobmorprev);      }
   fclose(ficgp);    }
   fclose(fichtm);    printf("\n");
     fprintf(ficlog,"\n");
 }  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
 /************ Variance of prevlim ******************/    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 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)    
 {    a=matrix(1,npar,1,npar);
   /* Variance of prevalence limit */    y=matrix(1,npar,1,npar);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    x=vector(1,npar);
   double **newm;    indx=ivector(1,npar);
   double **dnewm,**doldm;    for (i=1;i<=npar;i++)
   int i, j, nhstepm, hstepm;      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   int k, cptcode;    ludcmp(a,npar,indx,&pd);
   double *xp;  
   double *gp, *gm;    for (j=1;j<=npar;j++) {
   double **gradg, **trgradg;      for (i=1;i<=npar;i++) x[i]=0;
   double age,agelim;      x[j]=1;
   int theta;      lubksb(a,npar,indx,x);
          for (i=1;i<=npar;i++){ 
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");        matcov[i][j]=x[i];
   fprintf(ficresvpl,"# Age");      }
   for(i=1; i<=nlstate;i++)    }
       fprintf(ficresvpl," %1d-%1d",i,i);  
   fprintf(ficresvpl,"\n");    printf("\n#Hessian matrix#\n");
     fprintf(ficlog,"\n#Hessian matrix#\n");
   xp=vector(1,npar);    for (i=1;i<=npar;i++) { 
   dnewm=matrix(1,nlstate,1,npar);      for (j=1;j<=npar;j++) { 
   doldm=matrix(1,nlstate,1,nlstate);        printf("%.3e ",hess[i][j]);
          fprintf(ficlog,"%.3e ",hess[i][j]);
   hstepm=1*YEARM; /* Every year of age */      }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */      printf("\n");
   agelim = AGESUP;      fprintf(ficlog,"\n");
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     if (stepm >= YEARM) hstepm=1;    /* Recompute Inverse */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    for (i=1;i<=npar;i++)
     gradg=matrix(1,npar,1,nlstate);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     gp=vector(1,nlstate);    ludcmp(a,npar,indx,&pd);
     gm=vector(1,nlstate);  
     /*  printf("\n#Hessian matrix recomputed#\n");
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */    for (j=1;j<=npar;j++) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for (i=1;i<=npar;i++) x[i]=0;
       }      x[j]=1;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      lubksb(a,npar,indx,x);
       for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++){ 
         gp[i] = prlim[i][i];        y[i][j]=x[i];
            printf("%.3e ",y[i][j]);
       for(i=1; i<=npar; i++) /* Computes gradient */        fprintf(ficlog,"%.3e ",y[i][j]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      printf("\n");
       for(i=1;i<=nlstate;i++)      fprintf(ficlog,"\n");
         gm[i] = prlim[i][i];    }
     */
       for(i=1;i<=nlstate;i++)  
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];    free_matrix(a,1,npar,1,npar);
     } /* End theta */    free_matrix(y,1,npar,1,npar);
     free_vector(x,1,npar);
     trgradg =matrix(1,nlstate,1,npar);    free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
     for(j=1; j<=nlstate;j++)  
       for(theta=1; theta <=npar; theta++)  
         trgradg[j][theta]=gradg[theta][j];  }
   
     for(i=1;i<=nlstate;i++)  /*************** hessian matrix ****************/
       varpl[i][(int)age] =0.;  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);  {
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    int i;
     for(i=1;i<=nlstate;i++)    int l=1, lmax=20;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    double k1,k2;
     double p2[MAXPARM+1]; /* identical to x */
     fprintf(ficresvpl,"%.0f ",age );    double res;
     for(i=1; i<=nlstate;i++)    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    double fx;
     fprintf(ficresvpl,"\n");    int k=0,kmax=10;
     free_vector(gp,1,nlstate);    double l1;
     free_vector(gm,1,nlstate);  
     free_matrix(gradg,1,npar,1,nlstate);    fx=func(x);
     free_matrix(trgradg,1,nlstate,1,npar);    for (i=1;i<=npar;i++) p2[i]=x[i];
   } /* End age */    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
       l1=pow(10,l);
   free_vector(xp,1,npar);      delts=delt;
   free_matrix(doldm,1,nlstate,1,npar);      for(k=1 ; k <kmax; k=k+1){
   free_matrix(dnewm,1,nlstate,1,nlstate);        delt = delta*(l1*k);
         p2[theta]=x[theta] +delt;
 }        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
         p2[theta]=x[theta]-delt;
 /************ Variance of one-step probabilities  ******************/        k2=func(p2)-fx;
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)        /*res= (k1-2.0*fx+k2)/delt/delt; */
 {        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   int i, j=0,  i1, k1, l1, t, tj;        
   int k2, l2, j1,  z1;  #ifdef DEBUGHESS
   int k=0,l, cptcode;        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 first=1, first1;        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);
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;  #endif
   double **dnewm,**doldm;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   double *xp;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   double *gp, *gm;          k=kmax;
   double **gradg, **trgradg;        }
   double **mu;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   double age,agelim, cov[NCOVMAX];          k=kmax; l=lmax*10.;
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */        }
   int theta;        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
   char fileresprob[FILENAMELENGTH];          delts=delt;
   char fileresprobcov[FILENAMELENGTH];        }
   char fileresprobcor[FILENAMELENGTH];      }
     }
   double ***varpij;    delti[theta]=delts;
     return res; 
   strcpy(fileresprob,"prob");    
   strcat(fileresprob,fileres);  }
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  
     printf("Problem with resultfile: %s\n", fileresprob);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);  {
   }    int i;
   strcpy(fileresprobcov,"probcov");    int l=1, l1, lmax=20;
   strcat(fileresprobcov,fileres);    double k1,k2,k3,k4,res,fx;
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    double p2[MAXPARM+1];
     printf("Problem with resultfile: %s\n", fileresprobcov);    int k;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);  
   }    fx=func(x);
   strcpy(fileresprobcor,"probcor");    for (k=1; k<=2; k++) {
   strcat(fileresprobcor,fileres);      for (i=1;i<=npar;i++) p2[i]=x[i];
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {      p2[thetai]=x[thetai]+delti[thetai]/k;
     printf("Problem with resultfile: %s\n", fileresprobcor);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);      k1=func(p2)-fx;
   }    
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);      p2[thetai]=x[thetai]+delti[thetai]/k;
   fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);      k2=func(p2)-fx;
   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);      p2[thetai]=x[thetai]-delti[thetai]/k;
   fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
        k3=func(p2)-fx;
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");    
   fprintf(ficresprob,"# Age");      p2[thetai]=x[thetai]-delti[thetai]/k;
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   fprintf(ficresprobcov,"# Age");      k4=func(p2)-fx;
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   fprintf(ficresprobcov,"# Age");  #ifdef DEBUG
       printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
       fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   for(i=1; i<=nlstate;i++)  #endif
     for(j=1; j<=(nlstate+ndeath);j++){    }
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    return res;
       fprintf(ficresprobcov," p%1d-%1d ",i,j);  }
       fprintf(ficresprobcor," p%1d-%1d ",i,j);  
     }    /************** Inverse of matrix **************/
   fprintf(ficresprob,"\n");  void ludcmp(double **a, int n, int *indx, double *d) 
   fprintf(ficresprobcov,"\n");  { 
   fprintf(ficresprobcor,"\n");    int i,imax,j,k; 
   xp=vector(1,npar);    double big,dum,sum,temp; 
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);    double *vv; 
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));   
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);    vv=vector(1,n); 
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);    *d=1.0; 
   first=1;    for (i=1;i<=n;i++) { 
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      big=0.0; 
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);      for (j=1;j<=n;j++) 
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     exit(0);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   }      vv[i]=1.0/big; 
   else{    } 
     fprintf(ficgp,"\n# Routine varprob");    for (j=1;j<=n;j++) { 
   }      for (i=1;i<j;i++) { 
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {        sum=a[i][j]; 
     printf("Problem with html file: %s\n", optionfilehtm);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);        a[i][j]=sum; 
     exit(0);      } 
   }      big=0.0; 
   else{      for (i=j;i<=n;i++) { 
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");        sum=a[i][j]; 
     fprintf(fichtm,"\n");        for (k=1;k<j;k++) 
           sum -= a[i][k]*a[k][j]; 
     fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");        a[i][j]=sum; 
     fprintf(fichtm,"\nWe 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");        if ( (dum=vv[i]*fabs(sum)) >= big) { 
     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");          big=dum; 
           imax=i; 
   }        } 
       } 
        if (j != imax) { 
   cov[1]=1;        for (k=1;k<=n;k++) { 
   tj=cptcoveff;          dum=a[imax][k]; 
   if (cptcovn<1) {tj=1;ncodemax[1]=1;}          a[imax][k]=a[j][k]; 
   j1=0;          a[j][k]=dum; 
   for(t=1; t<=tj;t++){        } 
     for(i1=1; i1<=ncodemax[t];i1++){        *d = -(*d); 
       j1++;        vv[imax]=vv[j]; 
            } 
       if  (cptcovn>0) {      indx[j]=imax; 
         fprintf(ficresprob, "\n#********** Variable ");      if (a[j][j] == 0.0) a[j][j]=TINY; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      if (j != n) { 
         fprintf(ficresprob, "**********\n#");        dum=1.0/(a[j][j]); 
         fprintf(ficresprobcov, "\n#********** Variable ");        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      } 
         fprintf(ficresprobcov, "**********\n#");    } 
            free_vector(vv,1,n);  /* Doesn't work */
         fprintf(ficgp, "\n#********** Variable ");  ;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  } 
         fprintf(ficgp, "**********\n#");  
          void lubksb(double **a, int n, int *indx, double b[]) 
          { 
         fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable ");    int i,ii=0,ip,j; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    double sum; 
         fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");   
            for (i=1;i<=n;i++) { 
         fprintf(ficresprobcor, "\n#********** Variable ");          ip=indx[i]; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      sum=b[ip]; 
         fprintf(ficgp, "**********\n#");          b[ip]=b[i]; 
       }      if (ii) 
              for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       for (age=bage; age<=fage; age ++){      else if (sum) ii=i; 
         cov[2]=age;      b[i]=sum; 
         for (k=1; k<=cptcovn;k++) {    } 
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];    for (i=n;i>=1;i--) { 
         }      sum=b[i]; 
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
         for (k=1; k<=cptcovprod;k++)      b[i]=sum/a[i][i]; 
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    } 
          } 
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));  
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);  void pstamp(FILE *fichier)
         gp=vector(1,(nlstate)*(nlstate+ndeath));  {
         gm=vector(1,(nlstate)*(nlstate+ndeath));    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
      }
         for(theta=1; theta <=npar; theta++){  
           for(i=1; i<=npar; i++)  /************ Frequencies ********************/
             xp[i] = x[i] + (i==theta ?delti[theta]:0);  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[])
            {  /* Some frequencies */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    
              int i, m, jk, k1,i1, j1, bool, z1,j;
           k=0;    int first;
           for(i=1; i<= (nlstate); i++){    double ***freq; /* Frequencies */
             for(j=1; j<=(nlstate+ndeath);j++){    double *pp, **prop;
               k=k+1;    double pos,posprop, k2, dateintsum=0,k2cpt=0;
               gp[k]=pmmij[i][j];    char fileresp[FILENAMELENGTH];
             }    
           }    pp=vector(1,nlstate);
              prop=matrix(1,nlstate,iagemin,iagemax+3);
           for(i=1; i<=npar; i++)    strcpy(fileresp,"p");
             xp[i] = x[i] - (i==theta ?delti[theta]:0);    strcat(fileresp,fileres);
        if((ficresp=fopen(fileresp,"w"))==NULL) {
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      printf("Problem with prevalence resultfile: %s\n", fileresp);
           k=0;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
           for(i=1; i<=(nlstate); i++){      exit(0);
             for(j=1; j<=(nlstate+ndeath);j++){    }
               k=k+1;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
               gm[k]=pmmij[i][j];    j1=0;
             }    
           }    j=cptcoveff;
          if (cptcovn<1) {j=1;ncodemax[1]=1;}
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)  
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      first=1;
         }  
     /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
           for(theta=1; theta <=npar; theta++)    /*    j1++;
             trgradg[j][theta]=gradg[theta][j];  */
            for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);          scanf("%d", i);*/
                for (i=-5; i<=nlstate+ndeath; i++)  
         pmij(pmmij,cov,ncovmodel,x,nlstate);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
                    for(m=iagemin; m <= iagemax+3; m++)
         k=0;              freq[i][jk][m]=0;
         for(i=1; i<=(nlstate); i++){        
           for(j=1; j<=(nlstate+ndeath);j++){        for (i=1; i<=nlstate; i++)  
             k=k+1;          for(m=iagemin; m <= iagemax+3; m++)
             mu[k][(int) age]=pmmij[i][j];            prop[i][m]=0;
           }        
         }        dateintsum=0;
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)        k2cpt=0;
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)        for (i=1; i<=imx; i++) {
             varpij[i][j][(int)age] = doldm[i][j];          bool=1;
           if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
         /*printf("\n%d ",(int)age);            for (z1=1; z1<=cptcoveff; z1++)       
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
        fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));                bool=0;
      }*/                /* printf("bool=%d i=%d, z1=%d, Tvaraff[%d]=%d, covar[Tvarff][%d]=%2f, codtab[%d][%d]=%d, nbcode[Tvaraff][codtab[%d][%d]=%d, j1=%d\n", 
                   bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
         fprintf(ficresprob,"\n%d ",(int)age);                  j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
         fprintf(ficresprobcov,"\n%d ",(int)age);                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
         fprintf(ficresprobcor,"\n%d ",(int)age);              } 
           }
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)   
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));          if (bool==1){
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){            for(m=firstpass; m<=lastpass; m++){
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);              k2=anint[m][i]+(mint[m][i]/12.);
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
         }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
         i=0;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         for (k=1; k<=(nlstate);k++){                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
           for (l=1; l<=(nlstate+ndeath);l++){                if (m<lastpass) {
             i=i++;                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);                }
             for (j=1; j<=i;j++){                
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));                  dateintsum=dateintsum+k2;
             }                  k2cpt++;
           }                }
         }/* end of loop for state */                /*}*/
       } /* end of loop for age */            }
           }
       /* Confidence intervalle of pij  */        } /* end i */
       /*         
       fprintf(ficgp,"\nset noparametric;unset label");        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");        pstamp(ficresp);
       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");        if  (cptcovn>0) {
       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(ficresp, "\n#********** Variable "); 
       fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
       fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);          fprintf(ficresp, "**********\n#");
       fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);          fprintf(ficlog, "\n#********** Variable "); 
       */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficlog, "**********\n#");
       /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/        }
       first1=1;        for(i=1; i<=nlstate;i++) 
       for (k2=1; k2<=(nlstate);k2++){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         for (l2=1; l2<=(nlstate+ndeath);l2++){        fprintf(ficresp, "\n");
           if(l2==k2) continue;        
           j=(k2-1)*(nlstate+ndeath)+l2;        for(i=iagemin; i <= iagemax+3; i++){
           for (k1=1; k1<=(nlstate);k1++){          if(i==iagemax+3){
             for (l1=1; l1<=(nlstate+ndeath);l1++){            fprintf(ficlog,"Total");
               if(l1==k1) continue;          }else{
               i=(k1-1)*(nlstate+ndeath)+l1;            if(first==1){
               if(i<=j) continue;              first=0;
               for (age=bage; age<=fage; age ++){              printf("See log file for details...\n");
                 if ((int)age %5==0){            }
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;            fprintf(ficlog,"Age %d", i);
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;          }
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;          for(jk=1; jk <=nlstate ; jk++){
                   mu1=mu[i][(int) age]/stepm*YEARM ;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                   mu2=mu[j][(int) age]/stepm*YEARM;              pp[jk] += freq[jk][m][i]; 
                   c12=cv12/sqrt(v1*v2);          }
                   /* Computing eigen value of matrix of covariance */          for(jk=1; jk <=nlstate ; jk++){
                   lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;            for(m=-1, pos=0; m <=0 ; m++)
                   lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;              pos += freq[jk][m][i];
                   /* Eigen vectors */            if(pp[jk]>=1.e-10){
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));              if(first==1){
                   /*v21=sqrt(1.-v11*v11); *//* error */                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
                   v21=(lc1-v1)/cv12*v11;              }
                   v12=-v21;              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
                   v22=v11;            }else{
                   tnalp=v21/v11;              if(first==1)
                   if(first1==1){                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                     first1=0;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                     printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);            }
                   }          }
                   fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);  
                   /*printf(fignu*/          for(jk=1; jk <=nlstate ; jk++){
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
                   /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */              pp[jk] += freq[jk][m][i];
                   if(first==1){          }       
                     first=0;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
                     fprintf(ficgp,"\nset parametric;unset label");            pos += pp[jk];
                     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);            posprop += prop[jk][i];
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");          }
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);          for(jk=1; jk <=nlstate ; jk++){
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);            if(pos>=1.e-5){
                     fprintf(fichtm,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);              if(first==1)
                     fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);            }else{
                     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",\              if(first==1)
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
                   }else{            }
                     first=0;            if( i <= iagemax){
                     fprintf(fichtm," %d (%.3f),",(int) age, c12);              if(pos>=1.e-5){
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);                /*probs[i][jk][j1]= pp[jk]/pos;*/
                     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("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\              }
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));              else
                   }/* if first */                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
                 } /* age mod 5 */            }
               } /* end loop age */          }
               fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);          
               first=1;          for(jk=-1; jk <=nlstate+ndeath; jk++)
             } /*l12 */            for(m=-1; m <=nlstate+ndeath; m++)
           } /* k12 */              if(freq[jk][m][i] !=0 ) {
         } /*l1 */              if(first==1)
       }/* k1 */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     } /* loop covariates */                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);              }
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          if(i <= iagemax)
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));            fprintf(ficresp,"\n");
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);          if(first==1)
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);            printf("Others in log...\n");
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          fprintf(ficlog,"\n");
   }        }
   free_vector(xp,1,npar);        /*}*/
   fclose(ficresprob);    }
   fclose(ficresprobcov);    dateintmean=dateintsum/k2cpt; 
   fclose(ficresprobcor);   
   fclose(ficgp);    fclose(ficresp);
   fclose(fichtm);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 }    free_vector(pp,1,nlstate);
     free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     /* End of Freq */
 /******************* Printing html file ***********/  }
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \  
                   int lastpass, int stepm, int weightopt, char model[],\  /************ Prevalence ********************/
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\  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)
                   int popforecast, int estepm ,\  {  
                   double jprev1, double mprev1,double anprev1, \    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
                   double jprev2, double mprev2,double anprev2){       in each health status at the date of interview (if between dateprev1 and dateprev2).
   int jj1, k1, i1, cpt;       We still use firstpass and lastpass as another selection.
   /*char optionfilehtm[FILENAMELENGTH];*/    */
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {   
     printf("Problem with %s \n",optionfilehtm), exit(0);    int i, m, jk, k1, i1, j1, bool, z1,j;
     fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);    double ***freq; /* Frequencies */
   }    double *pp, **prop;
     double pos,posprop; 
    fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n    double  y2; /* in fractional years */
  - 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    int iagemin, iagemax;
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n    int first; /** to stop verbosity which is redirected to log file */
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n  
  - Life expectancies by age and initial health status (estepm=%2d months):    iagemin= (int) agemin;
    <a href=\"e%s\">e%s</a> <br>\n</li>", \    iagemax= (int) agemax;
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);    /*pp=vector(1,nlstate);*/
     prop=matrix(1,nlstate,iagemin,iagemax+3); 
 fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     j1=0;
  m=cptcoveff;    
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    /*j=cptcoveff;*/
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
  jj1=0;    
  for(k1=1; k1<=m;k1++){    first=1;
    for(i1=1; i1<=ncodemax[k1];i1++){    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
      jj1++;      /*for(i1=1; i1<=ncodemax[k1];i1++){
      if (cptcovn > 0) {        j1++;*/
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");        
        for (cpt=1; cpt<=cptcoveff;cpt++)        for (i=1; i<=nlstate; i++)  
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);          for(m=iagemin; m <= iagemax+3; m++)
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");            prop[i][m]=0.0;
      }       
      /* Pij */        for (i=1; i<=imx; i++) { /* Each individual */
      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>          bool=1;
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              if  (cptcovn>0) {
      /* Quasi-incidences */            for (z1=1; z1<=cptcoveff; z1++) 
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                bool=0;
        /* Stable prevalence in each health state */          } 
        for(cpt=1; cpt<nlstate;cpt++){          if (bool==1) { 
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
        }              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
      for(cpt=1; cpt<=nlstate;cpt++) {                if(agev[m][i]==0) agev[m][i]=iagemax+1;
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>                if(agev[m][i]==1) agev[m][i]=iagemax+2;
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
      }                if (s[m][i]>0 && s[m][i]<=nlstate) { 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and                  /*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]]);*/
 health expectancies in states (1) and (2): e%s%d.png<br>                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);                  prop[s[m][i]][iagemax+3] += weight[i]; 
    } /* end i1 */                } 
  }/* End k1 */              }
  fprintf(fichtm,"</ul>");            } /* end selection of waves */
           }
         }
  fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n        for(i=iagemin; i <= iagemax+3; i++){  
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n            posprop += prop[jk][i]; 
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n          } 
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n          
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n          for(jk=1; jk <=nlstate ; jk++){     
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n            if( i <=  iagemax){ 
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);              if(posprop>=1.e-5){ 
                 probs[i][jk][j1]= prop[jk][i]/posprop;
  if(popforecast==1) fprintf(fichtm,"\n              } else{
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n                if(first==1){
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n                  first=0;
         <br>",fileres,fileres,fileres,fileres);                  printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\nSee others on log file...\n",jk,i,j1,probs[i][jk][j1]);
  else                }
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);              }
 fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");            } 
           }/* end jk */ 
  m=cptcoveff;        }/* end i */ 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      /*} *//* end i1 */
     } /* end j1 */
  jj1=0;    
  for(k1=1; k1<=m;k1++){    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
    for(i1=1; i1<=ncodemax[k1];i1++){    /*free_vector(pp,1,nlstate);*/
      jj1++;    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
      if (cptcovn > 0) {  }  /* End of prevalence */
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");  
        for (cpt=1; cpt<=cptcoveff;cpt++)  /************* Waves Concatenation ***************/
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);  
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
      }  {
      for(cpt=1; cpt<=nlstate;cpt++) {    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident       Death is a valid wave (if date is known).
 interval) in state (%d): v%s%d%d.png <br>       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);         dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
      }       and mw[mi+1][i]. dh depends on stepm.
    } /* end i1 */       */
  }/* End k1 */  
  fprintf(fichtm,"</ul>");    int i, mi, m;
 fclose(fichtm);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
 }       double sum=0., jmean=0.;*/
     int first;
 /******************* Gnuplot file **************/    int j, k=0,jk, ju, jl;
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){    double sum=0.;
     first=0;
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;    jmin=1e+5;
   int ng;    jmax=-1;
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    jmean=0.;
     printf("Problem with file %s",optionfilegnuplot);    for(i=1; i<=imx; i++){
     fprintf(ficlog,"Problem with file %s",optionfilegnuplot);      mi=0;
   }      m=firstpass;
       while(s[m][i] <= nlstate){
 #ifdef windows        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     fprintf(ficgp,"cd \"%s\" \n",pathc);          mw[++mi][i]=m;
 #endif        if(m >=lastpass)
 m=pow(2,cptcoveff);          break;
          else
  /* 1eme*/          m++;
   for (cpt=1; cpt<= nlstate ; cpt ++) {      }/* end while */
    for (k1=1; k1<= m ; k1 ++) {      if (s[m][i] > nlstate){
         mi++;     /* Death is another wave */
 #ifdef windows        /* if(mi==0)  never been interviewed correctly before death */
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);           /* Only death is a correct wave */
      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);        mw[mi][i]=m;
 #endif      }
 #ifdef unix  
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);      wav[i]=mi;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);      if(mi==0){
 #endif        nbwarn++;
         if(first==0){
 for (i=1; i<= nlstate ; i ++) {          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          first=1;
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }        if(first==1){
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
     for (i=1; i<= nlstate ; i ++) {        }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      } /* end mi==0 */
   else fprintf(ficgp," \%%*lf (\%%*lf)");    } /* End individuals */
 }  
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    for(i=1; i<=imx; i++){
      for (i=1; i<= nlstate ; i ++) {      for(mi=1; mi<wav[i];mi++){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        if (stepm <=0)
   else fprintf(ficgp," \%%*lf (\%%*lf)");          dh[mi][i]=1;
 }          else{
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
 #ifdef unix            if (agedc[i] < 2*AGESUP) {
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
 #endif              if(j==0) j=1;  /* Survives at least one month after exam */
    }              else if(j<0){
   }                nberr++;
   /*2 eme*/                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]);
                 j=1; /* Temporary Dangerous patch */
   for (k1=1; k1<= m ; k1 ++) {                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
                  }
     for (i=1; i<= nlstate+1 ; i ++) {              k=k+1;
       k=2*i;              if (j >= jmax){
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);                jmax=j;
       for (j=1; j<= nlstate+1 ; j ++) {                ijmax=i;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              }
   else fprintf(ficgp," \%%*lf (\%%*lf)");              if (j <= jmin){
 }                  jmin=j;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");                ijmin=i;
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);              }
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);              sum=sum+j;
       for (j=1; j<= nlstate+1 ; j ++) {              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
         else fprintf(ficgp," \%%*lf (\%%*lf)");            }
 }            }
       fprintf(ficgp,"\" t\"\" w l 0,");          else{
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       for (j=1; j<= nlstate+1 ; j ++) {  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");            k=k+1;
 }              if (j >= jmax) {
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");              jmax=j;
       else fprintf(ficgp,"\" t\"\" w l 0,");              ijmax=i;
     }            }
   }            else if (j <= jmin){
                jmin=j;
   /*3eme*/              ijmin=i;
             }
   for (k1=1; k1<= m ; k1 ++) {            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     for (cpt=1; cpt<= nlstate ; cpt ++) {            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
       k=2+nlstate*(2*cpt-2);            if(j<0){
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              nberr++;
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");            }
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            sum=sum+j;
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          }
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          jk= j/stepm;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          jl= j -jk*stepm;
           ju= j -(jk+1)*stepm;
 */          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       for (i=1; i< nlstate ; i ++) {            if(jl==0){
         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);              dh[mi][i]=jk;
               bh[mi][i]=0;
       }            }else{ /* We want a negative bias in order to only have interpolation ie
     }                    * to avoid the price of an extra matrix product in likelihood */
   }              dh[mi][i]=jk+1;
                bh[mi][i]=ju;
   /* CV preval stat */            }
     for (k1=1; k1<= m ; k1 ++) {          }else{
     for (cpt=1; cpt<nlstate ; cpt ++) {            if(jl <= -ju){
       k=3;              dh[mi][i]=jk;
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);              bh[mi][i]=jl;       /* bias is positive if real duration
       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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);                                   * is higher than the multiple of stepm and negative otherwise.
                                    */
       for (i=1; i< nlstate ; i ++)            }
         fprintf(ficgp,"+$%d",k+i+1);            else{
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);              dh[mi][i]=jk+1;
                    bh[mi][i]=ju;
       l=3+(nlstate+ndeath)*cpt;            }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);            if(dh[mi][i]==0){
       for (i=1; i< nlstate ; i ++) {              dh[mi][i]=1; /* At least one step */
         l=3+(nlstate+ndeath)*cpt;              bh[mi][i]=ju; /* At least one step */
         fprintf(ficgp,"+$%d",l+i+1);              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
       }            }
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);            } /* end if mle */
     }        }
   }        } /* end wave */
      }
   /* proba elementaires */    jmean=sum/k;
    for(i=1,jk=1; i <=nlstate; i++){    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
     for(k=1; k <=(nlstate+ndeath); k++){    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %d) Max=%d (%d) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
       if (k != i) {   }
         for(j=1; j <=ncovmodel; j++){  
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);  /*********** Tricode ****************************/
           jk++;  void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
           fprintf(ficgp,"\n");  {
         }    /**< Uses cptcovn+2*cptcovprod as the number of covariates */
       }    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
     }    /* Boring subroutine which should only output nbcode[Tvar[j]][k]
    }     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
     /* nbcode[Tvar[j]][1]= 
    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 \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
        if (ng==2)    int modmaxcovj=0; /* Modality max of covariates j */
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");    int cptcode=0; /* Modality max of covariates j */
        else    int modmincovj=0; /* Modality min of covariates j */
          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;    cptcoveff=0; 
        for(k2=1; k2<=nlstate; k2++) {   
          k3=i;    for (k=-1; k < maxncov; k++) Ndum[k]=0;
          for(k=1; k<=(nlstate+ndeath); k++) {    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
            if (k != k2){  
              if(ng==2)    /* Loop on covariates without age and products */
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
              else      for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);                                 modality of this covariate Vj*/ 
              ij=1;        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
              for(j=3; j <=ncovmodel; j++) {                                      * If product of Vn*Vm, still boolean *:
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
                  ij++;        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
                }                                        modality of the nth covariate of individual i. */
                else        if (ij > modmaxcovj)
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          modmaxcovj=ij; 
              }        else if (ij < modmincovj) 
              fprintf(ficgp,")/(1");          modmincovj=ij; 
                      if ((ij < -1) && (ij > NCOVMAX)){
              for(k1=1; k1 <=nlstate; k1++){            printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);          exit(1);
                ij=1;        }else
                for(j=3; j <=ncovmodel; j++){        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
                    ij++;        /* getting the maximum value of the modality of the covariate
                  }           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
                  else           female is 1, then modmaxcovj=1.*/
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      }
                }      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
                fprintf(ficgp,")");      cptcode=modmaxcovj;
              }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);     /*for (i=0; i<=cptcode; i++) {*/
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");      for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
              i=i+ncovmodel;        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
            }        if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
          } /* end k */          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
        } /* end k2 */        }
      } /* end jk */        /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
    } /* end ng */           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
    fclose(ficgp);      } /* Ndum[-1] number of undefined modalities */
 }  /* end gnuplot */  
       /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
       /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
 /*************** Moving average **************/      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){         modmincovj=3; modmaxcovj = 7;
          There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
   int i, cpt, cptcod;         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)         variables V1_1 and V1_2.
       for (i=1; i<=nlstate;i++)         nbcode[Tvar[j]][ij]=k;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)         nbcode[Tvar[j]][1]=0;
           mobaverage[(int)agedeb][i][cptcod]=0.;         nbcode[Tvar[j]][2]=1;
             nbcode[Tvar[j]][3]=2;
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){      */
       for (i=1; i<=nlstate;i++){      ij=1; /* ij is similar to i but can jumps over null modalities */
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
           for (cpt=0;cpt<=4;cpt++){        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];          /*recode from 0 */
           }          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
         }                                       k is a modality. If we have model=V1+V1*sex 
       }                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
     }            ij++;
              }
 }          if (ij > ncodemax[j]) break; 
         }  /* end of loop on */
       } /* end of loop on modality */ 
 /************** Forecasting ******************/    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
 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){    
     for (k=-1; k< maxncov; k++) Ndum[k]=0; 
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    
   int *popage;    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
   double *popeffectif,*popcount;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
   double ***p3mat;     Ndum[ij]++; 
   char fileresf[FILENAMELENGTH];   } 
   
  agelim=AGESUP;   ij=1;
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
      /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);     if((Ndum[i]!=0) && (i<=ncovcol)){
         /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
         Tvaraff[ij]=i; /*For printing (unclear) */
   strcpy(fileresf,"f");       ij++;
   strcat(fileresf,fileres);     }else
   if((ficresf=fopen(fileresf,"w"))==NULL) {         Tvaraff[ij]=0;
     printf("Problem with forecast resultfile: %s\n", fileresf);   }
     fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);   ij--;
   }   cptcoveff=ij; /*Number of total covariates*/
   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;  
   /*********** Health Expectancies ****************/
   if (mobilav==1) {  
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
     movingaverage(agedeb, fage, ageminpar, mobaverage);  
   }  {
     /* Health expectancies, no variances */
   stepsize=(int) (stepm+YEARM-1)/YEARM;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
   if (stepm<=12) stepsize=1;    int nhstepma, nstepma; /* Decreasing with age */
      double age, agelim, hf;
   agelim=AGESUP;    double ***p3mat;
      double eip;
   hstepm=1;  
   hstepm=hstepm/stepm;    pstamp(ficreseij);
   yp1=modf(dateintmean,&yp);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   anprojmean=yp;    fprintf(ficreseij,"# Age");
   yp2=modf((yp1*12),&yp);    for(i=1; i<=nlstate;i++){
   mprojmean=yp;      for(j=1; j<=nlstate;j++){
   yp1=modf((yp2*30.5),&yp);        fprintf(ficreseij," e%1d%1d ",i,j);
   jprojmean=yp;      }
   if(jprojmean==0) jprojmean=1;      fprintf(ficreseij," e%1d. ",i);
   if(mprojmean==0) jprojmean=1;    }
      fprintf(ficreseij,"\n");
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  
      
   for(cptcov=1;cptcov<=i2;cptcov++){    if(estepm < stepm){
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      printf ("Problem %d lower than %d\n",estepm, stepm);
       k=k+1;    }
       fprintf(ficresf,"\n#******");    else  hstepm=estepm;   
       for(j=1;j<=cptcoveff;j++) {    /* We compute the life expectancy from trapezoids spaced every estepm months
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     * 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
       fprintf(ficresf,"******\n");     * we are calculating an estimate of the Life Expectancy assuming a linear 
       fprintf(ficresf,"# StartingAge FinalAge");     * progression in between and thus overestimating or underestimating according
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);     * to the curvature of the survival function. If, for the same date, we 
           * estimate the model with stepm=1 month, we can keep estepm to 24 months
           * to compare the new estimate of Life expectancy with the same linear 
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {     * hypothesis. A more precise result, taking into account a more precise
         fprintf(ficresf,"\n");     * curvature will be obtained if estepm is as small as stepm. */
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);    
     /* For example we decided to compute the life expectancy with the smallest unit */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);       nhstepm is the number of hstepm from age to agelim 
           nhstepm = nhstepm/hstepm;       nstepm is the number of stepm from age to agelin. 
                 Look at hpijx to understand the reason of that which relies in memory size
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       and note for a fixed period like estepm months */
           oldm=oldms;savm=savms;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);         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 (h=0; h<=nhstepm; h++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
             if (h==(int) (calagedate+YEARM*cpt)) {       results. So we changed our mind and took the option of the best precision.
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    */
             }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
             for(j=1; j<=nlstate+ndeath;j++) {  
               kk1=0.;kk2=0;    agelim=AGESUP;
               for(i=1; i<=nlstate;i++) {                  /* If stepm=6 months */
                 if (mobilav==1)      /* Computed by stepm unit matrices, product of hstepm matrices, stored
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
                 else {      
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];  /* nhstepm age range expressed in number of stepm */
                 }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
                    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
               }    /* if (stepm >= YEARM) hstepm=1;*/
               if (h==(int)(calagedate+12*cpt)){    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
                 fprintf(ficresf," %.3f", kk1);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                          
               }    for (age=bage; age<=fage; age ++){ 
             }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* if (stepm >= YEARM) hstepm=1;*/
         }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
       }  
     }      /* 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 */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      
       hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   fclose(ficresf);      
 }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 /************** Forecasting ******************/      
 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){      printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      
   int *popage;      /* Computing expectancies */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;      for(i=1; i<=nlstate;i++)
   double *popeffectif,*popcount;        for(j=1; j<=nlstate;j++)
   double ***p3mat,***tabpop,***tabpopprev;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   char filerespop[FILENAMELENGTH];            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            /* 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]);*/
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   agelim=AGESUP;          }
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;  
        fprintf(ficreseij,"%3.0f",age );
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      for(i=1; i<=nlstate;i++){
          eip=0;
          for(j=1; j<=nlstate;j++){
   strcpy(filerespop,"pop");          eip +=eij[i][j][(int)age];
   strcat(filerespop,fileres);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
   if((ficrespop=fopen(filerespop,"w"))==NULL) {        }
     printf("Problem with forecast resultfile: %s\n", filerespop);        fprintf(ficreseij,"%9.4f", eip );
     fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);      }
   }      fprintf(ficreseij,"\n");
   printf("Computing forecasting: result on file '%s' \n", filerespop);      
   fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);    }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    printf("\n");
     fprintf(ficlog,"\n");
   if (mobilav==1) {    
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  }
     movingaverage(agedeb, fage, ageminpar, mobaverage);  
   }  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[] )
   
   stepsize=(int) (stepm+YEARM-1)/YEARM;  {
   if (stepm<=12) stepsize=1;    /* Covariances of health expectancies eij and of total life expectancies according
       to initial status i, ei. .
   agelim=AGESUP;    */
      int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   hstepm=1;    int nhstepma, nstepma; /* Decreasing with age */
   hstepm=hstepm/stepm;    double age, agelim, hf;
      double ***p3matp, ***p3matm, ***varhe;
   if (popforecast==1) {    double **dnewm,**doldm;
     if((ficpop=fopen(popfile,"r"))==NULL) {    double *xp, *xm;
       printf("Problem with population file : %s\n",popfile);exit(0);    double **gp, **gm;
       fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);    double ***gradg, ***trgradg;
     }    int theta;
     popage=ivector(0,AGESUP);  
     popeffectif=vector(0,AGESUP);    double eip, vip;
     popcount=vector(0,AGESUP);  
        varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     i=1;      xp=vector(1,npar);
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    xm=vector(1,npar);
        dnewm=matrix(1,nlstate*nlstate,1,npar);
     imx=i;    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];    
   }    pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   for(cptcov=1;cptcov<=i2;cptcov++){    fprintf(ficresstdeij,"# Age");
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    for(i=1; i<=nlstate;i++){
       k=k+1;      for(j=1; j<=nlstate;j++)
       fprintf(ficrespop,"\n#******");        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
       for(j=1;j<=cptcoveff;j++) {      fprintf(ficresstdeij," e%1d. ",i);
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    }
       }    fprintf(ficresstdeij,"\n");
       fprintf(ficrespop,"******\n");  
       fprintf(ficrespop,"# Age");    pstamp(ficrescveij);
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
       if (popforecast==1)  fprintf(ficrespop," [Population]");    fprintf(ficrescveij,"# Age");
          for(i=1; i<=nlstate;i++)
       for (cpt=0; cpt<=0;cpt++) {      for(j=1; j<=nlstate;j++){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);          cptj= (j-1)*nlstate+i;
                for(i2=1; i2<=nlstate;i2++)
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){          for(j2=1; j2<=nlstate;j2++){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            cptj2= (j2-1)*nlstate+i2;
           nhstepm = nhstepm/hstepm;            if(cptj2 <= cptj)
                        fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           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(ficrescveij,"\n");
            
           for (h=0; h<=nhstepm; h++){    if(estepm < stepm){
             if (h==(int) (calagedate+YEARM*cpt)) {      printf ("Problem %d lower than %d\n",estepm, stepm);
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    }
             }    else  hstepm=estepm;   
             for(j=1; j<=nlstate+ndeath;j++) {    /* We compute the life expectancy from trapezoids spaced every estepm months
               kk1=0.;kk2=0;     * This is mainly to measure the difference between two models: for example
               for(i=1; i<=nlstate;i++) {                   * if stepm=24 months pijx are given only every 2 years and by summing them
                 if (mobilav==1)     * we are calculating an estimate of the Life Expectancy assuming a linear 
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];     * progression in between and thus overestimating or underestimating according
                 else {     * to the curvature of the survival function. If, for the same date, we 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];     * estimate the model with stepm=1 month, we can keep estepm to 24 months
                 }     * to compare the new estimate of Life expectancy with the same linear 
               }     * hypothesis. A more precise result, taking into account a more precise
               if (h==(int)(calagedate+12*cpt)){     * curvature will be obtained if estepm is as small as stepm. */
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;  
                   /*fprintf(ficrespop," %.3f", kk1);    /* For example we decided to compute the life expectancy with the smallest unit */
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
               }       nhstepm is the number of hstepm from age to agelim 
             }       nstepm is the number of stepm from age to agelin. 
             for(i=1; i<=nlstate;i++){       Look at hpijx to understand the reason of that which relies in memory size
               kk1=0.;       and note for a fixed period like estepm months */
                 for(j=1; j<=nlstate;j++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];       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
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];       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.
     */
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);  
           }    /* If stepm=6 months */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* nhstepm age range expressed in number of stepm */
         }    agelim=AGESUP;
       }    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 */
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
           nhstepm = nhstepm/hstepm;    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
              gp=matrix(0,nhstepm,1,nlstate*nlstate);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
           oldm=oldms;savm=savms;  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      for (age=bage; age<=fage; age ++){ 
           for (h=0; h<=nhstepm; h++){      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             if (h==(int) (calagedate+YEARM*cpt)) {      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);      /* if (stepm >= YEARM) hstepm=1;*/
             }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
             for(j=1; j<=nlstate+ndeath;j++) {  
               kk1=0.;kk2=0;      /* If stepm=6 months */
               for(i=1; i<=nlstate;i++) {                    /* Computed by stepm unit matrices, product of hstepma matrices, stored
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];             in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
               }      
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
             }  
           }      /* Computing  Variances of health expectancies */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
         }         decrease memory allocation */
       }      for(theta=1; theta <=npar; theta++){
    }        for(i=1; i<=npar; i++){ 
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
            xm[i] = x[i] - (i==theta ?delti[theta]:0);
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        }
         hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   if (popforecast==1) {        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     free_ivector(popage,0,AGESUP);    
     free_vector(popeffectif,0,AGESUP);        for(j=1; j<= nlstate; j++){
     free_vector(popcount,0,AGESUP);          for(i=1; i<=nlstate; i++){
   }            for(h=0; h<=nhstepm-1; h++){
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   fclose(ficrespop);            }
 }          }
         }
 /***********************************************/       
 /**************** Main Program *****************/        for(ij=1; ij<= nlstate*nlstate; ij++)
 /***********************************************/          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
 int main(int argc, char *argv[])          }
 {      }/* End theta */
       
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      
   double agedeb, agefin,hf;      for(h=0; h<=nhstepm-1; h++)
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;        for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
   double fret;            trgradg[h][j][theta]=gradg[h][theta][j];
   double **xi,tmp,delta;      
   
   double dum; /* Dummy variable */       for(ij=1;ij<=nlstate*nlstate;ij++)
   double ***p3mat;        for(ji=1;ji<=nlstate*nlstate;ji++)
   int *indx;          varhe[ij][ji][(int)age] =0.;
   char line[MAXLINE], linepar[MAXLINE];  
   char path[80],pathc[80],pathcd[80],pathtot[80],model[80];       printf("%d|",(int)age);fflush(stdout);
   int firstobs=1, lastobs=10;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   int sdeb, sfin; /* Status at beginning and end */       for(h=0;h<=nhstepm-1;h++){
   int c,  h , cpt,l;        for(k=0;k<=nhstepm-1;k++){
   int ju,jl, mi;          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          for(ij=1;ij<=nlstate*nlstate;ij++)
   int mobilav=0,popforecast=0;            for(ji=1;ji<=nlstate*nlstate;ji++)
   int hstepm, nhstepm;              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;        }
       }
   double bage, fage, age, agelim, agebase;  
   double ftolpl=FTOL;      /* Computing expectancies */
   double **prlim;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   double *severity;      for(i=1; i<=nlstate;i++)
   double ***param; /* Matrix of parameters */        for(j=1; j<=nlstate;j++)
   double  *p;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   double **matcov; /* Matrix of covariance */            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
   double ***delti3; /* Scale */            
   double *delti; /* Scale */            /* 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]);*/
   double ***eij, ***vareij;  
   double **varpl; /* Variances of prevalence limits by age */          }
   double *epj, vepp;  
   double kk1, kk2;      fprintf(ficresstdeij,"%3.0f",age );
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;      for(i=1; i<=nlstate;i++){
          eip=0.;
         vip=0.;
   char *alph[]={"a","a","b","c","d","e"}, str[4];        for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
           for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
   char z[1]="c", occ;            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
 #include <sys/time.h>          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
 #include <time.h>        }
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
        }
   /* long total_usecs;      fprintf(ficresstdeij,"\n");
   struct timeval start_time, end_time;  
        fprintf(ficrescveij,"%3.0f",age );
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      for(i=1; i<=nlstate;i++)
   getcwd(pathcd, size);        for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
   printf("\n%s",version);          for(i2=1; i2<=nlstate;i2++)
   if(argc <=1){            for(j2=1; j2<=nlstate;j2++){
     printf("\nEnter the parameter file name: ");              cptj2= (j2-1)*nlstate+i2;
     scanf("%s",pathtot);              if(cptj2 <= cptj)
   }                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   else{            }
     strcpy(pathtot,argv[1]);        }
   }      fprintf(ficrescveij,"\n");
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/     
   /*cygwin_split_path(pathtot,path,optionfile);    }
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   /* cutv(path,optionfile,pathtot,'\\');*/    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   chdir(path);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   replace(pathc,path);    printf("\n");
     fprintf(ficlog,"\n");
 /*-------- arguments in the command line --------*/  
     free_vector(xm,1,npar);
   /* Log file */    free_vector(xp,1,npar);
   strcat(filelog, optionfilefiname);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   strcat(filelog,".log");    /* */    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   if((ficlog=fopen(filelog,"w"))==NULL)    {    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     printf("Problem with logfile %s\n",filelog);  }
     goto end;  
   }  /************ Variance ******************/
   fprintf(ficlog,"Log filename:%s\n",filelog);  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[])
   fprintf(ficlog,"\n%s",version);  {
   fprintf(ficlog,"\nEnter the parameter file name: ");    /* Variance of health expectancies */
   fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   fflush(ficlog);    /* double **newm;*/
     double **dnewm,**doldm;
   /* */    double **dnewmp,**doldmp;
   strcpy(fileres,"r");    int i, j, nhstepm, hstepm, h, nstepm ;
   strcat(fileres, optionfilefiname);    int k, cptcode;
   strcat(fileres,".txt");    /* Other files have txt extension */    double *xp;
     double **gp, **gm;  /* for var eij */
   /*---------arguments file --------*/    double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    double *gpp, *gmp; /* for var p point j */
     printf("Problem with optionfile %s\n",optionfile);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     fprintf(ficlog,"Problem with optionfile %s\n",optionfile);    double ***p3mat;
     goto end;    double age,agelim, hf;
   }    double ***mobaverage;
     int theta;
   strcpy(filereso,"o");    char digit[4];
   strcat(filereso,fileres);    char digitp[25];
   if((ficparo=fopen(filereso,"w"))==NULL) {  
     printf("Problem with Output resultfile: %s\n", filereso);    char fileresprobmorprev[FILENAMELENGTH];
     fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);  
     goto end;    if(popbased==1){
   }      if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
   /* Reads comments: lines beginning with '#' */      else strcpy(digitp,"-populbased-nomobil-");
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    else 
     fgets(line, MAXLINE, ficpar);      strcpy(digitp,"-stablbased-");
     puts(line);  
     fputs(line,ficparo);    if (mobilav!=0) {
   }      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   ungetc(c,ficpar);      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   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);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
   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);    }
 while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    strcpy(fileresprobmorprev,"prmorprev"); 
     fgets(line, MAXLINE, ficpar);    sprintf(digit,"%-d",ij);
     puts(line);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     fputs(line,ficparo);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
   }    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   ungetc(c,ficpar);    strcat(fileresprobmorprev,fileres);
      if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
          printf("Problem with resultfile: %s\n", fileresprobmorprev);
   covar=matrix(0,NCOVMAX,1,n);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   cptcovn=0;    }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
   ncovmodel=2+cptcovn;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    pstamp(ficresprobmorprev);
      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);
   /* Read guess parameters */    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   /* Reads comments: lines beginning with '#' */    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficresprobmorprev," p.%-d SE",j);
     ungetc(c,ficpar);      for(i=1; i<=nlstate;i++)
     fgets(line, MAXLINE, ficpar);        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     puts(line);    }  
     fputs(line,ficparo);    fprintf(ficresprobmorprev,"\n");
   }    fprintf(ficgp,"\n# Routine varevsij");
   ungetc(c,ficpar);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
      fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
     for(i=1; i <=nlstate; i++)  /*   } */
     for(j=1; j <=nlstate+ndeath-1; j++){    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    pstamp(ficresvij);
       fprintf(ficparo,"%1d%1d",i1,j1);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
       if(mle==1)    if(popbased==1)
         printf("%1d%1d",i,j);      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);
       fprintf(ficlog,"%1d%1d",i,j);    else
       for(k=1; k<=ncovmodel;k++){      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
         fscanf(ficpar," %lf",&param[i][j][k]);    fprintf(ficresvij,"# Age");
         if(mle==1){    for(i=1; i<=nlstate;i++)
           printf(" %lf",param[i][j][k]);      for(j=1; j<=nlstate;j++)
           fprintf(ficlog," %lf",param[i][j][k]);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
         }    fprintf(ficresvij,"\n");
         else  
           fprintf(ficlog," %lf",param[i][j][k]);    xp=vector(1,npar);
         fprintf(ficparo," %lf",param[i][j][k]);    dnewm=matrix(1,nlstate,1,npar);
       }    doldm=matrix(1,nlstate,1,nlstate);
       fscanf(ficpar,"\n");    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       if(mle==1)    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         printf("\n");  
       fprintf(ficlog,"\n");    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       fprintf(ficparo,"\n");    gpp=vector(nlstate+1,nlstate+ndeath);
     }    gmp=vector(nlstate+1,nlstate+ndeath);
      trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    
     if(estepm < stepm){
   p=param[1][1];      printf ("Problem %d lower than %d\n",estepm, stepm);
      }
   /* Reads comments: lines beginning with '#' */    else  hstepm=estepm;   
   while((c=getc(ficpar))=='#' && c!= EOF){    /* For example we decided to compute the life expectancy with the smallest unit */
     ungetc(c,ficpar);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     fgets(line, MAXLINE, ficpar);       nhstepm is the number of hstepm from age to agelim 
     puts(line);       nstepm is the number of stepm from age to agelin. 
     fputs(line,ficparo);       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
   ungetc(c,ficpar);       survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */       results. So we changed our mind and took the option of the best precision.
   for(i=1; i <=nlstate; i++){    */
     for(j=1; j <=nlstate+ndeath-1; j++){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       fscanf(ficpar,"%1d%1d",&i1,&j1);    agelim = AGESUP;
       printf("%1d%1d",i,j);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       fprintf(ficparo,"%1d%1d",i1,j1);      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       for(k=1; k<=ncovmodel;k++){      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         fscanf(ficpar,"%le",&delti3[i][j][k]);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         printf(" %le",delti3[i][j][k]);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
         fprintf(ficparo," %le",delti3[i][j][k]);      gp=matrix(0,nhstepm,1,nlstate);
       }      gm=matrix(0,nhstepm,1,nlstate);
       fscanf(ficpar,"\n");  
       printf("\n");  
       fprintf(ficparo,"\n");      for(theta=1; theta <=npar; theta++){
     }        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   delti=delti3[1][1];        }
          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   /* Reads comments: lines beginning with '#' */        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);        if (popbased==1) {
     fgets(line, MAXLINE, ficpar);          if(mobilav ==0){
     puts(line);            for(i=1; i<=nlstate;i++)
     fputs(line,ficparo);              prlim[i][i]=probs[(int)age][i][ij];
   }          }else{ /* mobilav */ 
   ungetc(c,ficpar);            for(i=1; i<=nlstate;i++)
                prlim[i][i]=mobaverage[(int)age][i][ij];
   matcov=matrix(1,npar,1,npar);          }
   for(i=1; i <=npar; i++){        }
     fscanf(ficpar,"%s",&str);    
     if(mle==1)        for(j=1; j<= nlstate; j++){
       printf("%s",str);          for(h=0; h<=nhstepm; h++){
     fprintf(ficlog,"%s",str);            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     fprintf(ficparo,"%s",str);              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     for(j=1; j <=i; j++){          }
       fscanf(ficpar," %le",&matcov[i][j]);        }
       if(mle==1){        /* This for computing probability of death (h=1 means
         printf(" %.5le",matcov[i][j]);           computed over hstepm matrices product = hstepm*stepm months) 
         fprintf(ficlog," %.5le",matcov[i][j]);           as a weighted average of prlim.
       }        */
       else        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         fprintf(ficlog," %.5le",matcov[i][j]);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
       fprintf(ficparo," %.5le",matcov[i][j]);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
     }        }    
     fscanf(ficpar,"\n");        /* end probability of death */
     if(mle==1)  
       printf("\n");        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
     fprintf(ficlog,"\n");          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     fprintf(ficparo,"\n");        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   for(i=1; i <=npar; i++)   
     for(j=i+1;j<=npar;j++)        if (popbased==1) {
       matcov[i][j]=matcov[j][i];          if(mobilav ==0){
                for(i=1; i<=nlstate;i++)
   if(mle==1)              prlim[i][i]=probs[(int)age][i][ij];
     printf("\n");          }else{ /* mobilav */ 
   fprintf(ficlog,"\n");            for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
     /*-------- Rewriting paramater file ----------*/        }
      strcpy(rfileres,"r");    /* "Rparameterfile */  
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
      strcat(rfileres,".");    /* */          for(h=0; h<=nhstepm; h++){
      strcat(rfileres,optionfilext);    /* Other files have txt extension */            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
     if((ficres =fopen(rfileres,"w"))==NULL) {              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
       printf("Problem writing new parameter file: %s\n", fileres);goto end;          }
       fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;        }
     }        /* This for computing probability of death (h=1 means
     fprintf(ficres,"#%s\n",version);           computed over hstepm matrices product = hstepm*stepm months) 
               as a weighted average of prlim.
     /*-------- data file ----------*/        */
     if((fic=fopen(datafile,"r"))==NULL)    {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       printf("Problem with datafile: %s\n", datafile);goto end;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     }        }    
         /* end probability of death */
     n= lastobs;  
     severity = vector(1,maxwav);        for(j=1; j<= nlstate; j++) /* vareij */
     outcome=imatrix(1,maxwav+1,1,n);          for(h=0; h<=nhstepm; h++){
     num=ivector(1,n);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     moisnais=vector(1,n);          }
     annais=vector(1,n);  
     moisdc=vector(1,n);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     andc=vector(1,n);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     agedc=vector(1,n);        }
     cod=ivector(1,n);  
     weight=vector(1,n);      } /* End theta */
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */  
     mint=matrix(1,maxwav,1,n);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     anint=matrix(1,maxwav,1,n);  
     s=imatrix(1,maxwav+1,1,n);      for(h=0; h<=nhstepm; h++) /* veij */
     adl=imatrix(1,maxwav+1,1,n);            for(j=1; j<=nlstate;j++)
     tab=ivector(1,NCOVMAX);          for(theta=1; theta <=npar; theta++)
     ncodemax=ivector(1,8);            trgradg[h][j][theta]=gradg[h][theta][j];
   
     i=1;      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     while (fgets(line, MAXLINE, fic) != NULL)    {        for(theta=1; theta <=npar; theta++)
       if ((i >= firstobs) && (i <=lastobs)) {          trgradgp[j][theta]=gradgp[theta][j];
            
         for (j=maxwav;j>=1;j--){  
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
           strcpy(line,stra);      for(i=1;i<=nlstate;i++)
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        for(j=1;j<=nlstate;j++)
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          vareij[i][j][(int)age] =0.;
         }  
              for(h=0;h<=nhstepm;h++){
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        for(k=0;k<=nhstepm;k++){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);          for(i=1;i<=nlstate;i++)
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);            for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        }
         for (j=ncovcol;j>=1;j--){      }
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    
         }      /* pptj */
         num[i]=atol(stra);      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
              matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){      for(j=nlstate+1;j<=nlstate+ndeath;j++)
           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;}*/        for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
         i=i+1;      /* end ppptj */
       }      /*  x centered again */
     }      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     /* printf("ii=%d", ij);      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
        scanf("%d",i);*/   
   imx=i-1; /* Number of individuals */      if (popbased==1) {
         if(mobilav ==0){
   /* for (i=1; i<=imx; i++){          for(i=1; i<=nlstate;i++)
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;            prlim[i][i]=probs[(int)age][i][ij];
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;        }else{ /* mobilav */ 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;          for(i=1; i<=nlstate;i++)
     }*/            prlim[i][i]=mobaverage[(int)age][i][ij];
    /*  for (i=1; i<=imx; i++){        }
      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]));}*/               
        /* This for computing probability of death (h=1 means
           computed over hstepm (estepm) matrices product = hstepm*stepm months) 
   /* Calculation of the number of parameter from char model*/         as a weighted average of prlim.
   Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */      */
   Tprod=ivector(1,15);      for(j=nlstate+1;j<=nlstate+ndeath;j++){
   Tvaraff=ivector(1,15);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
   Tvard=imatrix(1,15,1,2);          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   Tage=ivector(1,15);            }    
          /* end probability of death */
   if (strlen(model) >1){  
     j=0, j1=0, k1=1, k2=1;      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     j=nbocc(model,'+');      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     j1=nbocc(model,'*');        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
     cptcovn=j+1;        for(i=1; i<=nlstate;i++){
     cptcovprod=j1;          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
            }
     strcpy(modelsav,model);      } 
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){      fprintf(ficresprobmorprev,"\n");
       printf("Error. Non available option model=%s ",model);  
       fprintf(ficlog,"Error. Non available option model=%s ",model);      fprintf(ficresvij,"%.0f ",age );
       goto end;      for(i=1; i<=nlstate;i++)
     }        for(j=1; j<=nlstate;j++){
              fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
     for(i=(j+1); i>=1;i--){        }
       cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */      fprintf(ficresvij,"\n");
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyze it */      free_matrix(gp,0,nhstepm,1,nlstate);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/      free_matrix(gm,0,nhstepm,1,nlstate);
       /*scanf("%d",i);*/      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       if (strchr(strb,'*')) {  /* Model includes a product */      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
         cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         if (strcmp(strc,"age")==0) { /* Vn*age */    } /* End age */
           cptcovprod--;    free_vector(gpp,nlstate+1,nlstate+ndeath);
           cutv(strb,stre,strd,'V');    free_vector(gmp,nlstate+1,nlstate+ndeath);
           Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
           cptcovage++;    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
             Tage[cptcovage]=i;    fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
             /*printf("stre=%s ", stre);*/    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
         }    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
         else if (strcmp(strd,"age")==0) { /* or age*Vn */  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
           cptcovprod--;  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
           cutv(strb,stre,strc,'V');  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
           Tvar[i]=atoi(stre);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
           cptcovage++;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
           Tage[cptcovage]=i;    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 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 {  /* Age is not in the model */    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);
           cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/    /*  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);
           Tvar[i]=ncovcol+k1;  */
           cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
           Tprod[k1]=i;    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
           Tvard[k1][1]=atoi(strc); /* m*/  
           Tvard[k1][2]=atoi(stre); /* n */    free_vector(xp,1,npar);
           Tvar[cptcovn+k2]=Tvard[k1][1];    free_matrix(doldm,1,nlstate,1,nlstate);
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    free_matrix(dnewm,1,nlstate,1,npar);
           for (k=1; k<=lastobs;k++)    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
           k1++;    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           k2=k2+2;    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         }    fclose(ficresprobmorprev);
       }    fflush(ficgp);
       else { /* no more sum */    fflush(fichtm); 
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/  }  /* end varevsij */
        /*  scanf("%d",i);*/  
       cutv(strd,strc,strb,'V');  /************ Variance of prevlim ******************/
       Tvar[i]=atoi(strc);  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[])
       }  {
       strcpy(modelsav,stra);      /* Variance of prevalence limit */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
         scanf("%d",i);*/    double **newm;
     } /* end of loop + */    double **dnewm,**doldm;
   } /* end model */    int i, j, nhstepm, hstepm;
      int k, cptcode;
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    double *xp;
   printf("cptcovprod=%d ", cptcovprod);    double *gp, *gm;
   fprintf(ficlog,"cptcovprod=%d ", cptcovprod);    double **gradg, **trgradg;
   scanf("%d ",i);*/    double age,agelim;
     fclose(fic);    int theta;
     
     /*  if(mle==1){*/    pstamp(ficresvpl);
     if (weightopt != 1) { /* Maximisation without weights*/    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
       for(i=1;i<=n;i++) weight[i]=1.0;    fprintf(ficresvpl,"# Age");
     }    for(i=1; i<=nlstate;i++)
     /*-calculation of age at interview from date of interview and age at death -*/        fprintf(ficresvpl," %1d-%1d",i,i);
     agev=matrix(1,maxwav,1,imx);    fprintf(ficresvpl,"\n");
   
     for (i=1; i<=imx; i++) {    xp=vector(1,npar);
       for(m=2; (m<= maxwav); m++) {    dnewm=matrix(1,nlstate,1,npar);
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    doldm=matrix(1,nlstate,1,nlstate);
          anint[m][i]=9999;    
          s[m][i]=-1;    hstepm=1*YEARM; /* Every year of age */
        }    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;    agelim = AGESUP;
       }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     }      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
     for (i=1; i<=imx; i++)  {      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);      gradg=matrix(1,npar,1,nlstate);
       for(m=1; (m<= maxwav); m++){      gp=vector(1,nlstate);
         if(s[m][i] >0){      gm=vector(1,nlstate);
           if (s[m][i] >= nlstate+1) {  
             if(agedc[i]>0)      for(theta=1; theta <=npar; theta++){
               if(moisdc[i]!=99 && andc[i]!=9999)        for(i=1; i<=npar; i++){ /* Computes gradient */
                 agev[m][i]=agedc[i];          xp[i] = x[i] + (i==theta ?delti[theta]:0);
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/        }
            else {        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
               if (andc[i]!=9999){        for(i=1;i<=nlstate;i++)
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          gp[i] = prlim[i][i];
               fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);      
               agev[m][i]=-1;        for(i=1; i<=npar; i++) /* Computes gradient */
               }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
             }        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
           }        for(i=1;i<=nlstate;i++)
           else if(s[m][i] !=9){ /* Should no more exist */          gm[i] = prlim[i][i];
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);  
             if(mint[m][i]==99 || anint[m][i]==9999)        for(i=1;i<=nlstate;i++)
               agev[m][i]=1;          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
             else if(agev[m][i] <agemin){      } /* End theta */
               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);*/      trgradg =matrix(1,nlstate,1,npar);
             }  
             else if(agev[m][i] >agemax){      for(j=1; j<=nlstate;j++)
               agemax=agev[m][i];        for(theta=1; theta <=npar; theta++)
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/          trgradg[j][theta]=gradg[theta][j];
             }  
             /*agev[m][i]=anint[m][i]-annais[i];*/      for(i=1;i<=nlstate;i++)
             /*   agev[m][i] = age[i]+2*m;*/        varpl[i][(int)age] =0.;
           }      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
           else { /* =9 */      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
             agev[m][i]=1;      for(i=1;i<=nlstate;i++)
             s[m][i]=-1;        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
           }  
         }      fprintf(ficresvpl,"%.0f ",age );
         else /*= 0 Unknown */      for(i=1; i<=nlstate;i++)
           agev[m][i]=1;        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       }      fprintf(ficresvpl,"\n");
          free_vector(gp,1,nlstate);
     }      free_vector(gm,1,nlstate);
     for (i=1; i<=imx; i++)  {      free_matrix(gradg,1,npar,1,nlstate);
       for(m=1; (m<= maxwav); m++){      free_matrix(trgradg,1,nlstate,1,npar);
         if (s[m][i] > (nlstate+ndeath)) {    } /* End age */
           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);      free_vector(xp,1,npar);
           goto end;    free_matrix(doldm,1,nlstate,1,npar);
         }    free_matrix(dnewm,1,nlstate,1,nlstate);
       }  
     }  }
   
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  /************ Variance of one-step probabilities  ******************/
  fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  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[])
   {
     free_vector(severity,1,maxwav);    int i, j=0,  i1, k1, l1, t, tj;
     free_imatrix(outcome,1,maxwav+1,1,n);    int k2, l2, j1,  z1;
     free_vector(moisnais,1,n);    int k=0,l, cptcode;
     free_vector(annais,1,n);    int first=1, first1, first2;
     /* free_matrix(mint,1,maxwav,1,n);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
        free_matrix(anint,1,maxwav,1,n);*/    double **dnewm,**doldm;
     free_vector(moisdc,1,n);    double *xp;
     free_vector(andc,1,n);    double *gp, *gm;
     double **gradg, **trgradg;
        double **mu;
     wav=ivector(1,imx);    double age,agelim, cov[NCOVMAX+1];
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    int theta;
        char fileresprob[FILENAMELENGTH];
     /* Concatenates waves */    char fileresprobcov[FILENAMELENGTH];
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    char fileresprobcor[FILENAMELENGTH];
     double ***varpij;
   
       Tcode=ivector(1,100);    strcpy(fileresprob,"prob"); 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    strcat(fileresprob,fileres);
       ncodemax[1]=1;    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      printf("Problem with resultfile: %s\n", fileresprob);
            fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
    codtab=imatrix(1,100,1,10);    }
    h=0;    strcpy(fileresprobcov,"probcov"); 
    m=pow(2,cptcoveff);    strcat(fileresprobcov,fileres);
      if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
    for(k=1;k<=cptcoveff; k++){      printf("Problem with resultfile: %s\n", fileresprobcov);
      for(i=1; i <=(m/pow(2,k));i++){      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
        for(j=1; j <= ncodemax[k]; j++){    }
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    strcpy(fileresprobcor,"probcor"); 
            h++;    strcat(fileresprobcor,fileres);
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/      printf("Problem with resultfile: %s\n", fileresprobcor);
          }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
        }    }
      }    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
    }    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
       codtab[1][2]=1;codtab[2][2]=2; */    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
    /* for(i=1; i <=m ;i++){    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
       for(k=1; k <=cptcovn; k++){    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    pstamp(ficresprob);
       }    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
       printf("\n");    fprintf(ficresprob,"# Age");
       }    pstamp(ficresprobcov);
       scanf("%d",i);*/    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
        fprintf(ficresprobcov,"# Age");
    /* Calculates basic frequencies. Computes observed prevalence at single age    pstamp(ficresprobcor);
        and prints on file fileres'p'. */    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcor,"# Age");
      
      
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    for(i=1; i<=nlstate;i++)
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(j=1; j<=(nlstate+ndeath);j++){
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresprobcov," p%1d-%1d ",i,j);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        fprintf(ficresprobcor," p%1d-%1d ",i,j);
            }  
     /* For Powell, parameters are in a vector p[] starting at p[1]   /* fprintf(ficresprob,"\n");
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    fprintf(ficresprobcov,"\n");
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficresprobcor,"\n");
    */
     if(mle==1){    xp=vector(1,npar);
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     }    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
        mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     /*--------- results files --------------*/    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     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);    first=1;
      fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
    jk=1;    fprintf(fichtm,"\n");
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");  
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
    fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
    for(i=1,jk=1; i <=nlstate; i++){    file %s<br>\n",optionfilehtmcov);
      for(k=1; k <=(nlstate+ndeath); k++){    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
        if (k != i)  and drawn. It helps understanding how is the covariance between two incidences.\
          {   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
            printf("%d%d ",i,k);    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. \
            fprintf(ficlog,"%d%d ",i,k);  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
            fprintf(ficres,"%1d%1d ",i,k);  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
            for(j=1; j <=ncovmodel; j++){  standard deviations wide on each axis. <br>\
              printf("%f ",p[jk]);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
              fprintf(ficlog,"%f ",p[jk]);   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
              fprintf(ficres,"%f ",p[jk]);  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
              jk++;  
            }    cov[1]=1;
            printf("\n");    /* tj=cptcoveff; */
            fprintf(ficlog,"\n");    tj = (int) pow(2,cptcoveff);
            fprintf(ficres,"\n");    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
          }    j1=0;
      }    for(j1=1; j1<=tj;j1++){
    }      /*for(i1=1; i1<=ncodemax[t];i1++){ */
    if(mle==1){      /*j1++;*/
      /* Computing hessian and covariance matrix */        if  (cptcovn>0) {
      ftolhess=ftol; /* Usually correct */          fprintf(ficresprob, "\n#********** Variable "); 
      hesscov(matcov, p, npar, delti, ftolhess, func);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    }          fprintf(ficresprob, "**********\n#\n");
    fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");          fprintf(ficresprobcov, "\n#********** Variable "); 
    printf("# Scales (for hessian or gradient estimation)\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");          fprintf(ficresprobcov, "**********\n#\n");
    for(i=1,jk=1; i <=nlstate; i++){          
      for(j=1; j <=nlstate+ndeath; j++){          fprintf(ficgp, "\n#********** Variable "); 
        if (j!=i) {          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
          fprintf(ficres,"%1d%1d",i,j);          fprintf(ficgp, "**********\n#\n");
          printf("%1d%1d",i,j);          
          fprintf(ficlog,"%1d%1d",i,j);          
          for(k=1; k<=ncovmodel;k++){          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
            printf(" %.5e",delti[jk]);          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            fprintf(ficlog," %.5e",delti[jk]);          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
            fprintf(ficres," %.5e",delti[jk]);          
            jk++;          fprintf(ficresprobcor, "\n#********** Variable ");    
          }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
          printf("\n");          fprintf(ficresprobcor, "**********\n#");    
          fprintf(ficlog,"\n");        }
          fprintf(ficres,"\n");        
        }        gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
      }        trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
    }        gp=vector(1,(nlstate)*(nlstate+ndeath));
            gm=vector(1,(nlstate)*(nlstate+ndeath));
    k=1;        for (age=bage; age<=fage; age ++){ 
    fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");          cov[2]=age;
    if(mle==1)          for (k=1; k<=cptcovn;k++) {
      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");            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];/* j1 1 2 3 4
    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");                                                           * 1  1 1 1 1
    for(i=1;i<=npar;i++){                                                           * 2  2 1 1 1
      /*  if (k>nlstate) k=1;                                                           * 3  1 2 1 1
          i1=(i-1)/(ncovmodel*nlstate)+1;                                                           */
          fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);            /* nbcode[1][1]=0 nbcode[1][2]=1;*/
          printf("%s%d%d",alph[k],i1,tab[i]);*/          }
      fprintf(ficres,"%3d",i);          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
      if(mle==1)          for (k=1; k<=cptcovprod;k++)
        printf("%3d",i);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
      fprintf(ficlog,"%3d",i);          
      for(j=1; j<=i;j++){      
        fprintf(ficres," %.5e",matcov[i][j]);          for(theta=1; theta <=npar; theta++){
        if(mle==1)            for(i=1; i<=npar; i++)
          printf(" %.5e",matcov[i][j]);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
        fprintf(ficlog," %.5e",matcov[i][j]);            
      }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
      fprintf(ficres,"\n");            
      if(mle==1)            k=0;
        printf("\n");            for(i=1; i<= (nlstate); i++){
      fprintf(ficlog,"\n");              for(j=1; j<=(nlstate+ndeath);j++){
      k++;                k=k+1;
    }                gp[k]=pmmij[i][j];
                  }
    while((c=getc(ficpar))=='#' && c!= EOF){            }
      ungetc(c,ficpar);            
      fgets(line, MAXLINE, ficpar);            for(i=1; i<=npar; i++)
      puts(line);              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
      fputs(line,ficparo);      
    }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
    ungetc(c,ficpar);            k=0;
    estepm=0;            for(i=1; i<=(nlstate); i++){
    fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);              for(j=1; j<=(nlstate+ndeath);j++){
    if (estepm==0 || estepm < stepm) estepm=stepm;                k=k+1;
    if (fage <= 2) {                gm[k]=pmmij[i][j];
      bage = ageminpar;              }
      fage = agemaxpar;            }
    }       
                for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
    fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
    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);  
              for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
    while((c=getc(ficpar))=='#' && c!= EOF){            for(theta=1; theta <=npar; theta++)
      ungetc(c,ficpar);              trgradg[j][theta]=gradg[theta][j];
      fgets(line, MAXLINE, ficpar);          
      puts(line);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
      fputs(line,ficparo);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
    }  
    ungetc(c,ficpar);          pmij(pmmij,cov,ncovmodel,x,nlstate);
            
    fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);          k=0;
    fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          for(i=1; i<=(nlstate); i++){
    fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);            for(j=1; j<=(nlstate+ndeath);j++){
                  k=k+1;
    while((c=getc(ficpar))=='#' && c!= EOF){              mu[k][(int) age]=pmmij[i][j];
      ungetc(c,ficpar);            }
      fgets(line, MAXLINE, ficpar);          }
      puts(line);          for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
      fputs(line,ficparo);            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
    }              varpij[i][j][(int)age] = doldm[i][j];
    ungetc(c,ficpar);  
            /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
    dateprev1=anprev1+mprev1/12.+jprev1/365.;            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
    dateprev2=anprev2+mprev2/12.+jprev2/365.;            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   fscanf(ficpar,"pop_based=%d\n",&popbased);  
   fprintf(ficparo,"pop_based=%d\n",popbased);            fprintf(ficresprob,"\n%d ",(int)age);
   fprintf(ficres,"pop_based=%d\n",popbased);            fprintf(ficresprobcov,"\n%d ",(int)age);
            fprintf(ficresprobcor,"\n%d ",(int)age);
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
     fgets(line, MAXLINE, ficpar);            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
     puts(line);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     fputs(line,ficparo);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
   }            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
   ungetc(c,ficpar);          }
           i=0;
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);          for (k=1; k<=(nlstate);k++){
 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 (l=1; l<=(nlstate+ndeath);l++){ 
 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);              i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
 while((c=getc(ficpar))=='#' && c!= EOF){              for (j=1; j<=i;j++){
     ungetc(c,ficpar);                /* printf(" k=%d l=%d i=%d j=%d\n",k,l,i,j);fflush(stdout); */
     fgets(line, MAXLINE, ficpar);                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
     puts(line);                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
     fputs(line,ficparo);              }
   }            }
   ungetc(c,ficpar);          }/* end of loop for state */
         } /* end of loop for age */
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);        free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);        free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);        free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        
         /* Confidence intervalle of pij  */
 /*------------ gnuplot -------------*/        /*
   strcpy(optionfilegnuplot,optionfilefiname);          fprintf(ficgp,"\nunset parametric;unset label");
   strcat(optionfilegnuplot,".gp");          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
     printf("Problem with file %s",optionfilegnuplot);          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);
   fclose(ficgp);          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
 /*--------- index.htm --------*/        */
   
   strcpy(optionfilehtm,optionfile);        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
   strcat(optionfilehtm,".htm");        first1=1;first2=2;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        for (k2=1; k2<=(nlstate);k2++){
     printf("Problem with %s \n",optionfilehtm), exit(0);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
   }            if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n            for (k1=1; k1<=(nlstate);k1++){
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
 \n                if(l1==k1) continue;
 Total number of observations=%d <br>\n                i=(k1-1)*(nlstate+ndeath)+l1;
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n                if(i<=j) continue;
 <hr  size=\"2\" color=\"#EC5E5E\">                for (age=bage; age<=fage; age ++){ 
  <ul><li><h4>Parameter files</h4>\n                  if ((int)age %5==0){
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
  - Log file of the run: <a href=\"%s\">%s</a><br>\n                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
  - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,filelog,filelog,optionfilegnuplot,optionfilegnuplot);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
   fclose(fichtm);                    mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);                    c12=cv12/sqrt(v1*v2);
                      /* Computing eigen value of matrix of covariance */
 /*------------ free_vector  -------------*/                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
  chdir(path);                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                      if ((lc2 <0) || (lc1 <0) ){
  free_ivector(wav,1,imx);                      if(first2==1){
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);                        first1=0;
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);                        printf("Strange: j1=%d 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. Probably WRONG RESULTS. See log file for details...\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
  free_ivector(num,1,n);                      }
  free_vector(agedc,1,n);                      fprintf(ficlog,"Strange: j1=%d 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. Probably WRONG RESULTS.\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);fflush(ficlog);
  /*free_matrix(covar,1,NCOVMAX,1,n);*/                      /* lc1=fabs(lc1); */ /* If we want to have them positive */
  fclose(ficparo);                      /* lc2=fabs(lc2); */
  fclose(ficres);                    }
   
                     /* Eigen vectors */
   /*--------------- Prevalence limit --------------*/                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                      /*v21=sqrt(1.-v11*v11); *//* error */
   strcpy(filerespl,"pl");                    v21=(lc1-v1)/cv12*v11;
   strcat(filerespl,fileres);                    v12=-v21;
   if((ficrespl=fopen(filerespl,"w"))==NULL) {                    v22=v11;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;                    tnalp=v21/v11;
     fprintf(ficlog,"Problem with Prev limit resultfile: %s\n", filerespl);goto end;                    if(first1==1){
   }                      first1=0;
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);                      printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
   fprintf(ficlog,"Computing prevalence limit: result on file '%s' \n", filerespl);                    }
   fprintf(ficrespl,"#Prevalence limit\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);
   fprintf(ficrespl,"#Age ");                    /*printf(fignu*/
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
   fprintf(ficrespl,"\n");                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                      if(first==1){
   prlim=matrix(1,nlstate,1,nlstate);                      first=0;
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      fprintf(ficgp,"\nset parametric;unset label");
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      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);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      fprintf(ficgp,"\nset ter png small size 320, 240");
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   k=0;  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
   agebase=ageminpar;                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
   agelim=agemaxpar;                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   ftolpl=1.e-10;                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   i1=cptcoveff;                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
   if (cptcovn < 1){i1=1;}                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
   for(cptcov=1;cptcov<=i1;cptcov++){                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                      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",\
         k=k+1;                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
         fprintf(ficrespl,"\n#******");                    }else{
         printf("\n#******");                      first=0;
         fprintf(ficlog,"\n#******");                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
         for(j=1;j<=cptcoveff;j++) {                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
           printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
           fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         }                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
         fprintf(ficrespl,"******\n");                    }/* if first */
         printf("******\n");                  } /* age mod 5 */
         fprintf(ficlog,"******\n");                } /* end loop age */
                        fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         for (age=agebase; age<=agelim; age++){                first=1;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);              } /*l12 */
           fprintf(ficrespl,"%.0f",age );            } /* k12 */
           for(i=1; i<=nlstate;i++)          } /*l1 */
           fprintf(ficrespl," %.5f", prlim[i][i]);        }/* k1 */
           fprintf(ficrespl,"\n");        /* } /* loop covariates */
         }    }
       }    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     }    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
   fclose(ficrespl);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   /*------------- h Pij x at various ages ------------*/    free_vector(xp,1,npar);
      fclose(ficresprob);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    fclose(ficresprobcov);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    fclose(ficresprobcor);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    fflush(ficgp);
     fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;    fflush(fichtmcov);
   }  }
   printf("Computing pij: result on file '%s' \n", filerespij);  
   fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);  
    /******************* Printing html file ***********/
   stepsize=(int) (stepm+YEARM-1)/YEARM;  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
   /*if (stepm<=24) stepsize=2;*/                    int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
   agelim=AGESUP;                    int popforecast, int estepm ,\
   hstepm=stepsize*YEARM; /* Every year of age */                    double jprev1, double mprev1,double anprev1, \
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */                    double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   /* hstepm=1;   aff par mois*/  
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
   k=0;     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   for(cptcov=1;cptcov<=i1;cptcov++){  </ul>");
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
       k=k+1;   - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
         fprintf(ficrespij,"\n#****** ");             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
         for(j=1;j<=cptcoveff;j++)     fprintf(fichtm,"\
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
         fprintf(ficrespij,"******\n");             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
             fprintf(fichtm,"\
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */     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): \
           /*      nhstepm=nhstepm*YEARM; aff par mois*/     <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     fprintf(fichtm,"\
           oldm=oldms;savm=savms;   - Population projections by age and states: \
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);       <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
           fprintf(ficrespij,"# Age");  
           for(i=1; i<=nlstate;i++)  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);   m=pow(2,cptcoveff);
           fprintf(ficrespij,"\n");   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
            for (h=0; h<=nhstepm; h++){  
             fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );   jj1=0;
             for(i=1; i<=nlstate;i++)   for(k1=1; k1<=m;k1++){
               for(j=1; j<=nlstate+ndeath;j++)     for(i1=1; i1<=ncodemax[k1];i1++){
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);       jj1++;
             fprintf(ficrespij,"\n");       if (cptcovn > 0) {
              }         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         for (cpt=1; cpt<=cptcoveff;cpt++) 
           fprintf(ficrespij,"\n");           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
         }         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
     }       }
   }       /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d_1.png\">%s%d_1.png</a><br> \
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);  <img src=\"%s%d_1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
   fclose(ficrespij);       fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d_2.png\">%s%d_2.png</a><br> \
   <img src=\"%s%d_2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
   /*---------- Forecasting ------------------*/         /* Period (stable) prevalence in each health state */
   if((stepm == 1) && (strcmp(model,".")==0)){         for(cpt=1; cpt<nlstate;cpt++){
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);           fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);  <img src=\"%s%d_%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
   }         }
   else{       for(cpt=1; cpt<=nlstate;cpt++) {
     erreur=108;          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> \
     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);  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
     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);       }
   }     } /* end i1 */
     }/* End k1 */
    fprintf(fichtm,"</ul>");
   /*---------- Health expectancies and variances ------------*/  
   
   strcpy(filerest,"t");   fprintf(fichtm,"\
   strcat(filerest,fileres);  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
   if((ficrest=fopen(filerest,"w"))==NULL) {   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  
     fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   }           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
   printf("Computing Total LEs with variances: file '%s' \n", filerest);   fprintf(fichtm,"\
   fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest);   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
   strcpy(filerese,"e");   fprintf(fichtm,"\
   strcat(filerese,fileres);   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   if((ficreseij=fopen(filerese,"w"))==NULL) {           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);   fprintf(fichtm,"\
     fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);   - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
   }     <a href=\"%s\">%s</a> <br>\n</li>",
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
   fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);   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): \
   strcpy(fileresv,"v");     <a href=\"%s\">%s</a> <br>\n</li>",
   strcat(fileresv,fileres);             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
   if((ficresvij=fopen(fileresv,"w"))==NULL) {   fprintf(fichtm,"\
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);   - 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",
     fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);           estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
   }   fprintf(fichtm,"\
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);   - 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",
   fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);           estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
   calagedate=-1;   fprintf(fichtm,"\
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);   - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){  /*  if(popforecast==1) fprintf(fichtm,"\n */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
       k=k+1;  /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
       fprintf(ficrest,"\n#****** ");  /*      <br>",fileres,fileres,fileres,fileres); */
       for(j=1;j<=cptcoveff;j++)  /*  else  */
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  /*    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(ficrest,"******\n");   fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
       fprintf(ficreseij,"\n#****** ");  
       for(j=1;j<=cptcoveff;j++)   m=pow(2,cptcoveff);
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
       fprintf(ficreseij,"******\n");  
    jj1=0;
       fprintf(ficresvij,"\n#****** ");   for(k1=1; k1<=m;k1++){
       for(j=1;j<=cptcoveff;j++)     for(i1=1; i1<=ncodemax[k1];i1++){
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       jj1++;
       fprintf(ficresvij,"******\n");       if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);         for (cpt=1; cpt<=cptcoveff;cpt++) 
       oldm=oldms;savm=savms;           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);           fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
         }
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);       for(cpt=1; cpt<=nlstate;cpt++) {
       oldm=oldms;savm=savms;         fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
       varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0);  prevalence (with 95%% confidence interval) in state (%d): %s%d_%d.png <br>\
       if(popbased==1){  <img src=\"%s%d_%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
         varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased);       }
        }       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
    true period expectancies (those weighted with period prevalences are also\
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");   drawn in addition to the population based expectancies computed using\
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);   observed and cahotic prevalences: %s%d.png<br>\
       fprintf(ficrest,"\n");  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
       epj=vector(1,nlstate+1);   }/* End k1 */
       for(age=bage; age <=fage ;age++){   fprintf(fichtm,"</ul>");
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);   fflush(fichtm);
         if (popbased==1) {  }
           for(i=1; i<=nlstate;i++)  
             prlim[i][i]=probs[(int)age][i][k];  /******************* Gnuplot file **************/
         }  void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
          
         fprintf(ficrest," %4.0f",age);    char dirfileres[132],optfileres[132];
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    int ng=0;
             epj[j] += prlim[i][i]*eij[i][j][(int)age];  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/  /*     printf("Problem with file %s",optionfilegnuplot); */
           }  /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
           epj[nlstate+1] +=epj[j];  /*   } */
         }  
     /*#ifdef windows */
         for(i=1, vepp=0.;i <=nlstate;i++)    fprintf(ficgp,"cd \"%s\" \n",pathc);
           for(j=1;j <=nlstate;j++)      /*#endif */
             vepp += vareij[i][j][(int)age];    m=pow(2,cptcoveff);
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));  
         for(j=1;j <=nlstate;j++){    strcpy(dirfileres,optionfilefiname);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));    strcpy(optfileres,"vpl");
         }   /* 1eme*/
         fprintf(ficrest,"\n");    fprintf(ficgp,"\n# 1st: Period (stable) prevalence with CI: 'vpl' files\n");
       }    for (cpt=1; cpt<= nlstate ; cpt ++) {
     }      for (k1=1; k1<= m ; k1 ++) { /* plot [100000000000000000000:-100000000000000000000] "mysbiaspar/vplrmysbiaspar.txt to check */
   }       fprintf(ficgp,"\nset out \"%s%d_%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
 free_matrix(mint,1,maxwav,1,n);       fprintf(ficgp,"\n#set out \"v%s%d_%d.png\" \n",optionfilefiname,cpt,k1);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);       fprintf(ficgp,"set xlabel \"Age\" \n\
     free_vector(weight,1,n);  set ylabel \"Probability\" \n\
   fclose(ficreseij);  set ter png small size 320, 240\n\
   fclose(ficresvij);  plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   fclose(ficrest);  
   fclose(ficpar);       for (i=1; i<= nlstate ; i ++) {
   free_vector(epj,1,nlstate+1);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
           else        fprintf(ficgp," \%%*lf (\%%*lf)");
   /*------- Variance limit prevalence------*/         }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l lt 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
   strcpy(fileresvpl,"vpl");       for (i=1; i<= nlstate ; i ++) {
   strcat(fileresvpl,fileres);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {         else fprintf(ficgp," \%%*lf (\%%*lf)");
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);       } 
     exit(0);       fprintf(ficgp,"\" t\"95\%% CI\" w l lt 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
   }       for (i=1; i<= nlstate ; i ++) {
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
   k=0;       }  
   for(cptcov=1;cptcov<=i1;cptcov++){       fprintf(ficgp,"\" t\"\" w l lt 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){     }
       k=k+1;    }
       fprintf(ficresvpl,"\n#****** ");    /*2 eme*/
       for(j=1;j<=cptcoveff;j++)    fprintf(ficgp,"\n# 2nd: Total life expectancy with CI: 't' files\n");
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficresvpl,"******\n");      fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
            fprintf(ficgp,"set ylabel \"Years\" \nset ter png small size 320, 240\nplot [%.f:%.f] ",ageminpar,fage);
       varpl=matrix(1,nlstate,(int) bage, (int) fage);      
       oldm=oldms;savm=savms;      for (i=1; i<= nlstate+1 ; i ++) {
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);        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)");
   fclose(ficresvpl);          else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
   /*---------- End : free ----------------*/        if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        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);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        for (j=1; j<= nlstate+1 ; j ++) {
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
            else fprintf(ficgp," \%%*lf (\%%*lf)");
          }   
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        fprintf(ficgp,"\" t\"\" w l lt 0,");
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for (j=1; j<= nlstate+1 ; j ++) {
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
            else fprintf(ficgp," \%%*lf (\%%*lf)");
   free_matrix(matcov,1,npar,1,npar);        }   
   free_vector(delti,1,npar);        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l lt 0");
   free_matrix(agev,1,maxwav,1,imx);        else fprintf(ficgp,"\" t\"\" w l lt 0,");
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);      }
     }
   fprintf(fichtm,"\n</body>");    
   fclose(fichtm);    /*3eme*/
   fclose(ficgp);    
      for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
   if(erreur >0){        /*       k=2+nlstate*(2*cpt-2); */
     printf("End of Imach with error or warning %d\n",erreur);        k=2+(nlstate+1)*(cpt-1);
     fprintf(ficlog,"End of Imach with error or warning %d\n",erreur);        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
   }else{        fprintf(ficgp,"set ter png small size 320, 240\n\
    printf("End of Imach\n");  plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
    fprintf(ficlog,"End of Imach\n");        /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
   }          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
   printf("See log file on %s\n",filelog);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
   fclose(ficlog);          fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
            fprintf(ficgp,"\" t \"e%d1\" w l",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);*/          
   /*printf("Total time was %d uSec.\n", total_usecs);*/        */
   /*------ End -----------*/        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);*/
  end:          
 #ifdef windows        } 
   /* chdir(pathcd);*/        fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
 #endif      }
  /*system("wgnuplot graph.plt");*/    }
  /*system("../gp37mgw/wgnuplot graph.plt");*/    
  /*system("cd ../gp37mgw");*/    /* CV preval stable (period) */
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/    for (k1=1; k1<= m ; k1 ++) { /* For each multivariate if any */
  strcpy(plotcmd,GNUPLOTPROGRAM);      for (cpt=1; cpt<=nlstate ; cpt ++) { /* For each life state */
  strcat(plotcmd," ");        k=3;
  strcat(plotcmd,optionfilegnuplot);        fprintf(ficgp,"\n#\n#\n#CV preval stable (period): 'pij' files, cov=%d state=%d",k1, cpt);
  system(plotcmd);        fprintf(ficgp,"\nset out \"%s%d_%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         l=(nlstate+ndeath)*(cpt-1)+1;
 #ifdef windows        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   while (z[0] != 'q') {  set ter png small size 320, 240\n\
     /* chdir(path); */  unset log y\n\
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");  plot [%.f:%.f]  ", ageminpar, agemaxpar);
     scanf("%s",z);        for (i=1; i<= nlstate ; i ++){
     if (z[0] == 'c') system("./imach");          if(i==1)
     else if (z[0] == 'e') system(optionfilehtm);            fprintf(ficgp,"\"%s\"",subdirf2(fileres,"pij"));
     else if (z[0] == 'g') system(plotcmd);          else
     else if (z[0] == 'q') exit(0);            fprintf(ficgp,", '' ");
   }          fprintf(ficgp," u ($1==%d ? ($3):1/0):($%d/($%d",k1,k+l,k+l);
 #endif          for (j=1; j<= (nlstate-1) ; j ++)
 }            fprintf(ficgp,"+$%d",k+l+j);
           fprintf(ficgp,")) t \"prev(%d,%d)\" w l",i,cpt);
         } /* nlstate */
         fprintf(ficgp,"\n");
       } /* end cpt state*/ 
     } /* end covariate */  
     
     /* 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");
           }
         }
       }
      }
     /*goto avoid;*/
      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 size 320, 240\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  /* if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /\* Bug valgrind *\/ */
                  /*        /\*fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);*\/ */
                  /*        ij++; */
                  /* } */
                  /* else */
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    /* if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { */
                    /*   fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]); */
                    /*   ij++; */
                    /* } */
                    /* else */
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
    avoid:
      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 size 320, 240\n set log y\n"); 
     /* fprintf(ficgp, "set size 0.65,0.65\n"); */
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.",dummy) != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.", dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   void removespace(char *str) {
     char *p1 = str, *p2 = str;
     do
       while (*p2 == ' ')
         p2++;
     while (*p1++ = *p2++);
   }
   
   int decodemodel ( char model[], int lastobs) /**< This routine decode the model and returns:
      * Model  V1+V2+V3+V8+V7*V8+V5*V6+V8*age+V3*age
      * - cptcovt total number of covariates of the model nbocc(+)+1 = 8
      * - cptcovn or number of covariates k of the models excluding age*products =6
      * - cptcovage number of covariates with age*products =2
      * - cptcovs number of simple covariates
      * - Tvar[k] is the id of the kth covariate Tvar[1]@12 {1, 2, 3, 8, 10, 11, 8, 3, 7, 8, 5, 6}, thus Tvar[5=V7*V8]=10
      *     which is a new column after the 9 (ncovcol) variables. 
      * - if k is a product Vn*Vm covar[k][i] is filled with correct values for each individual
      * - Tprod[l] gives the kth covariates of the product Vn*Vm l=1 to cptcovprod-cptcovage
      *    Tprod[1]@2 {5, 6}: position of first product V7*V8 is 5, and second V5*V6 is 6.
      * - Tvard[k]  p Tvard[1][1]@4 {7, 8, 5, 6} for V7*V8 and V5*V6 .
    */
   {
     int i, j, k, ks;
     int i1, j1, k1, k2;
     char modelsav[80];
     char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     /*removespace(model);*/
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=0, k2=-1, ks=0, cptcovn=0;
       j=nbocc(model,'+'); /**< j=Number of '+' */
       j1=nbocc(model,'*'); /**< j1=Number of '*' */
       cptcovs=j+1-j1; /**<  Number of simple covariates V1+V2*age+V3 +V3*V4=> V1 + V3 =2  */
       cptcovt= j+1; /* Number of total covariates in the model V1 + V2*age+ V3 + V3*V4=> 4*/
                     /* including age products which are counted in cptcovage.
                     /* but the covariates which are products must be treated separately: ncovn=4- 2=2 (V1+V3). */
       cptcovprod=j1; /**< Number of products  V1*V2 +v3*age = 2 */
       cptcovprodnoage=0; /**< Number of covariate products without age: V3*V4 =1  */
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /*   Design
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9 Weight
        *  <          ncovcol=8                >
        * Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8
        *   k=  1    2      3       4     5       6      7        8
        *  cptcovn number of covariates (not including constant and age ) = # of + plus 1 = 7+1=8
        *  covar[k,i], value of kth covariate if not including age for individual i:
        *       covar[1][i]= (V2), covar[4][i]=(V3), covar[8][i]=(V8)
        *  Tvar[k] # of the kth covariate:  Tvar[1]=2  Tvar[4]=3 Tvar[8]=8
        *       if multiplied by age: V3*age Tvar[3=V3*age]=3 (V3) Tvar[7]=8 and 
        *  Tage[++cptcovage]=k
        *       if products, new covar are created after ncovcol with k1
        *  Tvar[k]=ncovcol+k1; # of the kth covariate product:  Tvar[5]=ncovcol+1=10  Tvar[6]=ncovcol+1=11
        *  Tprod[k1]=k; Tprod[1]=5 Tprod[2]= 6; gives the position of the k1th product
        *  Tvard[k1][1]=m Tvard[k1][2]=m; Tvard[1][1]=5 (V5) Tvard[1][2]=6 Tvard[2][1]=7 (V7) Tvard[2][2]=8
        *  Tvar[cptcovn+k2]=Tvard[k1][1];Tvar[cptcovn+k2+1]=Tvard[k1][2];
        *  Tvar[8+1]=5;Tvar[8+2]=6;Tvar[8+3]=7;Tvar[8+4]=8 inverted
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9  V10  V11
        *  <          ncovcol=8                >
        *       Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8    d1   d1   d2  d2
        *          k=  1    2      3       4     5       6      7        8    9   10   11  12
        *     Tvar[k]= 2    1      3       3    10      11      8        8    5    6    7   8
        * p Tvar[1]@12={2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        * p Tprod[1]@2={                         6, 5}
        *p Tvard[1][1]@4= {7, 8, 5, 6}
        * covar[k][i]= V2   V1      ?      V3    V5*V6?   V7*V8?  ?       V8   
        *  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
        *How to reorganize?
        * Model V1 + V2 + V3 + V8 + V5*V6 + V7*V8 + V3*age + V8*age
        * Tvars {2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        *       {2,   1,     4,      8,    5,      6,     3,       7}
        * Struct []
        */
   
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       /*
        * Treating invertedly V2+V1+V3*age+V2*V4 is as if written V2*V4 +V3*age + V1 + V2 */
       for(k=cptcovt; k>=1;k--) /**< Number of covariates */
           Tvar[k]=0;
       cptcovage=0;
       for(k=1; k<=cptcovt;k++){ /* Loop on total covariates of the model */
         cutl(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /**< Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutl(strc,strd,strb,'*'); /**< strd*strc  Vm*Vn: strb=V3*age(input) strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /**< Model includes age: Vn*age */
             /* covar is not filled and then is empty */
             cptcovprod--;
             cutl(stre,strb,strd,'V'); /* strd=V3(input): stre="3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=3 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutl(stre,strb,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cptcovn++;
             cptcovprodnoage++;k1++;
             cutl(stre,strb,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1; /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutl(strc,strb,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1] =atoi(strc); /* m 1 for V1*/
             Tvard[k1][2] =atoi(stre); /* n 4 for V4*/
             k2=k2+2;
             Tvar[cptcovt+k2]=Tvard[k1][1]; /* Tvar[(cptcovt=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovt+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovt=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 May not be defined */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutl(strd,strc,strb,'V');
           ks++; /**< Number of simple covariates */
           cptcovn++;
           Tvar[k]=atoi(strd);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4]="1234";
     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 with errno=%s\n",optionfile,strerror(errno));
       fprintf(ficlog,"Problem with optionfile %s with errno=%s\n",optionfile,strerror(errno));
       fflush(ficlog);
       /* goto end; */
       exit(70); 
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line,stdout);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n);  /**< used in readdata */
     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) 
       ncovmodel=2+nbocc(model,'+')+1; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     else
       ncovmodel=2;
     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 guessed parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       /* Reads scales values */
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       /* Reads covariance matrix */
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,NCOVMAX); /* Number of code per covariate; if O and 1 only, 2**ncov; V1+V2+V3+V4=>16 */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,NCOVMAX); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,NCOVMAX); /* Unclear */
     Tvard=imatrix(1,NCOVMAX,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,NCOVMAX); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
     /* */
     
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
     /* */
    
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     Ndum =ivector(-1,NCOVMAX);  
     if (ncovmodel > 2)
       tricode(Tvar,nbcode,imx, Ndum); /**< Fills nbcode[Tvar[j]][l]; */
   
     codtab=imatrix(1,100,1,10); /* codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) */
     /*printf(" codtab[1,1],codtab[100,10]=%d,%d\n", codtab[1][1],codtab[100][10]);*/
     h=0;
   
   
     /*if (cptcovn > 0) */
         
    
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=pow(2,cptcoveff-k);i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             /**< codtab(h,k)  k   = codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) + 1
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     1
              */
             codtab[h][k]=j;
             /*codtab[h][Tvar[k]]=j;*/
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
   
    free_ivector(Ndum,-1,NCOVMAX);
   
   
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       fprintf(ficgp,"set datafile missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       /*p[1]=0.0268; p[NDIM]=0.083;*/
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
        /* freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint); */
       /* ,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2); */
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
   #include "prevlim.h"  /* Use ficrespl, ficlog */
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
   #include "hpijx.h"
       fclose(ficrespij);
   
     /*-------------- Variance of one-step probabilities---*/
       k=1;
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
   
       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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           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);  
           /*
            */
           /* goto endfree; */
    
           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; /* Segmentation fault */
             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,NCOVMAX,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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*here or after loop ? */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,NCOVMAX);
       free_ivector(Tvar,1,NCOVMAX);
       free_ivector(Tprod,1,NCOVMAX);
       free_ivector(Tvaraff,1,NCOVMAX);
       free_ivector(Tage,1,NCOVMAX);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot command %s, err=%d\n", plotcmd, outcmd);
       printf("\n Trying on same directory\n");
       sprintf(plotcmd,"%sgnuplot %s", pathimach, optionfilegnuplot);
       if((outcmd=system(plotcmd)) != 0)
         printf("\n Still a problem with gnuplot command %s, err=%d\n", plotcmd, outcmd);
     }
     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') {
   #ifdef OSX
         sprintf(pplotcmd, "open %s", optionfilehtm);
   #else
         sprintf(pplotcmd, "%s", optionfilehtm);
   #endif
         printf("Starting browser with: %s",pplotcmd);fflush(stdout);
         system(pplotcmd);
       }
       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.1.52  
changed lines
  Added in v.1.153


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