Diff for /imach/src/imach.c between versions 1.51 and 1.155

version 1.51, 2002/07/19 12:22:25 version 1.155, 2014/08/25 18:32:34
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.155  2014/08/25 18:32:34  brouard
      Summary: New compile, minor changes
   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 1.154  2014/06/20 17:32:08  brouard
   interviewed on their health status or degree of disability (in the    Summary: Outputs now all graphs of convergence to period prevalence
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.153  2014/06/20 16:45:46  brouard
   (if any) in individual health status.  Health expectancies are    Summary: If 3 live state, convergence to period prevalence on same graph
   computed from the time spent in each health state according to a    Author: Brouard
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.152  2014/06/18 17:54:09  brouard
   simplest model is the multinomial logistic model where pij is the    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   probability to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    Revision 1.151  2014/06/18 16:43:30  brouard
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    *** empty log message ***
   'age' is age and 'sex' is a covariate. If you want to have a more  
   complex model than "constant and age", you should modify the program    Revision 1.150  2014/06/18 16:42:35  brouard
   where the markup *Covariates have to be included here again* invites    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
   you to do it.  More covariates you add, slower the    Author: brouard
   convergence.  
     Revision 1.149  2014/06/18 15:51:14  brouard
   The advantage of this computer programme, compared to a simple    Summary: Some fixes in parameter files errors
   multinomial logistic model, is clear when the delay between waves is not    Author: Nicolas Brouard
   identical for each individual. Also, if a individual missed an  
   intermediate interview, the information is lost, but taken into    Revision 1.148  2014/06/17 17:38:48  brouard
   account using an interpolation or extrapolation.      Summary: Nothing new
     Author: Brouard
   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    Just a new packaging for OS/X version 0.98nS
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.147  2014/06/16 10:33:11  brouard
   semester or year) is model as a multinomial logistic.  The hPx    *** empty log message ***
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.146  2014/06/16 10:20:28  brouard
   hPijx.    Summary: Merge
     Author: Brouard
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Merge, before building revised version.
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.145  2014/06/10 21:23:15  brouard
            Institut national d'études démographiques, Paris.    Summary: Debugging with valgrind
   This software have been partly granted by Euro-REVES, a concerted action    Author: Nicolas Brouard
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Lot of changes in order to output the results with some covariates
   software can be distributed freely for non commercial use. Latest version    After the Edimburgh REVES conference 2014, it seems mandatory to
   can be accessed at http://euroreves.ined.fr/imach .    improve the code.
   **********************************************************************/    No more memory valgrind error but a lot has to be done in order to
      continue the work of splitting the code into subroutines.
 #include <math.h>    Also, decodemodel has been improved. Tricode is still not
 #include <stdio.h>    optimal. nbcode should be improved. Documentation has been added in
 #include <stdlib.h>    the source code.
 #include <unistd.h>  
     Revision 1.143  2014/01/26 09:45:38  brouard
 #define MAXLINE 256    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 #define GNUPLOTPROGRAM "gnuplot"  
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define FILENAMELENGTH 80    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 /*#define DEBUG*/  
 #define windows    Revision 1.142  2014/01/26 03:57:36  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.141  2014/01/26 02:42:01  brouard
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.140  2011/09/02 10:37:54  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Summary: times.h is ok with mingw32 now.
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.139  2010/06/14 07:50:17  brouard
 #define YEARM 12. /* Number of months per year */    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 #define AGESUP 130    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 #define AGEBASE 40  
 #ifdef windows    Revision 1.138  2010/04/30 18:19:40  brouard
 #define DIRSEPARATOR '\\'    *** empty log message ***
 #define ODIRSEPARATOR '/'  
 #else    Revision 1.137  2010/04/29 18:11:38  brouard
 #define DIRSEPARATOR '/'    (Module): Checking covariates for more complex models
 #define ODIRSEPARATOR '\\'    than V1+V2. A lot of change to be done. Unstable.
 #endif  
     Revision 1.136  2010/04/26 20:30:53  brouard
 char version[80]="Imach version 0.8i, June 2002, INED-EUROREVES ";    (Module): merging some libgsl code. Fixing computation
 int erreur; /* Error number */    of likelione (using inter/intrapolation if mle = 0) in order to
 int nvar;    get same likelihood as if mle=1.
 int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;    Some cleaning of code and comments added.
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.135  2009/10/29 15:33:14  brouard
 int ndeath=1; /* Number of dead states */    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.134  2009/10/29 13:18:53  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.133  2009/07/06 10:21:25  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    just nforces
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.132  2009/07/06 08:22:05  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Many tings
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.131  2009/06/20 16:22:47  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Some dimensions resccaled
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficlog;    Revision 1.130  2009/05/26 06:44:34  brouard
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    (Module): Max Covariate is now set to 20 instead of 8. A
 FILE *ficresprobmorprev;    lot of cleaning with variables initialized to 0. Trying to make
 FILE *fichtm; /* Html File */    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 FILE *ficreseij;  
 char filerese[FILENAMELENGTH];    Revision 1.129  2007/08/31 13:49:27  lievre
 FILE  *ficresvij;    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 char fileresv[FILENAMELENGTH];  
 FILE  *ficresvpl;    Revision 1.128  2006/06/30 13:02:05  brouard
 char fileresvpl[FILENAMELENGTH];    (Module): Clarifications on computing e.j
 char title[MAXLINE];  
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    Revision 1.127  2006/04/28 18:11:50  brouard
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    loop. Now we define nhstepma in the age loop.
 char filelog[FILENAMELENGTH]; /* Log file */    (Module): In order to speed up (in case of numerous covariates) we
 char filerest[FILENAMELENGTH];    compute health expectancies (without variances) in a first step
 char fileregp[FILENAMELENGTH];    and then all the health expectancies with variances or standard
 char popfile[FILENAMELENGTH];    deviation (needs data from the Hessian matrices) which slows the
     computation.
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.126  2006/04/28 17:23:28  brouard
 #define FTOL 1.0e-10    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 #define NRANSI    loop. Now we define nhstepma in the age loop.
 #define ITMAX 200    Version 0.98h
   
 #define TOL 2.0e-4    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 #define CGOLD 0.3819660    Forecasting file added.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.124  2006/03/22 17:13:53  lievre
     Parameters are printed with %lf instead of %f (more numbers after the comma).
 #define GOLD 1.618034    The log-likelihood is printed in the log file
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.123  2006/03/20 10:52:43  brouard
     * imach.c (Module): <title> changed, corresponds to .htm file
 static double maxarg1,maxarg2;    name. <head> headers where missing.
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    * imach.c (Module): Weights can have a decimal point as for
      English (a comma might work with a correct LC_NUMERIC environment,
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    otherwise the weight is truncated).
 #define rint(a) floor(a+0.5)    Modification of warning when the covariates values are not 0 or
     1.
 static double sqrarg;    Version 0.98g
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.122  2006/03/20 09:45:41  brouard
     (Module): Weights can have a decimal point as for
 int imx;    English (a comma might work with a correct LC_NUMERIC environment,
 int stepm;    otherwise the weight is truncated).
 /* Stepm, step in month: minimum step interpolation*/    Modification of warning when the covariates values are not 0 or
     1.
 int estepm;    Version 0.98g
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
     Revision 1.121  2006/03/16 17:45:01  lievre
 int m,nb;    * imach.c (Module): Comments concerning covariates added
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    * imach.c (Module): refinements in the computation of lli if
 double **pmmij, ***probs, ***mobaverage;    status=-2 in order to have more reliable computation if stepm is
 double dateintmean=0;    not 1 month. Version 0.98f
   
 double *weight;    Revision 1.120  2006/03/16 15:10:38  lievre
 int **s; /* Status */    (Module): refinements in the computation of lli if
 double *agedc, **covar, idx;    status=-2 in order to have more reliable computation if stepm is
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    not 1 month. Version 0.98f
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Revision 1.119  2006/03/15 17:42:26  brouard
 double ftolhess; /* Tolerance for computing hessian */    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
 /**************** split *************************/  
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    Revision 1.118  2006/03/14 18:20:07  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 1.117  2006/03/14 17:16:22  brouard
    if ( s == NULL ) {                   /* no directory, so use current */    (Module): varevsij Comments added explaining the second
      /*if(strrchr(path, ODIRSEPARATOR )==NULL)    table of variances if popbased=1 .
        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #if     defined(__bsd__)                /* get current working directory */    (Module): Function pstamp added
       extern char       *getwd( );    (Module): Version 0.98d
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.116  2006/03/06 10:29:27  brouard
 #else    (Module): Variance-covariance wrong links and
       extern char       *getcwd( );    varian-covariance of ej. is needed (Saito).
   
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Revision 1.115  2006/02/27 12:17:45  brouard
 #endif    (Module): One freematrix added in mlikeli! 0.98c
          return( GLOCK_ERROR_GETCWD );  
       }    Revision 1.114  2006/02/26 12:57:58  brouard
       strcpy( name, path );             /* we've got it */    (Module): Some improvements in processing parameter
    } else {                             /* strip direcotry from path */    filename with strsep.
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.113  2006/02/24 14:20:24  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): Memory leaks checks with valgrind and:
       strcpy( name, s );                /* save file name */    datafile was not closed, some imatrix were not freed and on matrix
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    allocation too.
       dirc[l1-l2] = 0;                  /* add zero */  
    }    Revision 1.112  2006/01/30 09:55:26  brouard
    l1 = strlen( dirc );                 /* length of directory */    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #ifdef windows  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    Revision 1.111  2006/01/25 20:38:18  brouard
 #else    (Module): Lots of cleaning and bugs added (Gompertz)
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    (Module): Comments can be added in data file. Missing date values
 #endif    can be a simple dot '.'.
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Revision 1.110  2006/01/25 00:51:50  brouard
    strcpy(ext,s);                       /* save extension */    (Module): Lots of cleaning and bugs added (Gompertz)
    l1= strlen( name);  
    l2= strlen( s)+1;    Revision 1.109  2006/01/24 19:37:15  brouard
    strncpy( finame, name, l1-l2);    (Module): Comments (lines starting with a #) are allowed in data.
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    Revision 1.108  2006/01/19 18:05:42  lievre
 }    Gnuplot problem appeared...
     To be fixed
   
 /******************************************/    Revision 1.107  2006/01/19 16:20:37  brouard
     Test existence of gnuplot in imach path
 void replace(char *s, char*t)  
 {    Revision 1.106  2006/01/19 13:24:36  brouard
   int i;    Some cleaning and links added in html output
   int lg=20;  
   i=0;    Revision 1.105  2006/01/05 20:23:19  lievre
   lg=strlen(t);    *** empty log message ***
   for(i=0; i<= lg; i++) {  
     (s[i] = t[i]);    Revision 1.104  2005/09/30 16:11:43  lievre
     if (t[i]== '\\') s[i]='/';    (Module): sump fixed, loop imx fixed, and simplifications.
   }    (Module): If the status is missing at the last wave but we know
 }    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 int nbocc(char *s, char occ)    contributions to the likelihood is 1 - Prob of dying from last
 {    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   int i,j=0;    the healthy state at last known wave). Version is 0.98
   int lg=20;  
   i=0;    Revision 1.103  2005/09/30 15:54:49  lievre
   lg=strlen(s);    (Module): sump fixed, loop imx fixed, and simplifications.
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Revision 1.102  2004/09/15 17:31:30  brouard
   }    Add the possibility to read data file including tab characters.
   return j;  
 }    Revision 1.101  2004/09/15 10:38:38  brouard
     Fix on curr_time
 void cutv(char *u,char *v, char*t, char occ)  
 {    Revision 1.100  2004/07/12 18:29:06  brouard
   /* cuts string t into u and v where u is ended by char occ excluding it    Add version for Mac OS X. Just define UNIX in Makefile
      and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)  
      gives u="abcedf" and v="ghi2j" */    Revision 1.99  2004/06/05 08:57:40  brouard
   int i,lg,j,p=0;    *** empty log message ***
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {    Revision 1.98  2004/05/16 15:05:56  brouard
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    New version 0.97 . First attempt to estimate force of mortality
   }    directly from the data i.e. without the need of knowing the health
     state at each age, but using a Gompertz model: log u =a + b*age .
   lg=strlen(t);    This is the basic analysis of mortality and should be done before any
   for(j=0; j<p; j++) {    other analysis, in order to test if the mortality estimated from the
     (u[j] = t[j]);    cross-longitudinal survey is different from the mortality estimated
   }    from other sources like vital statistic data.
      u[p]='\0';  
     The same imach parameter file can be used but the option for mle should be -3.
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);    Agnès, who wrote this part of the code, tried to keep most of the
   }    former routines in order to include the new code within the former code.
 }  
     The output is very simple: only an estimate of the intercept and of
 /********************** nrerror ********************/    the slope with 95% confident intervals.
   
 void nrerror(char error_text[])    Current limitations:
 {    A) Even if you enter covariates, i.e. with the
   fprintf(stderr,"ERREUR ...\n");    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   fprintf(stderr,"%s\n",error_text);    B) There is no computation of Life Expectancy nor Life Table.
   exit(1);  
 }    Revision 1.97  2004/02/20 13:25:42  lievre
 /*********************** vector *******************/    Version 0.96d. Population forecasting command line is (temporarily)
 double *vector(int nl, int nh)    suppressed.
 {  
   double *v;    Revision 1.96  2003/07/15 15:38:55  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   if (!v) nrerror("allocation failure in vector");    rewritten within the same printf. Workaround: many printfs.
   return v-nl+NR_END;  
 }    Revision 1.95  2003/07/08 07:54:34  brouard
     * imach.c (Repository):
 /************************ free vector ******************/    (Repository): Using imachwizard code to output a more meaningful covariance
 void free_vector(double*v, int nl, int nh)    matrix (cov(a12,c31) instead of numbers.
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.94  2003/06/27 13:00:02  brouard
 }    Just cleaning
   
 /************************ivector *******************************/    Revision 1.93  2003/06/25 16:33:55  brouard
 int *ivector(long nl,long nh)    (Module): On windows (cygwin) function asctime_r doesn't
 {    exist so I changed back to asctime which exists.
   int *v;    (Module): Version 0.96b
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Revision 1.92  2003/06/25 16:30:45  brouard
   return v-nl+NR_END;    (Module): On windows (cygwin) function asctime_r doesn't
 }    exist so I changed back to asctime which exists.
   
 /******************free ivector **************************/    Revision 1.91  2003/06/25 15:30:29  brouard
 void free_ivector(int *v, long nl, long nh)    * imach.c (Repository): Duplicated warning errors corrected.
 {    (Repository): Elapsed time after each iteration is now output. It
   free((FREE_ARG)(v+nl-NR_END));    helps to forecast when convergence will be reached. Elapsed time
 }    is stamped in powell.  We created a new html file for the graphs
     concerning matrix of covariance. It has extension -cov.htm.
 /******************* imatrix *******************************/  
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Revision 1.90  2003/06/24 12:34:15  brouard
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    of the covariance matrix to be input.
   int **m;  
      Revision 1.89  2003/06/24 12:30:52  brouard
   /* allocate pointers to rows */    (Module): Some bugs corrected for windows. Also, when
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    mle=-1 a template is output in file "or"mypar.txt with the design
   if (!m) nrerror("allocation failure 1 in matrix()");    of the covariance matrix to be input.
   m += NR_END;  
   m -= nrl;    Revision 1.88  2003/06/23 17:54:56  brouard
      * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
    
   /* allocate rows and set pointers to them */    Revision 1.87  2003/06/18 12:26:01  brouard
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    Version 0.96
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.86  2003/06/17 20:04:08  brouard
   m[nrl] -= ncl;    (Module): Change position of html and gnuplot routines and added
      routine fileappend.
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
      Revision 1.85  2003/06/17 13:12:43  brouard
   /* return pointer to array of pointers to rows */    * imach.c (Repository): Check when date of death was earlier that
   return m;    current date of interview. It may happen when the death was just
 }    prior to the death. In this case, dh was negative and likelihood
     was wrong (infinity). We still send an "Error" but patch by
 /****************** free_imatrix *************************/    assuming that the date of death was just one stepm after the
 void free_imatrix(m,nrl,nrh,ncl,nch)    interview.
       int **m;    (Repository): Because some people have very long ID (first column)
       long nch,ncl,nrh,nrl;    we changed int to long in num[] and we added a new lvector for
      /* free an int matrix allocated by imatrix() */    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    (Repository): No more line truncation errors.
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 /******************* matrix *******************************/    place. It differs from routine "prevalence" which may be called
 double **matrix(long nrl, long nrh, long ncl, long nch)    many times. Probs is memory consuming and must be used with
 {    parcimony.
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   double **m;  
     Revision 1.83  2003/06/10 13:39:11  lievre
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    *** empty log message ***
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.82  2003/06/05 15:57:20  brouard
   m -= nrl;    Add log in  imach.c and  fullversion number is now printed.
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  /*
   m[nrl] += NR_END;     Interpolated Markov Chain
   m[nrl] -= ncl;  
     Short summary of the programme:
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    
   return m;    This program computes Healthy Life Expectancies from
 }    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     first survey ("cross") where individuals from different ages are
 /*************************free matrix ************************/    interviewed on their health status or degree of disability (in the
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    case of a health survey which is our main interest) -2- at least a
 {    second wave of interviews ("longitudinal") which measure each change
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    (if any) in individual health status.  Health expectancies are
   free((FREE_ARG)(m+nrl-NR_END));    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
 /******************* ma3x *******************************/    simplest model is the multinomial logistic model where pij is the
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    probability to be observed in state j at the second wave
 {    conditional to be observed in state i at the first wave. Therefore
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   double ***m;    '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
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    where the markup *Covariates have to be included here again* invites
   if (!m) nrerror("allocation failure 1 in matrix()");    you to do it.  More covariates you add, slower the
   m += NR_END;    convergence.
   m -= nrl;  
     The advantage of this computer programme, compared to a simple
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    multinomial logistic model, is clear when the delay between waves is not
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    identical for each individual. Also, if a individual missed an
   m[nrl] += NR_END;    intermediate interview, the information is lost, but taken into
   m[nrl] -= ncl;    account using an interpolation or extrapolation.  
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    hPijx is the probability to be observed in state i at age x+h
     conditional to the observed state i at age x. The delay 'h' can be
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    split into an exact number (nh*stepm) of unobserved intermediate
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    states. This elementary transition (by month, quarter,
   m[nrl][ncl] += NR_END;    semester or year) is modelled as a multinomial logistic.  The hPx
   m[nrl][ncl] -= nll;    matrix is simply the matrix product of nh*stepm elementary matrices
   for (j=ncl+1; j<=nch; j++)    and the contribution of each individual to the likelihood is simply
     m[nrl][j]=m[nrl][j-1]+nlay;    hPijx.
    
   for (i=nrl+1; i<=nrh; i++) {    Also this programme outputs the covariance matrix of the parameters but also
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    of the life expectancies. It also computes the period (stable) prevalence. 
     for (j=ncl+1; j<=nch; j++)    
       m[i][j]=m[i][j-1]+nlay;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   }             Institut national d'études démographiques, Paris.
   return m;    This software have been partly granted by Euro-REVES, a concerted action
 }    from the European Union.
     It is copyrighted identically to a GNU software product, ie programme and
 /*************************free ma3x ************************/    software can be distributed freely for non commercial use. Latest version
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    can be accessed at http://euroreves.ined.fr/imach .
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   free((FREE_ARG)(m+nrl-NR_END));    
 }    **********************************************************************/
   /*
 /***************** f1dim *************************/    main
 extern int ncom;    read parameterfile
 extern double *pcom,*xicom;    read datafile
 extern double (*nrfunc)(double []);    concatwav
      freqsummary
 double f1dim(double x)    if (mle >= 1)
 {      mlikeli
   int j;    print results files
   double f;    if mle==1 
   double *xt;       computes hessian
      read end of parameter file: agemin, agemax, bage, fage, estepm
   xt=vector(1,ncom);        begin-prev-date,...
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    open gnuplot file
   f=(*nrfunc)(xt);    open html file
   free_vector(xt,1,ncom);    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
   return f;     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
 }                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
       freexexit2 possible for memory heap.
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    h Pij x                         | pij_nom  ficrestpij
 {     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
   int iter;         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
   double a,b,d,etemp;         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
   double fu,fv,fw,fx;  
   double ftemp;         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
   double p,q,r,tol1,tol2,u,v,w,x,xm;         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
   double e=0.0;    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
   a=(ax < cx ? ax : cx);     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
   b=(ax > cx ? ax : cx);  
   x=w=v=bx;    forecasting if prevfcast==1 prevforecast call prevalence()
   fw=fv=fx=(*f)(x);    health expectancies
   for (iter=1;iter<=ITMAX;iter++) {    Variance-covariance of DFLE
     xm=0.5*(a+b);    prevalence()
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);     movingaverage()
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    varevsij() 
     printf(".");fflush(stdout);    if popbased==1 varevsij(,popbased)
     fprintf(ficlog,".");fflush(ficlog);    total life expectancies
 #ifdef DEBUG    Variance of period (stable) prevalence
     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);   end
     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);  */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif  
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;   
       return fx;  #include <math.h>
     }  #include <stdio.h>
     ftemp=fu;  #include <stdlib.h>
     if (fabs(e) > tol1) {  #include <string.h>
       r=(x-w)*(fx-fv);  #include <unistd.h>
       q=(x-v)*(fx-fw);  
       p=(x-v)*q-(x-w)*r;  #include <limits.h>
       q=2.0*(q-r);  #include <sys/types.h>
       if (q > 0.0) p = -p;  #include <sys/stat.h>
       q=fabs(q);  #include <errno.h>
       etemp=e;  extern int errno;
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #ifdef LINUX
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #include <time.h>
       else {  #include "timeval.h"
         d=p/q;  #else
         u=x+d;  #include <sys/time.h>
         if (u-a < tol2 || b-u < tol2)  #endif
           d=SIGN(tol1,xm-x);  
       }  #ifdef GSL
     } else {  #include <gsl/gsl_errno.h>
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #include <gsl/gsl_multimin.h>
     }  #endif
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  
     fu=(*f)(u);  /* #include <libintl.h> */
     if (fu <= fx) {  /* #define _(String) gettext (String) */
       if (u >= x) a=x; else b=x;  
       SHFT(v,w,x,u)  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
         SHFT(fv,fw,fx,fu)  
         } else {  #define GNUPLOTPROGRAM "gnuplot"
           if (u < x) a=u; else b=u;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
           if (fu <= fw || w == x) {  #define FILENAMELENGTH 132
             v=w;  
             w=u;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
             fv=fw;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
             v=u;  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
             fv=fu;  
           }  #define NINTERVMAX 8
         }  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
   }  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
   nrerror("Too many iterations in brent");  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
   *xmin=x;  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
   return fx;  #define MAXN 20000
 }  #define YEARM 12. /**< Number of months per year */
   #define AGESUP 130
 /****************** mnbrak ***********************/  #define AGEBASE 40
   #define AGEGOMP 10. /**< Minimal age for Gompertz adjustment */
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  #ifdef UNIX
             double (*func)(double))  #define DIRSEPARATOR '/'
 {  #define CHARSEPARATOR "/"
   double ulim,u,r,q, dum;  #define ODIRSEPARATOR '\\'
   double fu;  #else
    #define DIRSEPARATOR '\\'
   *fa=(*func)(*ax);  #define CHARSEPARATOR "\\"
   *fb=(*func)(*bx);  #define ODIRSEPARATOR '/'
   if (*fb > *fa) {  #endif
     SHFT(dum,*ax,*bx,dum)  
       SHFT(dum,*fb,*fa,dum)  /* $Id$ */
       }  /* $State$ */
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);  char version[]="Imach version 0.98nV, August 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
   while (*fb > *fc) {  char fullversion[]="$Revision$ $Date$"; 
     r=(*bx-*ax)*(*fb-*fc);  char strstart[80];
     q=(*bx-*cx)*(*fb-*fa);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  int nvar=0, nforce=0; /* Number of variables, number of forces */
     ulim=(*bx)+GLIMIT*(*cx-*bx);  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
     if ((*bx-u)*(u-*cx) > 0.0) {  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
       fu=(*func)(u);  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
     } else if ((*cx-u)*(u-ulim) > 0.0) {  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
       fu=(*func)(u);  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
       if (fu < *fc) {  int cptcovprodnoage=0; /**< Number of covariate products without age */   
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  int cptcoveff=0; /* Total number of covariates to vary for printing results */
           SHFT(*fb,*fc,fu,(*func)(u))  int cptcov=0; /* Working variable */
           }  int npar=NPARMAX;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  int nlstate=2; /* Number of live states */
       u=ulim;  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 */
     } else {  int popbased=0;
       u=(*cx)+GOLD*(*cx-*bx);  
       fu=(*func)(u);  int *wav; /* Number of waves for this individuual 0 is possible */
     }  int maxwav=0; /* Maxim number of waves */
     SHFT(*ax,*bx,*cx,u)  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       SHFT(*fa,*fb,*fc,fu)  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       }  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
 }                     to the likelihood and the sum of weights (done by funcone)*/
   int mle=1, weightopt=0;
 /*************** linmin ************************/  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 */
 int ncom;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
 double *pcom,*xicom;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
 double (*nrfunc)(double []);  double jmean=1; /* Mean space between 2 waves */
    double **matprod2(); /* test */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  double **oldm, **newm, **savm; /* Working pointers to matrices */
 {  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   double brent(double ax, double bx, double cx,  /*FILE *fic ; */ /* Used in readdata only */
                double (*f)(double), double tol, double *xmin);  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   double f1dim(double x);  FILE *ficlog, *ficrespow;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  int globpr=0; /* Global variable for printing or not */
               double *fc, double (*func)(double));  double fretone; /* Only one call to likelihood */
   int j;  long ipmx=0; /* Number of contributions */
   double xx,xmin,bx,ax;  double sw; /* Sum of weights */
   double fx,fb,fa;  char filerespow[FILENAMELENGTH];
    char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   ncom=n;  FILE *ficresilk;
   pcom=vector(1,n);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   xicom=vector(1,n);  FILE *ficresprobmorprev;
   nrfunc=func;  FILE *fichtm, *fichtmcov; /* Html File */
   for (j=1;j<=n;j++) {  FILE *ficreseij;
     pcom[j]=p[j];  char filerese[FILENAMELENGTH];
     xicom[j]=xi[j];  FILE *ficresstdeij;
   }  char fileresstde[FILENAMELENGTH];
   ax=0.0;  FILE *ficrescveij;
   xx=1.0;  char filerescve[FILENAMELENGTH];
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  FILE  *ficresvij;
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  char fileresv[FILENAMELENGTH];
 #ifdef DEBUG  FILE  *ficresvpl;
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  char fileresvpl[FILENAMELENGTH];
   fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  char title[MAXLINE];
 #endif  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   for (j=1;j<=n;j++) {  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
     xi[j] *= xmin;  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
     p[j] += xi[j];  char command[FILENAMELENGTH];
   }  int  outcmd=0;
   free_vector(xicom,1,n);  
   free_vector(pcom,1,n);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 }  
   char filelog[FILENAMELENGTH]; /* Log file */
 /*************** powell ************************/  char filerest[FILENAMELENGTH];
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  char fileregp[FILENAMELENGTH];
             double (*func)(double []))  char popfile[FILENAMELENGTH];
 {  
   void linmin(double p[], double xi[], int n, double *fret,  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
               double (*func)(double []));  
   int i,ibig,j;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   double del,t,*pt,*ptt,*xit;  struct timezone tzp;
   double fp,fptt;  extern int gettimeofday();
   double *xits;  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   pt=vector(1,n);  long time_value;
   ptt=vector(1,n);  extern long time();
   xit=vector(1,n);  char strcurr[80], strfor[80];
   xits=vector(1,n);  
   *fret=(*func)(p);  char *endptr;
   for (j=1;j<=n;j++) pt[j]=p[j];  long lval;
   for (*iter=1;;++(*iter)) {  double dval;
     fp=(*fret);  
     ibig=0;  #define NR_END 1
     del=0.0;  #define FREE_ARG char*
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #define FTOL 1.0e-10
     fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)  #define NRANSI 
       printf(" %d %.12f",i, p[i]);  #define ITMAX 200 
     fprintf(ficlog," %d %.12f",i, p[i]);  
     printf("\n");  #define TOL 2.0e-4 
     fprintf(ficlog,"\n");  
     for (i=1;i<=n;i++) {  #define CGOLD 0.3819660 
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  #define ZEPS 1.0e-10 
       fptt=(*fret);  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
 #ifdef DEBUG  
       printf("fret=%lf \n",*fret);  #define GOLD 1.618034 
       fprintf(ficlog,"fret=%lf \n",*fret);  #define GLIMIT 100.0 
 #endif  #define TINY 1.0e-20 
       printf("%d",i);fflush(stdout);  
       fprintf(ficlog,"%d",i);fflush(ficlog);  static double maxarg1,maxarg2;
       linmin(p,xit,n,fret,func);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       if (fabs(fptt-(*fret)) > del) {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
         del=fabs(fptt-(*fret));    
         ibig=i;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
       }  #define rint(a) floor(a+0.5)
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  static double sqrarg;
       fprintf(ficlog,"%d %.12e",i,(*fret));  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       for (j=1;j<=n;j++) {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  int agegomp= AGEGOMP;
         printf(" x(%d)=%.12e",j,xit[j]);  
         fprintf(ficlog," x(%d)=%.12e",j,xit[j]);  int imx; 
       }  int stepm=1;
       for(j=1;j<=n;j++) {  /* Stepm, step in month: minimum step interpolation*/
         printf(" p=%.12e",p[j]);  
         fprintf(ficlog," p=%.12e",p[j]);  int estepm;
       }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
       printf("\n");  
       fprintf(ficlog,"\n");  int m,nb;
 #endif  long *num;
     }  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
 #ifdef DEBUG  double **pmmij, ***probs;
       int k[2],l;  double *ageexmed,*agecens;
       k[0]=1;  double dateintmean=0;
       k[1]=-1;  
       printf("Max: %.12e",(*func)(p));  double *weight;
       fprintf(ficlog,"Max: %.12e",(*func)(p));  int **s; /* Status */
       for (j=1;j<=n;j++) {  double *agedc;
         printf(" %.12e",p[j]);  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
         fprintf(ficlog," %.12e",p[j]);                    * covar=matrix(0,NCOVMAX,1,n); 
       }                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
       printf("\n");  double  idx; 
       fprintf(ficlog,"\n");  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
       for(l=0;l<=1;l++) {  int *Ndum; /** Freq of modality (tricode */
         for (j=1;j<=n;j++) {  int **codtab; /**< codtab=imatrix(1,100,1,10); */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  double *lsurv, *lpop, *tpop;
           fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  
         }  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  double ftolhess; /**< Tolerance for computing hessian */
         fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  
       }  /**************** split *************************/
 #endif  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   {
     /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       free_vector(xit,1,n);       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       free_vector(xits,1,n);    */ 
       free_vector(ptt,1,n);    char  *ss;                            /* pointer */
       free_vector(pt,1,n);    int   l1, l2;                         /* length counters */
       return;  
     }    l1 = strlen(path );                   /* length of path */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     for (j=1;j<=n;j++) {    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       ptt[j]=2.0*p[j]-pt[j];    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       xit[j]=p[j]-pt[j];      strcpy( name, path );               /* we got the fullname name because no directory */
       pt[j]=p[j];      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     fptt=(*func)(ptt);      /* get current working directory */
     if (fptt < fp) {      /*    extern  char* getcwd ( char *buf , int len);*/
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       if (t < 0.0) {        return( GLOCK_ERROR_GETCWD );
         linmin(p,xit,n,fret,func);      }
         for (j=1;j<=n;j++) {      /* got dirc from getcwd*/
           xi[j][ibig]=xi[j][n];      printf(" DIRC = %s \n",dirc);
           xi[j][n]=xit[j];    } else {                              /* strip direcotry from path */
         }      ss++;                               /* after this, the filename */
 #ifdef DEBUG      l2 = strlen( ss );                  /* length of filename */
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
         fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);      strcpy( name, ss );         /* save file name */
         for(j=1;j<=n;j++){      strncpy( dirc, path, l1 - l2 );     /* now the directory */
           printf(" %.12e",xit[j]);      dirc[l1-l2] = 0;                    /* add zero */
           fprintf(ficlog," %.12e",xit[j]);      printf(" DIRC2 = %s \n",dirc);
         }    }
         printf("\n");    /* We add a separator at the end of dirc if not exists */
         fprintf(ficlog,"\n");    l1 = strlen( dirc );                  /* length of directory */
 #endif    if( dirc[l1-1] != DIRSEPARATOR ){
       }      dirc[l1] =  DIRSEPARATOR;
     }      dirc[l1+1] = 0; 
   }      printf(" DIRC3 = %s \n",dirc);
 }    }
     ss = strrchr( name, '.' );            /* find last / */
 /**** Prevalence limit ****************/    if (ss >0){
       ss++;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)      strcpy(ext,ss);                     /* save extension */
 {      l1= strlen( name);
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit      l2= strlen(ss)+1;
      matrix by transitions matrix until convergence is reached */      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
   int i, ii,j,k;    }
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();    return( 0 );                          /* we're done */
   double **out, cov[NCOVMAX], **pmij();  }
   double **newm;  
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   /******************************************/
   for (ii=1;ii<=nlstate+ndeath;ii++)  
     for (j=1;j<=nlstate+ndeath;j++){  void replace_back_to_slash(char *s, char*t)
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  {
     }    int i;
     int lg=0;
    cov[1]=1.;    i=0;
      lg=strlen(t);
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    for(i=0; i<= lg; i++) {
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){      (s[i] = t[i]);
     newm=savm;      if (t[i]== '\\') s[i]='/';
     /* Covariates have to be included here again */    }
      cov[2]=agefin;  }
    
       for (k=1; k<=cptcovn;k++) {  char *trimbb(char *out, char *in)
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
         /*      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]]);*/    char *s;
       }    s=out;
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    while (*in != '\0'){
       for (k=1; k<=cptcovprod;k++)      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        in++;
       }
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/      *out++ = *in++;
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    }
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    *out='\0';
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    return s;
   }
     savm=oldm;  
     oldm=newm;  char *cutl(char *blocc, char *alocc, char *in, char occ)
     maxmax=0.;  {
     for(j=1;j<=nlstate;j++){    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
       min=1.;       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
       max=0.;       gives blocc="abcdef2ghi" and alocc="j".
       for(i=1; i<=nlstate; i++) {       If occ is not found blocc is null and alocc is equal to in. Returns blocc
         sumnew=0;    */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    char *s, *t, *bl;
         prlim[i][j]= newm[i][j]/(1-sumnew);    t=in;s=in;
         max=FMAX(max,prlim[i][j]);    while ((*in != occ) && (*in != '\0')){
         min=FMIN(min,prlim[i][j]);      *alocc++ = *in++;
       }    }
       maxmin=max-min;    if( *in == occ){
       maxmax=FMAX(maxmax,maxmin);      *(alocc)='\0';
     }      s=++in;
     if(maxmax < ftolpl){    }
       return prlim;   
     }    if (s == t) {/* occ not found */
   }      *(alocc-(in-s))='\0';
 }      in=s;
     }
 /*************** transition probabilities ***************/    while ( *in != '\0'){
       *blocc++ = *in++;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    }
 {  
   double s1, s2;    *blocc='\0';
   /*double t34;*/    return t;
   int i,j,j1, nc, ii, jj;  }
   char *cutv(char *blocc, char *alocc, char *in, char occ)
     for(i=1; i<= nlstate; i++){  {
     for(j=1; j<i;j++){    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
         /*s2 += param[i][j][nc]*cov[nc];*/       gives blocc="abcdef2ghi" and alocc="j".
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];       If occ is not found blocc is null and alocc is equal to in. Returns alocc
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    */
       }    char *s, *t;
       ps[i][j]=s2;    t=in;s=in;
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    while (*in != '\0'){
     }      while( *in == occ){
     for(j=i+1; j<=nlstate+ndeath;j++){        *blocc++ = *in++;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){        s=in;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      }
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/      *blocc++ = *in++;
       }    }
       ps[i][j]=s2;    if (s == t) /* occ not found */
     }      *(blocc-(in-s))='\0';
   }    else
     /*ps[3][2]=1;*/      *(blocc-(in-s)-1)='\0';
     in=s;
   for(i=1; i<= nlstate; i++){    while ( *in != '\0'){
      s1=0;      *alocc++ = *in++;
     for(j=1; j<i; j++)    }
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)    *alocc='\0';
       s1+=exp(ps[i][j]);    return s;
     ps[i][i]=1./(s1+1.);  }
     for(j=1; j<i; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];  int nbocc(char *s, char occ)
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    int i,j=0;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    int lg=20;
   } /* end i */    i=0;
     lg=strlen(s);
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    for(i=0; i<= lg; i++) {
     for(jj=1; jj<= nlstate+ndeath; jj++){    if  (s[i] == occ ) j++;
       ps[ii][jj]=0;    }
       ps[ii][ii]=1;    return j;
     }  }
   }  
   /* void cutv(char *u,char *v, char*t, char occ) */
   /* { */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
     for(jj=1; jj<= nlstate+ndeath; jj++){  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
      printf("%lf ",ps[ii][jj]);  /*      gives u="abcdef2ghi" and v="j" *\/ */
    }  /*   int i,lg,j,p=0; */
     printf("\n ");  /*   i=0; */
     }  /*   lg=strlen(t); */
     printf("\n ");printf("%lf ",cov[2]);*/  /*   for(j=0; j<=lg-1; j++) { */
 /*  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  /*   } */
   goto end;*/  
     return ps;  /*   for(j=0; j<p; j++) { */
 }  /*     (u[j] = t[j]); */
   /*   } */
 /**************** Product of 2 matrices ******************/  /*      u[p]='\0'; */
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  /*    for(j=0; j<= lg; j++) { */
 {  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
   /* 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  
      before: only the contents of out is modified. The function returns  /********************** nrerror ********************/
      a pointer to pointers identical to out */  
   long i, j, k;  void nrerror(char error_text[])
   for(i=nrl; i<= nrh; i++)  {
     for(k=ncolol; k<=ncoloh; k++)    fprintf(stderr,"ERREUR ...\n");
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    fprintf(stderr,"%s\n",error_text);
         out[i][k] +=in[i][j]*b[j][k];    exit(EXIT_FAILURE);
   }
   return out;  /*********************** vector *******************/
 }  double *vector(int nl, int nh)
   {
     double *v;
 /************* Higher Matrix Product ***************/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     if (!v) nrerror("allocation failure in vector");
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    return v-nl+NR_END;
 {  }
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until  /************************ free vector ******************/
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  void free_vector(double*v, int nl, int nh)
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  {
      (typically every 2 years instead of every month which is too big).    free((FREE_ARG)(v+nl-NR_END));
      Model is determined by parameters x and covariates have to be  }
      included manually here.  
   /************************ivector *******************************/
      */  int *ivector(long nl,long nh)
   {
   int i, j, d, h, k;    int *v;
   double **out, cov[NCOVMAX];    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   double **newm;    if (!v) nrerror("allocation failure in ivector");
     return v-nl+NR_END;
   /* Hstepm could be zero and should return the unit matrix */  }
   for (i=1;i<=nlstate+ndeath;i++)  
     for (j=1;j<=nlstate+ndeath;j++){  /******************free ivector **************************/
       oldm[i][j]=(i==j ? 1.0 : 0.0);  void free_ivector(int *v, long nl, long nh)
       po[i][j][0]=(i==j ? 1.0 : 0.0);  {
     }    free((FREE_ARG)(v+nl-NR_END));
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  }
   for(h=1; h <=nhstepm; h++){  
     for(d=1; d <=hstepm; d++){  /************************lvector *******************************/
       newm=savm;  long *lvector(long nl,long nh)
       /* Covariates have to be included here again */  {
       cov[1]=1.;    long *v;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if (!v) nrerror("allocation failure in ivector");
       for (k=1; k<=cptcovage;k++)    return v-nl+NR_END;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  }
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /******************free lvector **************************/
   void free_lvector(long *v, long nl, long nh)
   {
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    free((FREE_ARG)(v+nl-NR_END));
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  }
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  /******************* imatrix *******************************/
       savm=oldm;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
       oldm=newm;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     }  { 
     for(i=1; i<=nlstate+ndeath; i++)    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       for(j=1;j<=nlstate+ndeath;j++) {    int **m; 
         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 pointers to rows */ 
          */    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       }    if (!m) nrerror("allocation failure 1 in matrix()"); 
   } /* end h */    m += NR_END; 
   return po;    m -= nrl; 
 }    
     
     /* allocate rows and set pointers to them */ 
 /*************** log-likelihood *************/    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
 double func( double *x)    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 {    m[nrl] += NR_END; 
   int i, ii, j, k, mi, d, kk;    m[nrl] -= ncl; 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    
   double **out;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   double sw; /* Sum of weights */    
   double lli; /* Individual log likelihood */    /* return pointer to array of pointers to rows */ 
   long ipmx;    return m; 
   /*extern weight */  } 
   /* We are differentiating ll according to initial status */  
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  /****************** free_imatrix *************************/
   /*for(i=1;i<imx;i++)  void free_imatrix(m,nrl,nrh,ncl,nch)
     printf(" %d\n",s[4][i]);        int **m;
   */        long nch,ncl,nrh,nrl; 
   cov[1]=1.;       /* free an int matrix allocated by imatrix() */ 
   { 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    free((FREE_ARG) (m+nrl-NR_END)); 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  } 
     for(mi=1; mi<= wav[i]-1; mi++){  
       for (ii=1;ii<=nlstate+ndeath;ii++)  /******************* matrix *******************************/
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  double **matrix(long nrl, long nrh, long ncl, long nch)
       for(d=0; d<dh[mi][i]; d++){  {
         newm=savm;    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    double **m;
         for (kk=1; kk<=cptcovage;kk++) {  
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         }    if (!m) nrerror("allocation failure 1 in matrix()");
            m += NR_END;
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    m -= nrl;
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  
         savm=oldm;    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         oldm=newm;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
            m[nrl] += NR_END;
            m[nrl] -= ncl;
       } /* end mult */  
          for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    return m;
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
       ipmx +=1;  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
       sw += weight[i];  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;     */
     } /* end of wave */  }
   } /* end of individual */  
   /*************************free matrix ************************/
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   /* 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 */    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   return -l;    free((FREE_ARG)(m+nrl-NR_END));
 }  }
   
   /******************* ma3x *******************************/
 /*********** Maximum Likelihood Estimation ***************/  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   {
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
 {    double ***m;
   int i,j, iter;  
   double **xi,*delti;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double fret;    if (!m) nrerror("allocation failure 1 in matrix()");
   xi=matrix(1,npar,1,npar);    m += NR_END;
   for (i=1;i<=npar;i++)    m -= nrl;
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   printf("Powell\n");  fprintf(ficlog,"Powell\n");    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   powell(p,xi,npar,ftol,&iter,&fret,func);    m[nrl] += NR_END;
     m[nrl] -= ncl;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  
   fprintf(ficlog,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));  
     m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
 }    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     m[nrl][ncl] += NR_END;
 /**** Computes Hessian and covariance matrix ***/    m[nrl][ncl] -= nll;
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    for (j=ncl+1; j<=nch; j++) 
 {      m[nrl][j]=m[nrl][j-1]+nlay;
   double  **a,**y,*x,pd;    
   double **hess;    for (i=nrl+1; i<=nrh; i++) {
   int i, j,jk;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   int *indx;      for (j=ncl+1; j<=nch; j++) 
         m[i][j]=m[i][j-1]+nlay;
   double hessii(double p[], double delta, int theta, double delti[]);    }
   double hessij(double p[], double delti[], int i, int j);    return m; 
   void lubksb(double **a, int npar, int *indx, double b[]) ;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   void ludcmp(double **a, int npar, int *indx, double *d) ;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     */
   hess=matrix(1,npar,1,npar);  }
   
   printf("\nCalculation of the hessian matrix. Wait...\n");  /*************************free ma3x ************************/
   fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   for (i=1;i<=npar;i++){  {
     printf("%d",i);fflush(stdout);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     fprintf(ficlog,"%d",i);fflush(ficlog);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     hess[i][i]=hessii(p,ftolhess,i,delti);    free((FREE_ARG)(m+nrl-NR_END));
     /*printf(" %f ",p[i]);*/  }
     /*printf(" %lf ",hess[i][i]);*/  
   }  /*************** function subdirf ***********/
    char *subdirf(char fileres[])
   for (i=1;i<=npar;i++) {  {
     for (j=1;j<=npar;j++)  {    /* Caution optionfilefiname is hidden */
       if (j>i) {    strcpy(tmpout,optionfilefiname);
         printf(".%d%d",i,j);fflush(stdout);    strcat(tmpout,"/"); /* Add to the right */
         fprintf(ficlog,".%d%d",i,j);fflush(ficlog);    strcat(tmpout,fileres);
         hess[i][j]=hessij(p,delti,i,j);    return tmpout;
         hess[j][i]=hess[i][j];      }
         /*printf(" %lf ",hess[i][j]);*/  
       }  /*************** function subdirf2 ***********/
     }  char *subdirf2(char fileres[], char *preop)
   }  {
   printf("\n");    
   fprintf(ficlog,"\n");    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    strcat(tmpout,"/");
   fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");    strcat(tmpout,preop);
      strcat(tmpout,fileres);
   a=matrix(1,npar,1,npar);    return tmpout;
   y=matrix(1,npar,1,npar);  }
   x=vector(1,npar);  
   indx=ivector(1,npar);  /*************** function subdirf3 ***********/
   for (i=1;i<=npar;i++)  char *subdirf3(char fileres[], char *preop, char *preop2)
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  {
   ludcmp(a,npar,indx,&pd);    
     /* Caution optionfilefiname is hidden */
   for (j=1;j<=npar;j++) {    strcpy(tmpout,optionfilefiname);
     for (i=1;i<=npar;i++) x[i]=0;    strcat(tmpout,"/");
     x[j]=1;    strcat(tmpout,preop);
     lubksb(a,npar,indx,x);    strcat(tmpout,preop2);
     for (i=1;i<=npar;i++){    strcat(tmpout,fileres);
       matcov[i][j]=x[i];    return tmpout;
     }  }
   }  
   /***************** f1dim *************************/
   printf("\n#Hessian matrix#\n");  extern int ncom; 
   fprintf(ficlog,"\n#Hessian matrix#\n");  extern double *pcom,*xicom;
   for (i=1;i<=npar;i++) {  extern double (*nrfunc)(double []); 
     for (j=1;j<=npar;j++) {   
       printf("%.3e ",hess[i][j]);  double f1dim(double x) 
       fprintf(ficlog,"%.3e ",hess[i][j]);  { 
     }    int j; 
     printf("\n");    double f;
     fprintf(ficlog,"\n");    double *xt; 
   }   
     xt=vector(1,ncom); 
   /* Recompute Inverse */    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   for (i=1;i<=npar;i++)    f=(*nrfunc)(xt); 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    free_vector(xt,1,ncom); 
   ludcmp(a,npar,indx,&pd);    return f; 
   } 
   /*  printf("\n#Hessian matrix recomputed#\n");  
   /*****************brent *************************/
   for (j=1;j<=npar;j++) {  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     for (i=1;i<=npar;i++) x[i]=0;  { 
     x[j]=1;    int iter; 
     lubksb(a,npar,indx,x);    double a,b,d,etemp;
     for (i=1;i<=npar;i++){    double fu,fv,fw,fx;
       y[i][j]=x[i];    double ftemp;
       printf("%.3e ",y[i][j]);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       fprintf(ficlog,"%.3e ",y[i][j]);    double e=0.0; 
     }   
     printf("\n");    a=(ax < cx ? ax : cx); 
     fprintf(ficlog,"\n");    b=(ax > cx ? ax : cx); 
   }    x=w=v=bx; 
   */    fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
   free_matrix(a,1,npar,1,npar);      xm=0.5*(a+b); 
   free_matrix(y,1,npar,1,npar);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   free_vector(x,1,npar);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   free_ivector(indx,1,npar);      printf(".");fflush(stdout);
   free_matrix(hess,1,npar,1,npar);      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);
 }      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);
       /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
 /*************** hessian matrix ****************/  #endif
 double hessii( double x[], double delta, int theta, double delti[])      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
 {        *xmin=x; 
   int i;        return fx; 
   int l=1, lmax=20;      } 
   double k1,k2;      ftemp=fu;
   double p2[NPARMAX+1];      if (fabs(e) > tol1) { 
   double res;        r=(x-w)*(fx-fv); 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        q=(x-v)*(fx-fw); 
   double fx;        p=(x-v)*q-(x-w)*r; 
   int k=0,kmax=10;        q=2.0*(q-r); 
   double l1;        if (q > 0.0) p = -p; 
         q=fabs(q); 
   fx=func(x);        etemp=e; 
   for (i=1;i<=npar;i++) p2[i]=x[i];        e=d; 
   for(l=0 ; l <=lmax; l++){        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     l1=pow(10,l);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     delts=delt;        else { 
     for(k=1 ; k <kmax; k=k+1){          d=p/q; 
       delt = delta*(l1*k);          u=x+d; 
       p2[theta]=x[theta] +delt;          if (u-a < tol2 || b-u < tol2) 
       k1=func(p2)-fx;            d=SIGN(tol1,xm-x); 
       p2[theta]=x[theta]-delt;        } 
       k2=func(p2)-fx;      } else { 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      } 
            u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
 #ifdef DEBUG      fu=(*f)(u); 
       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);      if (fu <= fx) { 
       fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);        if (u >= x) a=x; else b=x; 
 #endif        SHFT(v,w,x,u) 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          SHFT(fv,fw,fx,fu) 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          } else { 
         k=kmax;            if (u < x) a=u; else b=u; 
       }            if (fu <= fw || w == x) { 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */              v=w; 
         k=kmax; l=lmax*10.;              w=u; 
       }              fv=fw; 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){              fw=fu; 
         delts=delt;            } else if (fu <= fv || v == x || v == w) { 
       }              v=u; 
     }              fv=fu; 
   }            } 
   delti[theta]=delts;          } 
   return res;    } 
      nrerror("Too many iterations in brent"); 
 }    *xmin=x; 
     return fx; 
 double hessij( double x[], double delti[], int thetai,int thetaj)  } 
 {  
   int i;  /****************** mnbrak ***********************/
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   double p2[NPARMAX+1];              double (*func)(double)) 
   int k;  { 
     double ulim,u,r,q, dum;
   fx=func(x);    double fu; 
   for (k=1; k<=2; k++) {   
     for (i=1;i<=npar;i++) p2[i]=x[i];    *fa=(*func)(*ax); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    *fb=(*func)(*bx); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    if (*fb > *fa) { 
     k1=func(p2)-fx;      SHFT(dum,*ax,*bx,dum) 
          SHFT(dum,*fb,*fa,dum) 
     p2[thetai]=x[thetai]+delti[thetai]/k;        } 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    *cx=(*bx)+GOLD*(*bx-*ax); 
     k2=func(p2)-fx;    *fc=(*func)(*cx); 
      while (*fb > *fc) { 
     p2[thetai]=x[thetai]-delti[thetai]/k;      r=(*bx-*ax)*(*fb-*fc); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      q=(*bx-*cx)*(*fb-*fa); 
     k3=func(p2)-fx;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
          (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     p2[thetai]=x[thetai]-delti[thetai]/k;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      if ((*bx-u)*(u-*cx) > 0.0) { 
     k4=func(p2)-fx;        fu=(*func)(u); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 #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);        if (fu < *fc) { 
     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);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
 #endif            SHFT(*fb,*fc,fu,(*func)(u)) 
   }            } 
   return res;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
 }        u=ulim; 
         fu=(*func)(u); 
 /************** Inverse of matrix **************/      } else { 
 void ludcmp(double **a, int n, int *indx, double *d)        u=(*cx)+GOLD*(*cx-*bx); 
 {        fu=(*func)(u); 
   int i,imax,j,k;      } 
   double big,dum,sum,temp;      SHFT(*ax,*bx,*cx,u) 
   double *vv;        SHFT(*fa,*fb,*fc,fu) 
          } 
   vv=vector(1,n);  } 
   *d=1.0;  
   for (i=1;i<=n;i++) {  /*************** linmin ************************/
     big=0.0;  
     for (j=1;j<=n;j++)  int ncom; 
       if ((temp=fabs(a[i][j])) > big) big=temp;  double *pcom,*xicom;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  double (*nrfunc)(double []); 
     vv[i]=1.0/big;   
   }  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for (j=1;j<=n;j++) {  { 
     for (i=1;i<j;i++) {    double brent(double ax, double bx, double cx, 
       sum=a[i][j];                 double (*f)(double), double tol, double *xmin); 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    double f1dim(double x); 
       a[i][j]=sum;    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     }                double *fc, double (*func)(double)); 
     big=0.0;    int j; 
     for (i=j;i<=n;i++) {    double xx,xmin,bx,ax; 
       sum=a[i][j];    double fx,fb,fa;
       for (k=1;k<j;k++)   
         sum -= a[i][k]*a[k][j];    ncom=n; 
       a[i][j]=sum;    pcom=vector(1,n); 
       if ( (dum=vv[i]*fabs(sum)) >= big) {    xicom=vector(1,n); 
         big=dum;    nrfunc=func; 
         imax=i;    for (j=1;j<=n;j++) { 
       }      pcom[j]=p[j]; 
     }      xicom[j]=xi[j]; 
     if (j != imax) {    } 
       for (k=1;k<=n;k++) {    ax=0.0; 
         dum=a[imax][k];    xx=1.0; 
         a[imax][k]=a[j][k];    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
         a[j][k]=dum;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
       }  #ifdef DEBUG
       *d = -(*d);    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       vv[imax]=vv[j];    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     }  #endif
     indx[j]=imax;    for (j=1;j<=n;j++) { 
     if (a[j][j] == 0.0) a[j][j]=TINY;      xi[j] *= xmin; 
     if (j != n) {      p[j] += xi[j]; 
       dum=1.0/(a[j][j]);    } 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    free_vector(xicom,1,n); 
     }    free_vector(pcom,1,n); 
   }  } 
   free_vector(vv,1,n);  /* Doesn't work */  
 ;  char *asc_diff_time(long time_sec, char ascdiff[])
 }  {
     long sec_left, days, hours, minutes;
 void lubksb(double **a, int n, int *indx, double b[])    days = (time_sec) / (60*60*24);
 {    sec_left = (time_sec) % (60*60*24);
   int i,ii=0,ip,j;    hours = (sec_left) / (60*60) ;
   double sum;    sec_left = (sec_left) %(60*60);
      minutes = (sec_left) /60;
   for (i=1;i<=n;i++) {    sec_left = (sec_left) % (60);
     ip=indx[i];    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     sum=b[ip];    return ascdiff;
     b[ip]=b[i];  }
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  /*************** powell ************************/
     else if (sum) ii=i;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
     b[i]=sum;              double (*func)(double [])) 
   }  { 
   for (i=n;i>=1;i--) {    void linmin(double p[], double xi[], int n, double *fret, 
     sum=b[i];                double (*func)(double [])); 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    int i,ibig,j; 
     b[i]=sum/a[i][i];    double del,t,*pt,*ptt,*xit;
   }    double fp,fptt;
 }    double *xits;
     int niterf, itmp;
 /************ Frequencies ********************/  
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)    pt=vector(1,n); 
 {  /* Some frequencies */    ptt=vector(1,n); 
      xit=vector(1,n); 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;    xits=vector(1,n); 
   int first;    *fret=(*func)(p); 
   double ***freq; /* Frequencies */    for (j=1;j<=n;j++) pt[j]=p[j]; 
   double *pp;    for (*iter=1;;++(*iter)) { 
   double pos, k2, dateintsum=0,k2cpt=0;      fp=(*fret); 
   FILE *ficresp;      ibig=0; 
   char fileresp[FILENAMELENGTH];      del=0.0; 
        last_time=curr_time;
   pp=vector(1,nlstate);      (void) gettimeofday(&curr_time,&tzp);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      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);
   strcpy(fileresp,"p");      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);
   strcat(fileresp,fileres);  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   if((ficresp=fopen(fileresp,"w"))==NULL) {     for (i=1;i<=n;i++) {
     printf("Problem with prevalence resultfile: %s\n", fileresp);        printf(" %d %.12f",i, p[i]);
     fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);        fprintf(ficlog," %d %.12lf",i, p[i]);
     exit(0);        fprintf(ficrespow," %.12lf", p[i]);
   }      }
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      printf("\n");
   j1=0;      fprintf(ficlog,"\n");
        fprintf(ficrespow,"\n");fflush(ficrespow);
   j=cptcoveff;      if(*iter <=3){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        tm = *localtime(&curr_time.tv_sec);
         strcpy(strcurr,asctime(&tm));
   first=1;  /*       asctime_r(&tm,strcurr); */
         forecast_time=curr_time; 
   for(k1=1; k1<=j;k1++){        itmp = strlen(strcurr);
     for(i1=1; i1<=ncodemax[k1];i1++){        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
       j1++;          strcurr[itmp-1]='\0';
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         scanf("%d", i);*/        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
       for (i=-1; i<=nlstate+ndeath; i++)          for(niterf=10;niterf<=30;niterf+=10){
         for (jk=-1; jk<=nlstate+ndeath; jk++)            forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
           for(m=agemin; m <= agemax+3; m++)          tmf = *localtime(&forecast_time.tv_sec);
             freq[i][jk][m]=0;  /*      asctime_r(&tmf,strfor); */
                strcpy(strfor,asctime(&tmf));
       dateintsum=0;          itmp = strlen(strfor);
       k2cpt=0;          if(strfor[itmp-1]=='\n')
       for (i=1; i<=imx; i++) {          strfor[itmp-1]='\0';
         bool=1;          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);
         if  (cptcovn>0) {          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);
           for (z1=1; z1<=cptcoveff; z1++)        }
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      }
               bool=0;      for (i=1;i<=n;i++) { 
         }        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         if (bool==1) {        fptt=(*fret); 
           for(m=firstpass; m<=lastpass; m++){  #ifdef DEBUG
             k2=anint[m][i]+(mint[m][i]/12.);        printf("fret=%lf \n",*fret);
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        fprintf(ficlog,"fret=%lf \n",*fret);
               if(agev[m][i]==0) agev[m][i]=agemax+1;  #endif
               if(agev[m][i]==1) agev[m][i]=agemax+2;        printf("%d",i);fflush(stdout);
               if (m<lastpass) {        fprintf(ficlog,"%d",i);fflush(ficlog);
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        linmin(p,xit,n,fret,func); 
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];        if (fabs(fptt-(*fret)) > del) { 
               }          del=fabs(fptt-(*fret)); 
                        ibig=i; 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        } 
                 dateintsum=dateintsum+k2;  #ifdef DEBUG
                 k2cpt++;        printf("%d %.12e",i,(*fret));
               }        fprintf(ficlog,"%d %.12e",i,(*fret));
             }        for (j=1;j<=n;j++) {
           }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
         }          printf(" x(%d)=%.12e",j,xit[j]);
       }          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
                }
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        for(j=1;j<=n;j++) {
           printf(" p=%.12e",p[j]);
       if  (cptcovn>0) {          fprintf(ficlog," p=%.12e",p[j]);
         fprintf(ficresp, "\n#********** Variable ");        }
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        printf("\n");
         fprintf(ficresp, "**********\n#");        fprintf(ficlog,"\n");
       }  #endif
       for(i=1; i<=nlstate;i++)      } 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       fprintf(ficresp, "\n");  #ifdef DEBUG
              int k[2],l;
       for(i=(int)agemin; i <= (int)agemax+3; i++){        k[0]=1;
         if(i==(int)agemax+3){        k[1]=-1;
           fprintf(ficlog,"Total");        printf("Max: %.12e",(*func)(p));
         }else{        fprintf(ficlog,"Max: %.12e",(*func)(p));
           if(first==1){        for (j=1;j<=n;j++) {
             first=0;          printf(" %.12e",p[j]);
             printf("See log file for details...\n");          fprintf(ficlog," %.12e",p[j]);
           }        }
           fprintf(ficlog,"Age %d", i);        printf("\n");
         }        fprintf(ficlog,"\n");
         for(jk=1; jk <=nlstate ; jk++){        for(l=0;l<=1;l++) {
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          for (j=1;j<=n;j++) {
             pp[jk] += freq[jk][m][i];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
         }            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
         for(jk=1; jk <=nlstate ; jk++){            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           for(m=-1, pos=0; m <=0 ; m++)          }
             pos += freq[jk][m][i];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           if(pp[jk]>=1.e-10){          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
             if(first==1){        }
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  #endif
             }  
             fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  
           }else{        free_vector(xit,1,n); 
             if(first==1)        free_vector(xits,1,n); 
               printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        free_vector(ptt,1,n); 
             fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        free_vector(pt,1,n); 
           }        return; 
         }      } 
       if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
         for(jk=1; jk <=nlstate ; jk++){      for (j=1;j<=n;j++) { 
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        ptt[j]=2.0*p[j]-pt[j]; 
             pp[jk] += freq[jk][m][i];        xit[j]=p[j]-pt[j]; 
         }        pt[j]=p[j]; 
       } 
         for(jk=1,pos=0; jk <=nlstate ; jk++)      fptt=(*func)(ptt); 
           pos += pp[jk];      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); 
           if(pos>=1.e-5){        if (t < 0.0) { 
             if(first==1)          linmin(p,xit,n,fret,func); 
               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);            xi[j][ibig]=xi[j][n]; 
           }else{            xi[j][n]=xit[j]; 
             if(first==1)          }
               printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  #ifdef DEBUG
             fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           }          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           if( i <= (int) agemax){          for(j=1;j<=n;j++){
             if(pos>=1.e-5){            printf(" %.12e",xit[j]);
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);            fprintf(ficlog," %.12e",xit[j]);
               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]);*/          printf("\n");
             }          fprintf(ficlog,"\n");
             else  #endif
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        }
           }      } 
         }    } 
          } 
         for(jk=-1; jk <=nlstate+ndeath; jk++)  
           for(m=-1; m <=nlstate+ndeath; m++)  /**** Prevalence limit (stable or period prevalence)  ****************/
             if(freq[jk][m][i] !=0 ) {  
             if(first==1)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
               printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);  {
               fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
             }       matrix by transitions matrix until convergence is reached */
         if(i <= (int) agemax)  
           fprintf(ficresp,"\n");    int i, ii,j,k;
         if(first==1)    double min, max, maxmin, maxmax,sumnew=0.;
           printf("Others in log...\n");    /* double **matprod2(); */ /* test */
         fprintf(ficlog,"\n");    double **out, cov[NCOVMAX+1], **pmij();
       }    double **newm;
     }    double agefin, delaymax=50 ; /* Max number of years to converge */
   }  
   dateintmean=dateintsum/k2cpt;    for (ii=1;ii<=nlstate+ndeath;ii++)
        for (j=1;j<=nlstate+ndeath;j++){
   fclose(ficresp);        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      }
   free_vector(pp,1,nlstate);  
       cov[1]=1.;
   /* End of Freq */   
 }   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
 /************ Prevalence ********************/      newm=savm;
 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)      /* Covariates have to be included here again */
 {  /* Some frequencies */      cov[2]=agefin;
        
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      for (k=1; k<=cptcovn;k++) {
   double ***freq; /* Frequencies */        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   double *pp;        /*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]]);*/
   double pos, k2;      }
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
   pp=vector(1,nlstate);      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
        
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   j1=0;      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   j=cptcoveff;      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
        out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
   for(k1=1; k1<=j;k1++){      
     for(i1=1; i1<=ncodemax[k1];i1++){      savm=oldm;
       j1++;      oldm=newm;
            maxmax=0.;
       for (i=-1; i<=nlstate+ndeath; i++)        for(j=1;j<=nlstate;j++){
         for (jk=-1; jk<=nlstate+ndeath; jk++)          min=1.;
           for(m=agemin; m <= agemax+3; m++)        max=0.;
             freq[i][jk][m]=0;        for(i=1; i<=nlstate; i++) {
                sumnew=0;
       for (i=1; i<=imx; i++) {          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
         bool=1;          prlim[i][j]= newm[i][j]/(1-sumnew);
         if  (cptcovn>0) {          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
           for (z1=1; z1<=cptcoveff; z1++)          max=FMAX(max,prlim[i][j]);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          min=FMIN(min,prlim[i][j]);
               bool=0;        }
         }        maxmin=max-min;
         if (bool==1) {        maxmax=FMAX(maxmax,maxmin);
           for(m=firstpass; m<=lastpass; m++){      }
             k2=anint[m][i]+(mint[m][i]/12.);      if(maxmax < ftolpl){
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        return prlim;
               if(agev[m][i]==0) agev[m][i]=agemax+1;      }
               if(agev[m][i]==1) agev[m][i]=agemax+2;    }
               if (m<lastpass) {  }
                 if (calagedate>0)  
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];  /*************** transition probabilities ***************/ 
                 else  
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];  {
               }    /* According to parameters values stored in x and the covariate's values stored in cov,
             }       computes the probability to be observed in state j being in state i by appying the
           }       model to the ncovmodel covariates (including constant and age).
         }       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
       }       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
       for(i=(int)agemin; i <= (int)agemax+3; i++){       ncth covariate in the global vector x is given by the formula:
         for(jk=1; jk <=nlstate ; jk++){       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
             pp[jk] += freq[jk][m][i];       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.
         for(jk=1; jk <=nlstate ; jk++){       Outputs ps[i][j] the probability to be observed in j being in j according to
           for(m=-1, pos=0; m <=0 ; m++)       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
             pos += freq[jk][m][i];    */
         }    double s1, lnpijopii;
            /*double t34;*/
         for(jk=1; jk <=nlstate ; jk++){    int i,j,j1, nc, ii, jj;
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  
             pp[jk] += freq[jk][m][i];      for(i=1; i<= nlstate; i++){
         }        for(j=1; j<i;j++){
                  for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];            /*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); */
           if( i <= (int) agemax){          }
             if(pos>=1.e-5){          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
               probs[i][jk][j1]= pp[jk]/pos;  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
             }        }
           }        for(j=i+1; j<=nlstate+ndeath;j++){
         }/* end jk */          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
       }/* end i */            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
     } /* end i1 */            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
   } /* end k1 */  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
           }
            ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        }
   free_vector(pp,1,nlstate);      }
        
 }  /* End of Freq */      for(i=1; i<= nlstate; i++){
         s1=0;
 /************* Waves Concatenation ***************/        for(j=1; j<i; j++){
           s1+=exp(ps[i][j]); /* In fact sums pij/pii */
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
 {        }
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        for(j=i+1; j<=nlstate+ndeath; j++){
      Death is a valid wave (if date is known).          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        }
      and mw[mi+1][i]. dh depends on stepm.        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
      */        ps[i][i]=1./(s1+1.);
         /* Computing other pijs */
   int i, mi, m;        for(j=1; j<i; j++)
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          ps[i][j]= exp(ps[i][j])*ps[i][i];
      double sum=0., jmean=0.;*/        for(j=i+1; j<=nlstate+ndeath; j++)
   int first;          ps[i][j]= exp(ps[i][j])*ps[i][i];
   int j, k=0,jk, ju, jl;        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   double sum=0.;      } /* end i */
   first=0;      
   jmin=1e+5;      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   jmax=-1;        for(jj=1; jj<= nlstate+ndeath; jj++){
   jmean=0.;          ps[ii][jj]=0;
   for(i=1; i<=imx; i++){          ps[ii][ii]=1;
     mi=0;        }
     m=firstpass;      }
     while(s[m][i] <= nlstate){      
       if(s[m][i]>=1)      
         mw[++mi][i]=m;      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
       if(m >=lastpass)      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
         break;      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
       else      /*   } */
         m++;      /*   printf("\n "); */
     }/* end while */      /* } */
     if (s[m][i] > nlstate){      /* printf("\n ");printf("%lf ",cov[2]);*/
       mi++;     /* Death is another wave */      /*
       /* if(mi==0)  never been interviewed correctly before death */        for(i=1; i<= npar; i++) printf("%f ",x[i]);
          /* Only death is a correct wave */        goto end;*/
       mw[mi][i]=m;      return ps;
     }  }
   
     wav[i]=mi;  /**************** Product of 2 matrices ******************/
     if(mi==0){  
       if(first==0){  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
         printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);  {
         first=1;    /* 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(...) */
       if(first==1){    /* in, b, out are matrice of pointers which should have been initialized 
         fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);       before: only the contents of out is modified. The function returns
       }       a pointer to pointers identical to out */
     } /* end mi==0 */    int i, j, k;
   }    for(i=nrl; i<= nrh; i++)
       for(k=ncolol; k<=ncoloh; k++){
   for(i=1; i<=imx; i++){        out[i][k]=0.;
     for(mi=1; mi<wav[i];mi++){        for(j=ncl; j<=nch; j++)
       if (stepm <=0)          out[i][k] +=in[i][j]*b[j][k];
         dh[mi][i]=1;      }
       else{    return out;
         if (s[mw[mi+1][i]][i] > nlstate) {  }
           if (agedc[i] < 2*AGESUP) {  
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);  
           if(j==0) j=1;  /* Survives at least one month after exam */  /************* Higher Matrix Product ***************/
           k=k+1;  
           if (j >= jmax) jmax=j;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
           if (j <= jmin) jmin=j;  {
           sum=sum+j;    /* Computes the transition matrix starting at age 'age' over 
           /*if (j<0) printf("j=%d num=%d \n",j,i); */       'nhstepm*hstepm*stepm' months (i.e. until
           }       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
         }       nhstepm*hstepm matrices. 
         else{       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));       (typically every 2 years instead of every month which is too big 
           k=k+1;       for the memory).
           if (j >= jmax) jmax=j;       Model is determined by parameters x and covariates have to be 
           else if (j <= jmin)jmin=j;       included manually here. 
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */  
           sum=sum+j;       */
         }  
         jk= j/stepm;    int i, j, d, h, k;
         jl= j -jk*stepm;    double **out, cov[NCOVMAX+1];
         ju= j -(jk+1)*stepm;    double **newm;
         if(jl <= -ju)  
           dh[mi][i]=jk;    /* Hstepm could be zero and should return the unit matrix */
         else    for (i=1;i<=nlstate+ndeath;i++)
           dh[mi][i]=jk+1;      for (j=1;j<=nlstate+ndeath;j++){
         if(dh[mi][i]==0)        oldm[i][j]=(i==j ? 1.0 : 0.0);
           dh[mi][i]=1; /* At least one step */        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }      }
     }    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   }    for(h=1; h <=nhstepm; h++){
   jmean=sum/k;      for(d=1; d <=hstepm; d++){
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        newm=savm;
   fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        /* Covariates have to be included here again */
  }        cov[1]=1.;
         cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
 /*********** Tricode ****************************/        for (k=1; k<=cptcovn;k++) 
 void tricode(int *Tvar, int **nbcode, int imx)          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
 {        for (k=1; k<=cptcovage;k++)
   int Ndum[20],ij=1, k, j, i;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   int cptcode=0;        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
   cptcoveff=0;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
    
   for (k=0; k<19; k++) Ndum[k]=0;  
   for (k=1; k<=7; k++) ncodemax[k]=0;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
         /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     for (i=1; i<=imx; i++) {                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       ij=(int)(covar[Tvar[j]][i]);        savm=oldm;
       Ndum[ij]++;        oldm=newm;
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/      }
       if (ij > cptcode) cptcode=ij;      for(i=1; i<=nlstate+ndeath; i++)
     }        for(j=1;j<=nlstate+ndeath;j++) {
           po[i][j][h]=newm[i][j];
     for (i=0; i<=cptcode; i++) {          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
       if(Ndum[i]!=0) ncodemax[j]++;        }
     }      /*printf("h=%d ",h);*/
     ij=1;    } /* end h */
   /*     printf("\n H=%d \n",h); */
     return po;
     for (i=1; i<=ncodemax[j]; i++) {  }
       for (k=0; k<=19; k++) {  
         if (Ndum[k] != 0) {  
           nbcode[Tvar[j]][ij]=k;  /*************** log-likelihood *************/
            double func( double *x)
           ij++;  {
         }    int i, ii, j, k, mi, d, kk;
         if (ij > ncodemax[j]) break;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
       }      double **out;
     }    double sw; /* Sum of weights */
   }      double lli; /* Individual log likelihood */
     int s1, s2;
  for (k=0; k<19; k++) Ndum[k]=0;    double bbh, survp;
     long ipmx;
  for (i=1; i<=ncovmodel-2; i++) {    /*extern weight */
    ij=Tvar[i];    /* We are differentiating ll according to initial status */
    Ndum[ij]++;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
  }    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
  ij=1;    */
  for (i=1; i<=10; i++) {    cov[1]=1.;
    if((Ndum[i]!=0) && (i<=ncovcol)){  
      Tvaraff[ij]=i;    for(k=1; k<=nlstate; k++) ll[k]=0.;
      ij++;  
    }    if(mle==1){
  }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          /* Computes the values of the ncovmodel covariates of the model
  cptcoveff=ij-1;           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
 }           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
            to be observed in j being in i according to the model.
 /*********** Health Expectancies ****************/         */
         for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
 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 )          cov[2+k]=covar[Tvar[k]][i];
         }
 {        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
   /* Health expectancies */           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;           has been calculated etc */
   double age, agelim, hf;        for(mi=1; mi<= wav[i]-1; mi++){
   double ***p3mat,***varhe;          for (ii=1;ii<=nlstate+ndeath;ii++)
   double **dnewm,**doldm;            for (j=1;j<=nlstate+ndeath;j++){
   double *xp;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **gp, **gm;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double ***gradg, ***trgradg;            }
   int theta;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   xp=vector(1,npar);            for (kk=1; kk<=cptcovage;kk++) {
   dnewm=matrix(1,nlstate*2,1,npar);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
   doldm=matrix(1,nlstate*2,1,nlstate*2);            }
              out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   fprintf(ficreseij,"# Health expectancies\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   fprintf(ficreseij,"# Age");            savm=oldm;
   for(i=1; i<=nlstate;i++)            oldm=newm;
     for(j=1; j<=nlstate;j++)          } /* end mult */
       fprintf(ficreseij," %1d-%1d (SE)",i,j);        
   fprintf(ficreseij,"\n");          /*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.
   if(estepm < stepm){           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     printf ("Problem %d lower than %d\n",estepm, stepm);           * (in months) between two waves is not a multiple of stepm, we rounded to 
   }           * the nearest (and in case of equal distance, to the lowest) interval but now
   else  hstepm=estepm;             * we keep into memory the bias bh[mi][i] and also the previous matrix product
   /* We compute the life expectancy from trapezoids spaced every estepm months           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
    * This is mainly to measure the difference between two models: for example           * probability in order to take into account the bias as a fraction of the way
    * if stepm=24 months pijx are given only every 2 years and by summing them           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
    * we are calculating an estimate of the Life Expectancy assuming a linear           * -stepm/2 to stepm/2 .
    * progression inbetween and thus overestimating or underestimating according           * For stepm=1 the results are the same as for previous versions of Imach.
    * to the curvature of the survival function. If, for the same date, we           * For stepm > 1 the results are less biased than in previous versions. 
    * 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          s1=s[mw[mi][i]][i];
    * hypothesis. A more precise result, taking into account a more precise          s2=s[mw[mi+1][i]][i];
    * curvature will be obtained if estepm is as small as stepm. */          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias bh is positive if real duration
   /* For example we decided to compute the life expectancy with the smallest unit */           * is higher than the multiple of stepm and negative otherwise.
   /* 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          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
      nstepm is the number of stepm from age to agelin.          if( s2 > nlstate){ 
      Look at hpijx to understand the reason of that which relies in memory size            /* i.e. if s2 is a death state and if the date of death is known 
      and note for a fixed period like estepm months */               then the contribution to the likelihood is the probability to 
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the               die between last step unit time and current  step unit time, 
      survival function given by stepm (the optimization length). Unfortunately it               which is also equal to probability to die before dh 
      means that if the survival funtion is printed only each two years of age and if               minus probability to die before dh-stepm . 
      you sum them up and add 1 year (area under the trapezoids) you won't get the same               In version up to 0.92 likelihood was computed
      results. So we changed our mind and took the option of the best precision.          as if date of death was unknown. Death was treated as any other
   */          health state: the date of the interview describes the actual state
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          and not the date of a change in health state. The former idea was
           to consider that at each interview the state was recorded
   agelim=AGESUP;          (healthy, disable or death) and IMaCh was corrected; but when we
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          introduced the exact date of death then we should have modified
     /* nhstepm age range expressed in number of stepm */          the contribution of an exact death to the likelihood. This new
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          contribution is smaller and very dependent of the step unit
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */          stepm. It is no more the probability to die between last interview
     /* if (stepm >= YEARM) hstepm=1;*/          and month of death but the probability to survive from last
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          interview up to one month before death multiplied by the
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          probability to die within a month. Thanks to Chris
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);          Jackson for correcting this bug.  Former versions increased
     gp=matrix(0,nhstepm,1,nlstate*2);          mortality artificially. The bad side is that we add another loop
     gm=matrix(0,nhstepm,1,nlstate*2);          which slows down the processing. The difference can be up to 10%
           lower mortality.
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */            lli=log(out[s1][s2] - savm[s1][s2]);
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);    
    
           } else if  (s2==-2) {
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */            for (j=1,survp=0. ; j<=nlstate; j++) 
               survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     /* Computing Variances of health expectancies */            /*survp += out[s1][j]; */
             lli= log(survp);
      for(theta=1; theta <=npar; theta++){          }
       for(i=1; i<=npar; i++){          
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          else if  (s2==-4) { 
       }            for (j=3,survp=0. ; j<=nlstate; j++)  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
              lli= log(survp); 
       cptj=0;          } 
       for(j=1; j<= nlstate; j++){  
         for(i=1; i<=nlstate; i++){          else if  (s2==-5) { 
           cptj=cptj+1;            for (j=1,survp=0. ; j<=2; j++)  
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            lli= log(survp); 
           }          } 
         }          
       }          else{
                  lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
                  /*  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(i=1; i<=npar; i++)          } 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            /*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); */
       cptj=0;          ipmx +=1;
       for(j=1; j<= nlstate; j++){          sw += weight[i];
         for(i=1;i<=nlstate;i++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           cptj=cptj+1;        } /* end of wave */
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){      } /* end of individual */
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;    }  else if(mle==2){
           }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j<= nlstate*2; j++)          for (ii=1;ii<=nlstate+ndeath;ii++)
         for(h=0; h<=nhstepm-1; h++){            for (j=1;j<=nlstate+ndeath;j++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
      }            }
              for(d=0; d<=dh[mi][i]; d++){
 /* End theta */            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      for(h=0; h<=nhstepm-1; h++)            }
       for(j=1; j<=nlstate*2;j++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(theta=1; theta <=npar; theta++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           trgradg[h][j][theta]=gradg[h][theta][j];            savm=oldm;
                  oldm=newm;
           } /* end mult */
      for(i=1;i<=nlstate*2;i++)        
       for(j=1;j<=nlstate*2;j++)          s1=s[mw[mi][i]][i];
         varhe[i][j][(int)age] =0.;          s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
      printf("%d|",(int)age);fflush(stdout);          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 */
      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);          ipmx +=1;
      for(h=0;h<=nhstepm-1;h++){          sw += weight[i];
       for(k=0;k<=nhstepm-1;k++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);        } /* end of wave */
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      } /* end of individual */
         for(i=1;i<=nlstate*2;i++)    }  else if(mle==3){  /* exponential inter-extrapolation */
           for(j=1;j<=nlstate*2;j++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
     /* Computing expectancies */            for (j=1;j<=nlstate+ndeath;j++){
     for(i=1; i<=nlstate;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate;j++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){            }
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;          for(d=0; d<dh[mi][i]; d++){
                      newm=savm;
 /* 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]);*/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
     fprintf(ficreseij,"%3.0f",age );            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     cptj=0;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(i=1; i<=nlstate;i++)            savm=oldm;
       for(j=1; j<=nlstate;j++){            oldm=newm;
         cptj++;          } /* end mult */
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );        
       }          s1=s[mw[mi][i]][i];
     fprintf(ficreseij,"\n");          s2=s[mw[mi+1][i]][i];
              bbh=(double)bh[mi][i]/(double)stepm; 
     free_matrix(gm,0,nhstepm,1,nlstate*2);          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 */
     free_matrix(gp,0,nhstepm,1,nlstate*2);          ipmx +=1;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);          sw += weight[i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        } /* end of wave */
   }      } /* end of individual */
   printf("\n");    }else if (mle==4){  /* ml=4 no inter-extrapolation */
   fprintf(ficlog,"\n");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   free_vector(xp,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
   free_matrix(dnewm,1,nlstate*2,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);            for (j=1;j<=nlstate+ndeath;j++){
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
 /************ Variance ******************/          for(d=0; d<dh[mi][i]; d++){
 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)            newm=savm;
 {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* Variance of health expectancies */            for (kk=1; kk<=cptcovage;kk++) {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   /* double **newm;*/            }
   double **dnewm,**doldm;          
   double **dnewmp,**doldmp;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int i, j, nhstepm, hstepm, h, nstepm ;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   int k, cptcode;            savm=oldm;
   double *xp;            oldm=newm;
   double **gp, **gm;  /* for var eij */          } /* end mult */
   double ***gradg, ***trgradg; /*for var eij */        
   double **gradgp, **trgradgp; /* for var p point j */          s1=s[mw[mi][i]][i];
   double *gpp, *gmp; /* for var p point j */          s2=s[mw[mi+1][i]][i];
   double **varppt; /* for var p point j nlstate to nlstate+ndeath */          if( s2 > nlstate){ 
   double ***p3mat;            lli=log(out[s1][s2] - savm[s1][s2]);
   double age,agelim, hf;          }else{
   int theta;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   char digit[4];          }
   char digitp[16];          ipmx +=1;
           sw += weight[i];
   char fileresprobmorprev[FILENAMELENGTH];          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(popbased==1)        } /* end of wave */
     strcpy(digitp,"-populbased-");      } /* end of individual */
   else    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     strcpy(digitp,"-stablbased-");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   strcpy(fileresprobmorprev,"prmorprev");        for(mi=1; mi<= wav[i]-1; mi++){
   sprintf(digit,"%-d",ij);          for (ii=1;ii<=nlstate+ndeath;ii++)
   /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/            for (j=1;j<=nlstate+ndeath;j++){
   strcat(fileresprobmorprev,digit); /* Tvar to be done */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   strcat(fileresprobmorprev,digitp); /* Popbased or not */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   strcat(fileresprobmorprev,fileres);            }
   if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {          for(d=0; d<dh[mi][i]; d++){
     printf("Problem with resultfile: %s\n", fileresprobmorprev);            newm=savm;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   }            for (kk=1; kk<=cptcovage;kk++) {
   printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   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");          
   fprintf(ficresprobmorprev,"# Age cov=%-d",ij);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   for(j=nlstate+1; j<=(nlstate+ndeath);j++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     fprintf(ficresprobmorprev," p.%-d SE",j);            savm=oldm;
     for(i=1; i<=nlstate;i++)            oldm=newm;
       fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);          } /* end mult */
   }          
   fprintf(ficresprobmorprev,"\n");          s1=s[mw[mi][i]][i];
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {          s2=s[mw[mi+1][i]][i];
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);          ipmx +=1;
     exit(0);          sw += weight[i];
   }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   else{          /*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(ficgp,"\n# Routine varevsij");        } /* end of wave */
   }      } /* end of individual */
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    } /* End of if */
     printf("Problem with html file: %s\n", optionfilehtm);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     exit(0);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   }    return -l;
   else{  }
     fprintf(fichtm,"\n<li><h4> Computing step probabilities of dying and weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");  
   }  /*************** log-likelihood *************/
   varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);  double funcone( double *x)
   {
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");    /* Same as likeli but slower because of a lot of printf and if */
   fprintf(ficresvij,"# Age");    int i, ii, j, k, mi, d, kk;
   for(i=1; i<=nlstate;i++)    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     for(j=1; j<=nlstate;j++)    double **out;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);    double lli; /* Individual log likelihood */
   fprintf(ficresvij,"\n");    double llt;
     int s1, s2;
   xp=vector(1,npar);    double bbh, survp;
   dnewm=matrix(1,nlstate,1,npar);    /*extern weight */
   doldm=matrix(1,nlstate,1,nlstate);    /* We are differentiating ll according to initial status */
   dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
   gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);    */
   gpp=vector(nlstate+1,nlstate+ndeath);    cov[1]=1.;
   gmp=vector(nlstate+1,nlstate+ndeath);  
   trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/    for(k=1; k<=nlstate; k++) ll[k]=0.;
    
   if(estepm < stepm){    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     printf ("Problem %d lower than %d\n",estepm, stepm);      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   }      for(mi=1; mi<= wav[i]-1; mi++){
   else  hstepm=estepm;          for (ii=1;ii<=nlstate+ndeath;ii++)
   /* For example we decided to compute the life expectancy with the smallest unit */          for (j=1;j<=nlstate+ndeath;j++){
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      nhstepm is the number of hstepm from age to agelim            savm[ii][j]=(ii==j ? 1.0 : 0.0);
      nstepm is the number of stepm from age to agelin.          }
      Look at hpijx to understand the reason of that which relies in memory size        for(d=0; d<dh[mi][i]; d++){
      and note for a fixed period like k years */          newm=savm;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      survival function given by stepm (the optimization length). Unfortunately it          for (kk=1; kk<=cptcovage;kk++) {
      means that if the survival funtion is printed only each two years of age and if            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      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.          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   */          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   agelim = AGESUP;          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          savm=oldm;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */          oldm=newm;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        } /* end mult */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        
     gp=matrix(0,nhstepm,1,nlstate);        s1=s[mw[mi][i]][i];
     gm=matrix(0,nhstepm,1,nlstate);        s2=s[mw[mi+1][i]][i];
         bbh=(double)bh[mi][i]/(double)stepm; 
         /* bias is positive if real duration
     for(theta=1; theta <=npar; theta++){         * is higher than the multiple of stepm and negative otherwise.
       for(i=1; i<=npar; i++){ /* Computes gradient */         */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
       }          lli=log(out[s1][s2] - savm[s1][s2]);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          } else if  (s2==-2) {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          for (j=1,survp=0. ; j<=nlstate; j++) 
             survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       if (popbased==1) {          lli= log(survp);
         for(i=1; i<=nlstate;i++)        }else if (mle==1){
           prlim[i][i]=probs[(int)age][i][ij];          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       }        } else if(mle==2){
            lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       for(j=1; j<= nlstate; j++){        } else if(mle==3){  /* exponential inter-extrapolation */
         for(h=0; h<=nhstepm; h++){          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        } else if (mle==4){  /* mle=4 no inter-extrapolation */
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          lli=log(out[s1][s2]); /* Original formula */
         }        } else{  /* mle=0 back to 1 */
       }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       /* This for computing forces of mortality (h=1)as a weighted average */          /*lli=log(out[s1][s2]); */ /* Original formula */
       for(j=nlstate+1,gpp[j]=0.;j<=nlstate+ndeath;j++){        } /* End of if */
         for(i=1; i<= nlstate; i++)        ipmx +=1;
           gpp[j] += prlim[i][i]*p3mat[i][j][1];        sw += weight[i];
       }            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       /* end force of mortality */        /*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){
       for(i=1; i<=npar; i++) /* Computes gradient */          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
         xp[i] = x[i] - (i==theta ?delti[theta]:0);   %11.6f %11.6f %11.6f ", \
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                    num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
            for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       if (popbased==1) {            llt +=ll[k]*gipmx/gsw;
         for(i=1; i<=nlstate;i++)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           prlim[i][i]=probs[(int)age][i][ij];          }
       }          fprintf(ficresilk," %10.6f\n", -llt);
         }
       for(j=1; j<= nlstate; j++){      } /* end of wave */
         for(h=0; h<=nhstepm; h++){    } /* end of individual */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    /* 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 */
       }    if(globpr==0){ /* First time we count the contributions and weights */
       /* This for computing force of mortality (h=1)as a weighted average */      gipmx=ipmx;
       for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){      gsw=sw;
         for(i=1; i<= nlstate; i++)    }
           gmp[j] += prlim[i][i]*p3mat[i][j][1];    return -l;
       }      }
       /* end force of mortality */  
   
       for(j=1; j<= nlstate; j++) /* vareij */  /*************** function likelione ***********/
         for(h=0; h<=nhstepm; h++){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  {
         }    /* This routine should help understanding what is done with 
       for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */       the selection of individuals/waves and
         gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];       to check the exact contribution to the likelihood.
       }       Plotting could be done.
      */
     } /* End theta */    int k;
   
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */    if(*globpri !=0){ /* Just counts and sums, no printings */
       strcpy(fileresilk,"ilk"); 
     for(h=0; h<=nhstepm; h++) /* veij */      strcat(fileresilk,fileres);
       for(j=1; j<=nlstate;j++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         for(theta=1; theta <=npar; theta++)        printf("Problem with resultfile: %s\n", fileresilk);
           trgradg[h][j][theta]=gradg[h][theta][j];        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
     for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */      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");
       for(theta=1; theta <=npar; theta++)      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
         trgradgp[j][theta]=gradgp[theta][j];      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
       for(k=1; k<=nlstate; k++) 
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     for(i=1;i<=nlstate;i++)      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       for(j=1;j<=nlstate;j++)    }
         vareij[i][j][(int)age] =0.;  
     *fretone=(*funcone)(p);
     for(h=0;h<=nhstepm;h++){    if(*globpri !=0){
       for(k=0;k<=nhstepm;k++){      fclose(ficresilk);
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      fflush(fichtm); 
         for(i=1;i<=nlstate;i++)    } 
           for(j=1;j<=nlstate;j++)    return;
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;  }
       }  
     }  
   /*********** Maximum Likelihood Estimation ***************/
     /* pptj */  
     matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);  {
     for(j=nlstate+1;j<=nlstate+ndeath;j++)    int i,j, iter;
       for(i=nlstate+1;i<=nlstate+ndeath;i++)    double **xi;
         varppt[j][i]=doldmp[j][i];    double fret;
     /* end ppptj */    double fretone; /* Only one call to likelihood */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);      /*  char filerespow[FILENAMELENGTH];*/
     prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);    xi=matrix(1,npar,1,npar);
      for (i=1;i<=npar;i++)
     if (popbased==1) {      for (j=1;j<=npar;j++)
       for(i=1; i<=nlstate;i++)        xi[i][j]=(i==j ? 1.0 : 0.0);
         prlim[i][i]=probs[(int)age][i][ij];    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     }    strcpy(filerespow,"pow"); 
        strcat(filerespow,fileres);
     /* This for computing force of mortality (h=1)as a weighted average */    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){      printf("Problem with resultfile: %s\n", filerespow);
       for(i=1; i<= nlstate; i++)      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
         gmp[j] += prlim[i][i]*p3mat[i][j][1];    }
     }        fprintf(ficrespow,"# Powell\n# iter -2*LL");
     /* end force of mortality */    for (i=1;i<=nlstate;i++)
       for(j=1;j<=nlstate+ndeath;j++)
     fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){    fprintf(ficrespow,"\n");
       fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));  
       for(i=1; i<=nlstate;i++){    powell(p,xi,npar,ftol,&iter,&fret,func);
         fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);  
       }    free_matrix(xi,1,npar,1,npar);
     }    fclose(ficrespow);
     fprintf(ficresprobmorprev,"\n");    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     fprintf(ficresvij,"%.0f ",age );    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++){  }
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);  
       }  /**** Computes Hessian and covariance matrix ***/
     fprintf(ficresvij,"\n");  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     free_matrix(gp,0,nhstepm,1,nlstate);  {
     free_matrix(gm,0,nhstepm,1,nlstate);    double  **a,**y,*x,pd;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    double **hess;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    int i, j,jk;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int *indx;
   } /* End age */  
   free_vector(gpp,nlstate+1,nlstate+ndeath);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   free_vector(gmp,nlstate+1,nlstate+ndeath);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);    void lubksb(double **a, int npar, int *indx, double b[]) ;
   free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/    void ludcmp(double **a, int npar, int *indx, double *d) ;
   fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");    double gompertz(double p[]);
   /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */    hess=matrix(1,npar,1,npar);
   fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");  
   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm);    printf("\nCalculation of the hessian matrix. Wait...\n");
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm);    for (i=1;i<=npar;i++){
   fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);      printf("%d",i);fflush(stdout);
   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);      fprintf(ficlog,"%d",i);fflush(ficlog);
   fprintf(ficgp,"\nset out \"varmuptjgr%s%s.png\";replot;",digitp,digit);     
        hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   free_vector(xp,1,npar);      
   free_matrix(doldm,1,nlstate,1,nlstate);      /*  printf(" %f ",p[i]);
   free_matrix(dnewm,1,nlstate,1,npar);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    }
   free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);    
   free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    for (i=1;i<=npar;i++) {
   fclose(ficresprobmorprev);      for (j=1;j<=npar;j++)  {
   fclose(ficgp);        if (j>i) { 
   fclose(fichtm);          printf(".%d%d",i,j);fflush(stdout);
           fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
 }          hess[i][j]=hessij(p,delti,i,j,func,npar);
           
 /************ Variance of prevlim ******************/          hess[j][i]=hess[i][j];    
 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)          /*printf(" %lf ",hess[i][j]);*/
 {        }
   /* Variance of prevalence limit */      }
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    }
   double **newm;    printf("\n");
   double **dnewm,**doldm;    fprintf(ficlog,"\n");
   int i, j, nhstepm, hstepm;  
   int k, cptcode;    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   double *xp;    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   double *gp, *gm;    
   double **gradg, **trgradg;    a=matrix(1,npar,1,npar);
   double age,agelim;    y=matrix(1,npar,1,npar);
   int theta;    x=vector(1,npar);
        indx=ivector(1,npar);
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");    for (i=1;i<=npar;i++)
   fprintf(ficresvpl,"# Age");      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   for(i=1; i<=nlstate;i++)    ludcmp(a,npar,indx,&pd);
       fprintf(ficresvpl," %1d-%1d",i,i);  
   fprintf(ficresvpl,"\n");    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   xp=vector(1,npar);      x[j]=1;
   dnewm=matrix(1,nlstate,1,npar);      lubksb(a,npar,indx,x);
   doldm=matrix(1,nlstate,1,nlstate);      for (i=1;i<=npar;i++){ 
          matcov[i][j]=x[i];
   hstepm=1*YEARM; /* Every year of age */      }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    }
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    printf("\n#Hessian matrix#\n");
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    fprintf(ficlog,"\n#Hessian matrix#\n");
     if (stepm >= YEARM) hstepm=1;    for (i=1;i<=npar;i++) { 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for (j=1;j<=npar;j++) { 
     gradg=matrix(1,npar,1,nlstate);        printf("%.3e ",hess[i][j]);
     gp=vector(1,nlstate);        fprintf(ficlog,"%.3e ",hess[i][j]);
     gm=vector(1,nlstate);      }
       printf("\n");
     for(theta=1; theta <=npar; theta++){      fprintf(ficlog,"\n");
       for(i=1; i<=npar; i++){ /* Computes gradient */    }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  
       }    /* Recompute Inverse */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for (i=1;i<=npar;i++)
       for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
         gp[i] = prlim[i][i];    ludcmp(a,npar,indx,&pd);
      
       for(i=1; i<=npar; i++) /* Computes gradient */    /*  printf("\n#Hessian matrix recomputed#\n");
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for (j=1;j<=npar;j++) {
       for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++) x[i]=0;
         gm[i] = prlim[i][i];      x[j]=1;
       lubksb(a,npar,indx,x);
       for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++){ 
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        y[i][j]=x[i];
     } /* End theta */        printf("%.3e ",y[i][j]);
         fprintf(ficlog,"%.3e ",y[i][j]);
     trgradg =matrix(1,nlstate,1,npar);      }
       printf("\n");
     for(j=1; j<=nlstate;j++)      fprintf(ficlog,"\n");
       for(theta=1; theta <=npar; theta++)    }
         trgradg[j][theta]=gradg[theta][j];    */
   
     for(i=1;i<=nlstate;i++)    free_matrix(a,1,npar,1,npar);
       varpl[i][(int)age] =0.;    free_matrix(y,1,npar,1,npar);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    free_vector(x,1,npar);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    free_ivector(indx,1,npar);
     for(i=1;i<=nlstate;i++)    free_matrix(hess,1,npar,1,npar);
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  
   
     fprintf(ficresvpl,"%.0f ",age );  }
     for(i=1; i<=nlstate;i++)  
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));  /*************** hessian matrix ****************/
     fprintf(ficresvpl,"\n");  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     free_vector(gp,1,nlstate);  {
     free_vector(gm,1,nlstate);    int i;
     free_matrix(gradg,1,npar,1,nlstate);    int l=1, lmax=20;
     free_matrix(trgradg,1,nlstate,1,npar);    double k1,k2;
   } /* End age */    double p2[MAXPARM+1]; /* identical to x */
     double res;
   free_vector(xp,1,npar);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   free_matrix(doldm,1,nlstate,1,npar);    double fx;
   free_matrix(dnewm,1,nlstate,1,nlstate);    int k=0,kmax=10;
     double l1;
 }  
     fx=func(x);
 /************ Variance of one-step probabilities  ******************/    for (i=1;i<=npar;i++) p2[i]=x[i];
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
 {      l1=pow(10,l);
   int i, j=0,  i1, k1, l1, t, tj;      delts=delt;
   int k2, l2, j1,  z1;      for(k=1 ; k <kmax; k=k+1){
   int k=0,l, cptcode;        delt = delta*(l1*k);
   int first=1, first1;        p2[theta]=x[theta] +delt;
   double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
   double **dnewm,**doldm;        p2[theta]=x[theta]-delt;
   double *xp;        k2=func(p2)-fx;
   double *gp, *gm;        /*res= (k1-2.0*fx+k2)/delt/delt; */
   double **gradg, **trgradg;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   double **mu;        
   double age,agelim, cov[NCOVMAX];  #ifdef DEBUGHESS
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */        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 theta;        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);
   char fileresprob[FILENAMELENGTH];  #endif
   char fileresprobcov[FILENAMELENGTH];        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   char fileresprobcor[FILENAMELENGTH];        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           k=kmax;
   double ***varpij;        }
         else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   strcpy(fileresprob,"prob");          k=kmax; l=lmax*10.;
   strcat(fileresprob,fileres);        }
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
     printf("Problem with resultfile: %s\n", fileresprob);          delts=delt;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);        }
   }      }
   strcpy(fileresprobcov,"probcov");    }
   strcat(fileresprobcov,fileres);    delti[theta]=delts;
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {    return res; 
     printf("Problem with resultfile: %s\n", fileresprobcov);    
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);  }
   }  
   strcpy(fileresprobcor,"probcor");  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   strcat(fileresprobcor,fileres);  {
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {    int i;
     printf("Problem with resultfile: %s\n", fileresprobcor);    int l=1, l1, lmax=20;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);    double k1,k2,k3,k4,res,fx;
   }    double p2[MAXPARM+1];
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    int k;
   fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);  
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    fx=func(x);
   fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);    for (k=1; k<=2; k++) {
   printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      for (i=1;i<=npar;i++) p2[i]=x[i];
   fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);      p2[thetai]=x[thetai]+delti[thetai]/k;
        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");      k1=func(p2)-fx;
   fprintf(ficresprob,"# Age");    
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");      p2[thetai]=x[thetai]+delti[thetai]/k;
   fprintf(ficresprobcov,"# Age");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");      k2=func(p2)-fx;
   fprintf(ficresprobcov,"# Age");    
       p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   for(i=1; i<=nlstate;i++)      k3=func(p2)-fx;
     for(j=1; j<=(nlstate+ndeath);j++){    
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);      p2[thetai]=x[thetai]-delti[thetai]/k;
       fprintf(ficresprobcov," p%1d-%1d ",i,j);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       fprintf(ficresprobcor," p%1d-%1d ",i,j);      k4=func(p2)-fx;
     }        res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   fprintf(ficresprob,"\n");  #ifdef DEBUG
   fprintf(ficresprobcov,"\n");      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   fprintf(ficresprobcor,"\n");      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);
   xp=vector(1,npar);  #endif
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);    }
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));    return res;
   mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);  }
   varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);  
   first=1;  /************** Inverse of matrix **************/
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {  void ludcmp(double **a, int n, int *indx, double *d) 
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);  { 
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);    int i,imax,j,k; 
     exit(0);    double big,dum,sum,temp; 
   }    double *vv; 
   else{   
     fprintf(ficgp,"\n# Routine varprob");    vv=vector(1,n); 
   }    *d=1.0; 
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    for (i=1;i<=n;i++) { 
     printf("Problem with html file: %s\n", optionfilehtm);      big=0.0; 
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);      for (j=1;j<=n;j++) 
     exit(0);        if ((temp=fabs(a[i][j])) > big) big=temp; 
   }      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   else{      vv[i]=1.0/big; 
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");    } 
     fprintf(fichtm,"\n");    for (j=1;j<=n;j++) { 
       for (i=1;i<j;i++) { 
     fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");        sum=a[i][j]; 
     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");        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     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");        a[i][j]=sum; 
       } 
   }      big=0.0; 
       for (i=j;i<=n;i++) { 
          sum=a[i][j]; 
   cov[1]=1;        for (k=1;k<j;k++) 
   tj=cptcoveff;          sum -= a[i][k]*a[k][j]; 
   if (cptcovn<1) {tj=1;ncodemax[1]=1;}        a[i][j]=sum; 
   j1=0;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
   for(t=1; t<=tj;t++){          big=dum; 
     for(i1=1; i1<=ncodemax[t];i1++){          imax=i; 
       j1++;        } 
            } 
       if  (cptcovn>0) {      if (j != imax) { 
         fprintf(ficresprob, "\n#********** Variable ");        for (k=1;k<=n;k++) { 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          dum=a[imax][k]; 
         fprintf(ficresprob, "**********\n#");          a[imax][k]=a[j][k]; 
         fprintf(ficresprobcov, "\n#********** Variable ");          a[j][k]=dum; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        } 
         fprintf(ficresprobcov, "**********\n#");        *d = -(*d); 
                vv[imax]=vv[j]; 
         fprintf(ficgp, "\n#********** Variable ");      } 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      indx[j]=imax; 
         fprintf(ficgp, "**********\n#");      if (a[j][j] == 0.0) a[j][j]=TINY; 
              if (j != n) { 
                dum=1.0/(a[j][j]); 
         fprintf(fichtm, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable ");        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      } 
         fprintf(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");    } 
            free_vector(vv,1,n);  /* Doesn't work */
         fprintf(ficresprobcor, "\n#********** Variable ");      ;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  } 
         fprintf(ficgp, "**********\n#");      
       }  void lubksb(double **a, int n, int *indx, double b[]) 
        { 
       for (age=bage; age<=fage; age ++){    int i,ii=0,ip,j; 
         cov[2]=age;    double sum; 
         for (k=1; k<=cptcovn;k++) {   
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];    for (i=1;i<=n;i++) { 
         }      ip=indx[i]; 
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      sum=b[ip]; 
         for (k=1; k<=cptcovprod;k++)      b[ip]=b[i]; 
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];      if (ii) 
                for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));      else if (sum) ii=i; 
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);      b[i]=sum; 
         gp=vector(1,(nlstate)*(nlstate+ndeath));    } 
         gm=vector(1,(nlstate)*(nlstate+ndeath));    for (i=n;i>=1;i--) { 
          sum=b[i]; 
         for(theta=1; theta <=npar; theta++){      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
           for(i=1; i<=npar; i++)      b[i]=sum/a[i][i]; 
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    } 
            } 
           pmij(pmmij,cov,ncovmodel,xp,nlstate);  
            void pstamp(FILE *fichier)
           k=0;  {
           for(i=1; i<= (nlstate); i++){    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
             for(j=1; j<=(nlstate+ndeath);j++){  }
               k=k+1;  
               gp[k]=pmmij[i][j];  /************ Frequencies ********************/
             }  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
           }  {  /* Some frequencies */
              
           for(i=1; i<=npar; i++)    int i, m, jk, k1,i1, j1, bool, z1,j;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);    int first;
        double ***freq; /* Frequencies */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    double *pp, **prop;
           k=0;    double pos,posprop, k2, dateintsum=0,k2cpt=0;
           for(i=1; i<=(nlstate); i++){    char fileresp[FILENAMELENGTH];
             for(j=1; j<=(nlstate+ndeath);j++){    
               k=k+1;    pp=vector(1,nlstate);
               gm[k]=pmmij[i][j];    prop=matrix(1,nlstate,iagemin,iagemax+3);
             }    strcpy(fileresp,"p");
           }    strcat(fileresp,fileres);
          if((ficresp=fopen(fileresp,"w"))==NULL) {
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)      printf("Problem with prevalence resultfile: %s\n", fileresp);
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
         }      exit(0);
     }
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
           for(theta=1; theta <=npar; theta++)    j1=0;
             trgradg[j][theta]=gradg[theta][j];    
            j=cptcoveff;
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);  
            first=1;
         pmij(pmmij,cov,ncovmodel,x,nlstate);  
            /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
         k=0;    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
         for(i=1; i<=(nlstate); i++){    /*    j1++;
           for(j=1; j<=(nlstate+ndeath);j++){  */
             k=k+1;    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
             mu[k][(int) age]=pmmij[i][j];        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           }          scanf("%d", i);*/
         }        for (i=-5; i<=nlstate+ndeath; i++)  
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)            for(m=iagemin; m <= iagemax+3; m++)
             varpij[i][j][(int)age] = doldm[i][j];              freq[i][jk][m]=0;
         
         /*printf("\n%d ",(int)age);        for (i=1; i<=nlstate; i++)  
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){          for(m=iagemin; m <= iagemax+3; m++)
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));            prop[i][m]=0;
        fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));        
      }*/        dateintsum=0;
         k2cpt=0;
         fprintf(ficresprob,"\n%d ",(int)age);        for (i=1; i<=imx; i++) {
         fprintf(ficresprobcov,"\n%d ",(int)age);          bool=1;
         fprintf(ficresprobcor,"\n%d ",(int)age);          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
             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]]){
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){                bool=0;
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);                /* 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", 
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
         }                  j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
         i=0;                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
         for (k=1; k<=(nlstate);k++){              } 
           for (l=1; l<=(nlstate+ndeath);l++){          }
             i=i++;   
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);          if (bool==1){
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);            for(m=firstpass; m<=lastpass; m++){
             for (j=1; j<=i;j++){              k2=anint[m][i]+(mint[m][i]/12.);
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));                if(agev[m][i]==0) agev[m][i]=iagemax+1;
             }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
           }                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
         }/* end of loop for state */                if (m<lastpass) {
       } /* end of loop for age */                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
       /* Confidence intervalle of pij  */                }
       /*                
       fprintf(ficgp,"\nset noparametric;unset label");                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
       fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");                  dateintsum=dateintsum+k2;
       fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");                  k2cpt++;
       fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);                }
       fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);                /*}*/
       fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);            }
       fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);          }
       */        } /* end i */
          
       /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       first1=1;        pstamp(ficresp);
       for (k2=1; k2<=(nlstate);k2++){        if  (cptcovn>0) {
         for (l2=1; l2<=(nlstate+ndeath);l2++){          fprintf(ficresp, "\n#********** Variable "); 
           if(l2==k2) continue;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           j=(k2-1)*(nlstate+ndeath)+l2;          fprintf(ficresp, "**********\n#");
           for (k1=1; k1<=(nlstate);k1++){          fprintf(ficlog, "\n#********** Variable "); 
             for (l1=1; l1<=(nlstate+ndeath);l1++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
               if(l1==k1) continue;          fprintf(ficlog, "**********\n#");
               i=(k1-1)*(nlstate+ndeath)+l1;        }
               if(i<=j) continue;        for(i=1; i<=nlstate;i++) 
               for (age=bage; age<=fage; age ++){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
                 if ((int)age %5==0){        fprintf(ficresp, "\n");
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;        
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;        for(i=iagemin; i <= iagemax+3; i++){
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;          if(i==iagemax+3){
                   mu1=mu[i][(int) age]/stepm*YEARM ;            fprintf(ficlog,"Total");
                   mu2=mu[j][(int) age]/stepm*YEARM;          }else{
                   c12=cv12/sqrt(v1*v2);            if(first==1){
                   /* Computing eigen value of matrix of covariance */              first=0;
                   lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;              printf("See log file for details...\n");
                   lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;            }
                   /* Eigen vectors */            fprintf(ficlog,"Age %d", i);
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));          }
                   /*v21=sqrt(1.-v11*v11); *//* error */          for(jk=1; jk <=nlstate ; jk++){
                   v21=(lc1-v1)/cv12*v11;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                   v12=-v21;              pp[jk] += freq[jk][m][i]; 
                   v22=v11;          }
                   tnalp=v21/v11;          for(jk=1; jk <=nlstate ; jk++){
                   if(first1==1){            for(m=-1, pos=0; m <=0 ; m++)
                     first1=0;              pos += freq[jk][m][i];
                     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);            if(pp[jk]>=1.e-10){
                   }              if(first==1){
                   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(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
                   /*printf(fignu*/              }
                   /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
                   /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */            }else{
                   if(first==1){              if(first==1)
                     first=0;                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                     fprintf(ficgp,"\nset parametric;unset label");              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],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);            }
                     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);  
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);          for(jk=1; jk <=nlstate ; jk++){
                     fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);              pp[jk] += freq[jk][m][i];
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);          }       
                     fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\            pos += pp[jk];
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));            posprop += prop[jk][i];
                   }else{          }
                     first=0;          for(jk=1; jk <=nlstate ; jk++){
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);            if(pos>=1.e-5){
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);              if(first==1)
                     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(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));            }else{
                   }/* if first */              if(first==1)
                 } /* age mod 5 */                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               } /* end loop age */              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);            }
               first=1;            if( i <= iagemax){
             } /*l12 */              if(pos>=1.e-5){
           } /* k12 */                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         } /*l1 */                /*probs[i][jk][j1]= pp[jk]/pos;*/
       }/* k1 */                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     } /* loop covariates */              }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);              else
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));            }
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);          }
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          for(jk=-1; jk <=nlstate+ndeath; jk++)
   }            for(m=-1; m <=nlstate+ndeath; m++)
   free_vector(xp,1,npar);              if(freq[jk][m][i] !=0 ) {
   fclose(ficresprob);              if(first==1)
   fclose(ficresprobcov);                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   fclose(ficresprobcor);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   fclose(ficgp);              }
   fclose(fichtm);          if(i <= iagemax)
 }            fprintf(ficresp,"\n");
           if(first==1)
             printf("Others in log...\n");
 /******************* Printing html file ***********/          fprintf(ficlog,"\n");
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        }
                   int lastpass, int stepm, int weightopt, char model[],\        /*}*/
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\    }
                   int popforecast, int estepm ,\    dateintmean=dateintsum/k2cpt; 
                   double jprev1, double mprev1,double anprev1, \   
                   double jprev2, double mprev2,double anprev2){    fclose(ficresp);
   int jj1, k1, i1, cpt;    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   /*char optionfilehtm[FILENAMELENGTH];*/    free_vector(pp,1,nlstate);
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     printf("Problem with %s \n",optionfilehtm), exit(0);    /* End of Freq */
     fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);  }
   }  
   /************ Prevalence ********************/
    fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n  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)
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n  {  
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n       in each health status at the date of interview (if between dateprev1 and dateprev2).
  - Life expectancies by age and initial health status (estepm=%2d months):       We still use firstpass and lastpass as another selection.
    <a href=\"e%s\">e%s</a> <br>\n</li>", \    */
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);   
     int i, m, jk, k1, i1, j1, bool, z1,j;
 fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");    double ***freq; /* Frequencies */
     double *pp, **prop;
  m=cptcoveff;    double pos,posprop; 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    double  y2; /* in fractional years */
     int iagemin, iagemax;
  jj1=0;    int first; /** to stop verbosity which is redirected to log file */
  for(k1=1; k1<=m;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){    iagemin= (int) agemin;
      jj1++;    iagemax= (int) agemax;
      if (cptcovn > 0) {    /*pp=vector(1,nlstate);*/
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    prop=matrix(1,nlstate,iagemin,iagemax+3); 
        for (cpt=1; cpt<=cptcoveff;cpt++)    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);    j1=0;
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    
      }    /*j=cptcoveff;*/
      /* Pij */    if (cptcovn<1) {j=1;ncodemax[1]=1;}
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>    
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        first=1;
      /* Quasi-incidences */    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
      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>      /*for(i1=1; i1<=ncodemax[k1];i1++){
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        j1++;*/
        /* Stable prevalence in each health state */        
        for(cpt=1; cpt<nlstate;cpt++){        for (i=1; i<=nlstate; i++)  
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>          for(m=iagemin; m <= iagemax+3; m++)
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            prop[i][m]=0.0;
        }       
      for(cpt=1; cpt<=nlstate;cpt++) {        for (i=1; i<=imx; i++) { /* Each individual */
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>          bool=1;
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          if  (cptcovn>0) {
      }            for (z1=1; z1<=cptcoveff; z1++) 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
 health expectancies in states (1) and (2): e%s%d.png<br>                bool=0;
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);          } 
    } /* end i1 */          if (bool==1) { 
  }/* End k1 */            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
  fprintf(fichtm,"</ul>");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
               if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
  fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n                if(agev[m][i]==1) agev[m][i]=iagemax+2;
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n                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); 
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n                if (s[m][i]>0 && s[m][i]<=nlstate) { 
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n                  /*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]]);*/
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n                  prop[s[m][i]][iagemax+3] += weight[i]; 
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n                } 
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);              }
             } /* end selection of waves */
  if(popforecast==1) fprintf(fichtm,"\n          }
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n        }
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n        for(i=iagemin; i <= iagemax+3; i++){  
         <br>",fileres,fileres,fileres,fileres);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
  else            posprop += prop[jk][i]; 
    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>");          
           for(jk=1; jk <=nlstate ; jk++){     
  m=cptcoveff;            if( i <=  iagemax){ 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}              if(posprop>=1.e-5){ 
                 probs[i][jk][j1]= prop[jk][i]/posprop;
  jj1=0;              } else{
  for(k1=1; k1<=m;k1++){                if(first==1){
    for(i1=1; i1<=ncodemax[k1];i1++){                  first=0;
      jj1++;                  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]);
      if (cptcovn > 0) {                }
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");              }
        for (cpt=1; cpt<=cptcoveff;cpt++)            } 
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);          }/* end jk */ 
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");        }/* end i */ 
      }      /*} *//* end i1 */
      for(cpt=1; cpt<=nlstate;cpt++) {    } /* end j1 */
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    
 interval) in state (%d): v%s%d%d.png <br>    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      /*free_vector(pp,1,nlstate);*/
      }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
    } /* end i1 */  }  /* End of prevalence */
  }/* End k1 */  
  fprintf(fichtm,"</ul>");  /************* Waves Concatenation ***************/
 fclose(fichtm);  
 }  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)
   {
 /******************* Gnuplot file **************/    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){       Death is a valid wave (if date is known).
        mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
   int ng;       and mw[mi+1][i]. dh depends on stepm.
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {       */
     printf("Problem with file %s",optionfilegnuplot);  
     fprintf(ficlog,"Problem with file %s",optionfilegnuplot);    int i, mi, m;
   }    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
 #ifdef windows    int first;
     fprintf(ficgp,"cd \"%s\" \n",pathc);    int j, k=0,jk, ju, jl;
 #endif    double sum=0.;
 m=pow(2,cptcoveff);    first=0;
      jmin=1e+5;
  /* 1eme*/    jmax=-1;
   for (cpt=1; cpt<= nlstate ; cpt ++) {    jmean=0.;
    for (k1=1; k1<= m ; k1 ++) {    for(i=1; i<=imx; i++){
       mi=0;
 #ifdef windows      m=firstpass;
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);      while(s[m][i] <= nlstate){
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
 #endif          mw[++mi][i]=m;
 #ifdef unix        if(m >=lastpass)
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          break;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);        else
 #endif          m++;
       }/* end while */
 for (i=1; i<= nlstate ; i ++) {      if (s[m][i] > nlstate){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        mi++;     /* Death is another wave */
   else fprintf(ficgp," \%%*lf (\%%*lf)");        /* if(mi==0)  never been interviewed correctly before death */
 }           /* Only death is a correct wave */
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);        mw[mi][i]=m;
     for (i=1; i<= nlstate ; i ++) {      }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");      wav[i]=mi;
 }      if(mi==0){
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        nbwarn++;
      for (i=1; i<= nlstate ; i ++) {        if(first==0){
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   else fprintf(ficgp," \%%*lf (\%%*lf)");          first=1;
 }          }
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));        if(first==1){
 #ifdef unix          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");        }
 #endif      } /* end mi==0 */
    }    } /* End individuals */
   }  
   /*2 eme*/    for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
   for (k1=1; k1<= m ; k1 ++) {        if (stepm <=0)
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);          dh[mi][i]=1;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);        else{
              if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     for (i=1; i<= nlstate+1 ; i ++) {            if (agedc[i] < 2*AGESUP) {
       k=2*i;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);              if(j==0) j=1;  /* Survives at least one month after exam */
       for (j=1; j<= nlstate+1 ; j ++) {              else if(j<0){
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                nberr++;
   else fprintf(ficgp," \%%*lf (\%%*lf)");                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 */
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");                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);
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);                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,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);                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 (j=1; j<= nlstate+1 ; j ++) {              }
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              k=k+1;
         else fprintf(ficgp," \%%*lf (\%%*lf)");              if (j >= jmax){
 }                  jmax=j;
       fprintf(ficgp,"\" t\"\" w l 0,");                ijmax=i;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);              }
       for (j=1; j<= nlstate+1 ; j ++) {              if (j <= jmin){
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                jmin=j;
   else fprintf(ficgp," \%%*lf (\%%*lf)");                ijmin=i;
 }                }
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");              sum=sum+j;
       else fprintf(ficgp,"\" t\"\" w l 0,");              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
     }              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
   }            }
            }
   /*3eme*/          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   for (k1=1; k1<= m ; k1 ++) {  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
     for (cpt=1; cpt<= nlstate ; cpt ++) {  
       k=2+nlstate*(2*cpt-2);            k=k+1;
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            if (j >= jmax) {
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);              jmax=j;
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              ijmax=i;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");            }
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            else if (j <= jmin){
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              jmin=j;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");              ijmin=i;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            }
             /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
 */            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
       for (i=1; i< nlstate ; i ++) {            if(j<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);              nberr++;
               printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       }              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     }            }
   }            sum=sum+j;
            }
   /* CV preval stat */          jk= j/stepm;
     for (k1=1; k1<= m ; k1 ++) {          jl= j -jk*stepm;
     for (cpt=1; cpt<nlstate ; cpt ++) {          ju= j -(jk+1)*stepm;
       k=3;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            if(jl==0){
       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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);              dh[mi][i]=jk;
               bh[mi][i]=0;
       for (i=1; i< nlstate ; i ++)            }else{ /* We want a negative bias in order to only have interpolation ie
         fprintf(ficgp,"+$%d",k+i+1);                    * to avoid the price of an extra matrix product in likelihood */
       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/($%d",fileres,k1,l+cpt+1,l+1);          }else{
       for (i=1; i< nlstate ; i ++) {            if(jl <= -ju){
         l=3+(nlstate+ndeath)*cpt;              dh[mi][i]=jk;
         fprintf(ficgp,"+$%d",l+i+1);              bh[mi][i]=jl;       /* bias is positive if real duration
       }                                   * is higher than the multiple of stepm and negative otherwise.
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                                     */
     }            }
   }              else{
                dh[mi][i]=jk+1;
   /* proba elementaires */              bh[mi][i]=ju;
    for(i=1,jk=1; i <=nlstate; i++){            }
     for(k=1; k <=(nlstate+ndeath); k++){            if(dh[mi][i]==0){
       if (k != i) {              dh[mi][i]=1; /* At least one step */
         for(j=1; j <=ncovmodel; j++){              bh[mi][i]=ju; /* At least one step */
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);              /*  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);*/
           jk++;            }
           fprintf(ficgp,"\n");          } /* end if mle */
         }        }
       }      } /* end wave */
     }    }
    }    jmean=sum/k;
     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(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/    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);
      for(jk=1; jk <=m; jk++) {   }
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);  
        if (ng==2)  /*********** Tricode ****************************/
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");  void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
        else  {
          fprintf(ficgp,"\nset title \"Probability\"\n");    /**< Uses cptcovn+2*cptcovprod as the number of covariates */
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
        i=1;    /* Boring subroutine which should only output nbcode[Tvar[j]][k]
        for(k2=1; k2<=nlstate; k2++) {     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
          k3=i;    /* nbcode[Tvar[j]][1]= 
          for(k=1; k<=(nlstate+ndeath); k++) {    */
            if (k != k2){  
              if(ng==2)    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);    int modmaxcovj=0; /* Modality max of covariates j */
              else    int cptcode=0; /* Modality max of covariates j */
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    int modmincovj=0; /* Modality min of covariates j */
              ij=1;  
              for(j=3; j <=ncovmodel; j++) {  
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    cptcoveff=0; 
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);   
                  ij++;    for (k=-1; k < maxncov; k++) Ndum[k]=0;
                }    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
                else  
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    /* Loop on covariates without age and products */
              }    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
              fprintf(ficgp,")/(1");      for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
                                               modality of this covariate Vj*/ 
              for(k1=1; k1 <=nlstate; k1++){          ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);                                      * If product of Vn*Vm, still boolean *:
                ij=1;                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
                for(j=3; j <=ncovmodel; j++){                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                                        modality of the nth covariate of individual i. */
                    ij++;        if (ij > modmaxcovj)
                  }          modmaxcovj=ij; 
                  else        else if (ij < modmincovj) 
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          modmincovj=ij; 
                }        if ((ij < -1) && (ij > NCOVMAX)){
                fprintf(ficgp,")");          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
              }          exit(1);
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);        }else
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
              i=i+ncovmodel;        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
            }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
          } /* end k */        /* getting the maximum value of the modality of the covariate
        } /* end k2 */           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
      } /* end jk */           female is 1, then modmaxcovj=1.*/
    } /* end ng */      }
    fclose(ficgp);      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
 }  /* end gnuplot */      cptcode=modmaxcovj;
       /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
      /*for (i=0; i<=cptcode; i++) {*/
 /*************** Moving average **************/      for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
         if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
   int i, cpt, cptcod;          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)        }
       for (i=1; i<=nlstate;i++)        /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
           mobaverage[(int)agedeb][i][cptcod]=0.;      } /* Ndum[-1] number of undefined modalities */
      
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
       for (i=1; i<=nlstate;i++){      /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
           for (cpt=0;cpt<=4;cpt++){         modmincovj=3; modmaxcovj = 7;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];         There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
           }         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;         variables V1_1 and V1_2.
         }         nbcode[Tvar[j]][ij]=k;
       }         nbcode[Tvar[j]][1]=0;
     }         nbcode[Tvar[j]][2]=1;
             nbcode[Tvar[j]][3]=2;
 }      */
       ij=1; /* ij is similar to i but can jumps over null modalities */
       for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
 /************** Forecasting ******************/        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
 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){          /*recode from 0 */
            if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
   int *popage;                                       k is a modality. If we have model=V1+V1*sex 
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   double *popeffectif,*popcount;            ij++;
   double ***p3mat;          }
   char fileresf[FILENAMELENGTH];          if (ij > ncodemax[j]) break; 
         }  /* end of loop on */
  agelim=AGESUP;      } /* end of loop on modality */ 
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
     
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);   for (k=-1; k< maxncov; k++) Ndum[k]=0; 
      
      for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
   strcpy(fileresf,"f");     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
   strcat(fileresf,fileres);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
   if((ficresf=fopen(fileresf,"w"))==NULL) {     Ndum[ij]++; 
     printf("Problem with forecast resultfile: %s\n", fileresf);   } 
     fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);  
   }   ij=1;
   printf("Computing forecasting: result on file '%s' \n", fileresf);   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
   fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);     /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
      if((Ndum[i]!=0) && (i<=ncovcol)){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;       /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
        Tvaraff[ij]=i; /*For printing (unclear) */
   if (mobilav==1) {       ij++;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);     }else
     movingaverage(agedeb, fage, ageminpar, mobaverage);         Tvaraff[ij]=0;
   }   }
    ij--;
   stepsize=(int) (stepm+YEARM-1)/YEARM;   cptcoveff=ij; /*Number of total covariates*/
   if (stepm<=12) stepsize=1;  
    }
   agelim=AGESUP;  
    
   hstepm=1;  /*********** Health Expectancies ****************/
   hstepm=hstepm/stepm;  
   yp1=modf(dateintmean,&yp);  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   anprojmean=yp;  
   yp2=modf((yp1*12),&yp);  {
   mprojmean=yp;    /* Health expectancies, no variances */
   yp1=modf((yp2*30.5),&yp);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
   jprojmean=yp;    int nhstepma, nstepma; /* Decreasing with age */
   if(jprojmean==0) jprojmean=1;    double age, agelim, hf;
   if(mprojmean==0) jprojmean=1;    double ***p3mat;
      double eip;
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);  
      pstamp(ficreseij);
   for(cptcov=1;cptcov<=i2;cptcov++){    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    fprintf(ficreseij,"# Age");
       k=k+1;    for(i=1; i<=nlstate;i++){
       fprintf(ficresf,"\n#******");      for(j=1; j<=nlstate;j++){
       for(j=1;j<=cptcoveff;j++) {        fprintf(ficreseij," e%1d%1d ",i,j);
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      }
       }      fprintf(ficreseij," e%1d. ",i);
       fprintf(ficresf,"******\n");    }
       fprintf(ficresf,"# StartingAge FinalAge");    fprintf(ficreseij,"\n");
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  
          
          if(estepm < stepm){
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {      printf ("Problem %d lower than %d\n",estepm, stepm);
         fprintf(ficresf,"\n");    }
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     * This is mainly to measure the difference between two models: for example
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);     * if stepm=24 months pijx are given only every 2 years and by summing them
           nhstepm = nhstepm/hstepm;     * we are calculating an estimate of the Life Expectancy assuming a linear 
               * progression in between and thus overestimating or underestimating according
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     * to the curvature of the survival function. If, for the same date, we 
           oldm=oldms;savm=savms;     * estimate the model with stepm=1 month, we can keep estepm to 24 months
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);       * to compare the new estimate of Life expectancy with the same linear 
             * hypothesis. A more precise result, taking into account a more precise
           for (h=0; h<=nhstepm; h++){     * curvature will be obtained if estepm is as small as stepm. */
             if (h==(int) (calagedate+YEARM*cpt)) {  
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    /* For example we decided to compute the life expectancy with the smallest unit */
             }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
             for(j=1; j<=nlstate+ndeath;j++) {       nhstepm is the number of hstepm from age to agelim 
               kk1=0.;kk2=0;       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
                 if (mobilav==1)       and note for a fixed period like estepm months */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
                 else {       survival function given by stepm (the optimization length). Unfortunately it
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];       means that if the survival funtion is printed only each two years of age and if
                 }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
                       results. So we changed our mind and took the option of the best precision.
               }    */
               if (h==(int)(calagedate+12*cpt)){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
                 fprintf(ficresf," %.3f", kk1);  
                            agelim=AGESUP;
               }    /* If stepm=6 months */
             }      /* Computed by stepm unit matrices, product of hstepm matrices, stored
           }         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      
         }  /* 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;*/
            nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   
   fclose(ficresf);    for (age=bage; age<=fage; age ++){ 
 }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
 /************** Forecasting ******************/      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
 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){      /* if (stepm >= YEARM) hstepm=1;*/
        nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;  
   int *popage;      /* If stepm=6 months */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   double *popeffectif,*popcount;         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   double ***p3mat,***tabpop,***tabpopprev;      
   char filerespop[FILENAMELENGTH];      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      
   agelim=AGESUP;      printf("%d|",(int)age);fflush(stdout);
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      /* Computing expectancies */
        for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++)
   strcpy(filerespop,"pop");          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   strcat(filerespop,fileres);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
   if((ficrespop=fopen(filerespop,"w"))==NULL) {            
     printf("Problem with forecast resultfile: %s\n", filerespop);            /* 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]);*/
     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);      fprintf(ficreseij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        eip=0;
         for(j=1; j<=nlstate;j++){
   if (mobilav==1) {          eip +=eij[i][j][(int)age];
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
     movingaverage(agedeb, fage, ageminpar, mobaverage);        }
   }        fprintf(ficreseij,"%9.4f", eip );
       }
   stepsize=(int) (stepm+YEARM-1)/YEARM;      fprintf(ficreseij,"\n");
   if (stepm<=12) stepsize=1;      
      }
   agelim=AGESUP;    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      printf("\n");
   hstepm=1;    fprintf(ficlog,"\n");
   hstepm=hstepm/stepm;    
    }
   if (popforecast==1) {  
     if((ficpop=fopen(popfile,"r"))==NULL) {  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[] )
       printf("Problem with population file : %s\n",popfile);exit(0);  
       fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);  {
     }    /* Covariances of health expectancies eij and of total life expectancies according
     popage=ivector(0,AGESUP);     to initial status i, ei. .
     popeffectif=vector(0,AGESUP);    */
     popcount=vector(0,AGESUP);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
        int nhstepma, nstepma; /* Decreasing with age */
     i=1;      double age, agelim, hf;
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    double ***p3matp, ***p3matm, ***varhe;
        double **dnewm,**doldm;
     imx=i;    double *xp, *xm;
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];    double **gp, **gm;
   }    double ***gradg, ***trgradg;
     int theta;
   for(cptcov=1;cptcov<=i2;cptcov++){  
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    double eip, vip;
       k=k+1;  
       fprintf(ficrespop,"\n#******");    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
       for(j=1;j<=cptcoveff;j++) {    xp=vector(1,npar);
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    xm=vector(1,npar);
       }    dnewm=matrix(1,nlstate*nlstate,1,npar);
       fprintf(ficrespop,"******\n");    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
       fprintf(ficrespop,"# Age");    
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    pstamp(ficresstdeij);
       if (popforecast==1)  fprintf(ficrespop," [Population]");    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
          fprintf(ficresstdeij,"# Age");
       for (cpt=0; cpt<=0;cpt++) {    for(i=1; i<=nlstate;i++){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        for(j=1; j<=nlstate;j++)
                fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      fprintf(ficresstdeij," e%1d. ",i);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    }
           nhstepm = nhstepm/hstepm;    fprintf(ficresstdeij,"\n");
            
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    pstamp(ficrescveij);
           oldm=oldms;savm=savms;    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      fprintf(ficrescveij,"# Age");
            for(i=1; i<=nlstate;i++)
           for (h=0; h<=nhstepm; h++){      for(j=1; j<=nlstate;j++){
             if (h==(int) (calagedate+YEARM*cpt)) {        cptj= (j-1)*nlstate+i;
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);        for(i2=1; i2<=nlstate;i2++)
             }          for(j2=1; j2<=nlstate;j2++){
             for(j=1; j<=nlstate+ndeath;j++) {            cptj2= (j2-1)*nlstate+i2;
               kk1=0.;kk2=0;            if(cptj2 <= cptj)
               for(i=1; i<=nlstate;i++) {                            fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
                 if (mobilav==1)          }
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      }
                 else {    fprintf(ficrescveij,"\n");
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    
                 }    if(estepm < stepm){
               }      printf ("Problem %d lower than %d\n",estepm, stepm);
               if (h==(int)(calagedate+12*cpt)){    }
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    else  hstepm=estepm;   
                   /*fprintf(ficrespop," %.3f", kk1);    /* We compute the life expectancy from trapezoids spaced every estepm months
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/     * This is mainly to measure the difference between two models: for example
               }     * if stepm=24 months pijx are given only every 2 years and by summing them
             }     * we are calculating an estimate of the Life Expectancy assuming a linear 
             for(i=1; i<=nlstate;i++){     * progression in between and thus overestimating or underestimating according
               kk1=0.;     * to the curvature of the survival function. If, for the same date, we 
                 for(j=1; j<=nlstate;j++){     * estimate the model with stepm=1 month, we can keep estepm to 24 months
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];     * to compare the new estimate of Life expectancy with the same linear 
                 }     * hypothesis. A more precise result, taking into account a more precise
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];     * curvature will be obtained if estepm is as small as stepm. */
             }  
     /* For example we decided to compute the life expectancy with the smallest unit */
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);       nhstepm is the number of hstepm from age to agelim 
           }       nstepm is the number of stepm from age to agelin. 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       Look at hpijx to understand the reason of that which relies in memory size
         }       and note for a fixed period like estepm months */
       }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         survival function given by stepm (the optimization length). Unfortunately it
   /******/       means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {       results. So we changed our mind and took the option of the best precision.
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
           nhstepm = nhstepm/hstepm;    /* If stepm=6 months */
              /* nhstepm age range expressed in number of stepm */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    agelim=AGESUP;
           oldm=oldms;savm=savms;    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           for (h=0; h<=nhstepm; h++){    /* if (stepm >= YEARM) hstepm=1;*/
             if (h==(int) (calagedate+YEARM*cpt)) {    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    
             }    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             for(j=1; j<=nlstate+ndeath;j++) {    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
               kk1=0.;kk2=0;    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
               for(i=1; i<=nlstate;i++) {                  trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        gp=matrix(0,nhstepm,1,nlstate*nlstate);
               }    gm=matrix(0,nhstepm,1,nlstate*nlstate);
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);  
             }    for (age=bage; age<=fage; age ++){ 
           }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         }      /* 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
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   if (popforecast==1) {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     free_ivector(popage,0,AGESUP);  
     free_vector(popeffectif,0,AGESUP);      /* Computing  Variances of health expectancies */
     free_vector(popcount,0,AGESUP);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   }         decrease memory allocation */
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(theta=1; theta <=npar; theta++){
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(i=1; i<=npar; i++){ 
   fclose(ficrespop);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 }          xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
 /***********************************************/        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
 /**************** Main Program *****************/        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
 /***********************************************/    
         for(j=1; j<= nlstate; j++){
 int main(int argc, char *argv[])          for(i=1; i<=nlstate; i++){
 {            for(h=0; h<=nhstepm-1; h++){
               gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   double agedeb, agefin,hf;            }
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          }
         }
   double fret;       
   double **xi,tmp,delta;        for(ij=1; ij<= nlstate*nlstate; ij++)
           for(h=0; h<=nhstepm-1; h++){
   double dum; /* Dummy variable */            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   double ***p3mat;          }
   int *indx;      }/* End theta */
   char line[MAXLINE], linepar[MAXLINE];      
   char path[80],pathc[80],pathcd[80],pathtot[80],model[80];      
   int firstobs=1, lastobs=10;      for(h=0; h<=nhstepm-1; h++)
   int sdeb, sfin; /* Status at beginning and end */        for(j=1; j<=nlstate*nlstate;j++)
   int c,  h , cpt,l;          for(theta=1; theta <=npar; theta++)
   int ju,jl, mi;            trgradg[h][j][theta]=gradg[h][theta][j];
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;  
   int mobilav=0,popforecast=0;       for(ij=1;ij<=nlstate*nlstate;ij++)
   int hstepm, nhstepm;        for(ji=1;ji<=nlstate*nlstate;ji++)
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;          varhe[ij][ji][(int)age] =0.;
   
   double bage, fage, age, agelim, agebase;       printf("%d|",(int)age);fflush(stdout);
   double ftolpl=FTOL;       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   double **prlim;       for(h=0;h<=nhstepm-1;h++){
   double *severity;        for(k=0;k<=nhstepm-1;k++){
   double ***param; /* Matrix of parameters */          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   double  *p;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   double **matcov; /* Matrix of covariance */          for(ij=1;ij<=nlstate*nlstate;ij++)
   double ***delti3; /* Scale */            for(ji=1;ji<=nlstate*nlstate;ji++)
   double *delti; /* Scale */              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   double ***eij, ***vareij;        }
   double **varpl; /* Variances of prevalence limits by age */      }
   double *epj, vepp;  
   double kk1, kk2;      /* Computing expectancies */
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
        for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   char *alph[]={"a","a","b","c","d","e"}, str[4];          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
   char z[1]="c", occ;            /* 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]);*/
 #include <sys/time.h>  
 #include <time.h>          }
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  
        fprintf(ficresstdeij,"%3.0f",age );
   /* long total_usecs;      for(i=1; i<=nlstate;i++){
   struct timeval start_time, end_time;        eip=0.;
          vip=0.;
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */        for(j=1; j<=nlstate;j++){
   getcwd(pathcd, size);          eip += eij[i][j][(int)age];
           for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
   printf("\n%s",version);            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
   if(argc <=1){          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
     printf("\nEnter the parameter file name: ");        }
     scanf("%s",pathtot);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
   }      }
   else{      fprintf(ficresstdeij,"\n");
     strcpy(pathtot,argv[1]);  
   }      fprintf(ficrescveij,"%3.0f",age );
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/      for(i=1; i<=nlstate;i++)
   /*cygwin_split_path(pathtot,path,optionfile);        for(j=1; j<=nlstate;j++){
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/          cptj= (j-1)*nlstate+i;
   /* cutv(path,optionfile,pathtot,'\\');*/          for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);              cptj2= (j2-1)*nlstate+i2;
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);              if(cptj2 <= cptj)
   chdir(path);                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   replace(pathc,path);            }
         }
 /*-------- arguments in the command line --------*/      fprintf(ficrescveij,"\n");
      
   /* Log file */    }
   strcat(filelog, optionfilefiname);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   strcat(filelog,".log");    /* */    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   if((ficlog=fopen(filelog,"w"))==NULL)    {    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     printf("Problem with logfile %s\n",filelog);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     goto end;    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fprintf(ficlog,"Log filename:%s\n",filelog);    printf("\n");
   fprintf(ficlog,"\n%s",version);    fprintf(ficlog,"\n");
   fprintf(ficlog,"\nEnter the parameter file name: ");  
   fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    free_vector(xm,1,npar);
   fflush(ficlog);    free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   /* */    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   strcpy(fileres,"r");    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   strcat(fileres, optionfilefiname);  }
   strcat(fileres,".txt");    /* Other files have txt extension */  
   /************ Variance ******************/
   /*---------arguments file --------*/  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[])
   {
   if((ficpar=fopen(optionfile,"r"))==NULL)    {    /* Variance of health expectancies */
     printf("Problem with optionfile %s\n",optionfile);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     fprintf(ficlog,"Problem with optionfile %s\n",optionfile);    /* double **newm;*/
     goto end;    double **dnewm,**doldm;
   }    double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
   strcpy(filereso,"o");    int k, cptcode;
   strcat(filereso,fileres);    double *xp;
   if((ficparo=fopen(filereso,"w"))==NULL) {    double **gp, **gm;  /* for var eij */
     printf("Problem with Output resultfile: %s\n", filereso);    double ***gradg, ***trgradg; /*for var eij */
     fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);    double **gradgp, **trgradgp; /* for var p point j */
     goto end;    double *gpp, *gmp; /* for var p point j */
   }    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
   /* Reads comments: lines beginning with '#' */    double age,agelim, hf;
   while((c=getc(ficpar))=='#' && c!= EOF){    double ***mobaverage;
     ungetc(c,ficpar);    int theta;
     fgets(line, MAXLINE, ficpar);    char digit[4];
     puts(line);    char digitp[25];
     fputs(line,ficparo);  
   }    char fileresprobmorprev[FILENAMELENGTH];
   ungetc(c,ficpar);  
     if(popbased==1){
   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);      if(mobilav!=0)
   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);        strcpy(digitp,"-populbased-mobilav-");
   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);      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);
            printf(" Error in movingaverage mobilav=%d\n",mobilav);
   covar=matrix(0,NCOVMAX,1,n);      }
   cptcovn=0;    }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;  
     strcpy(fileresprobmorprev,"prmorprev"); 
   ncovmodel=2+cptcovn;    sprintf(digit,"%-d",ij);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
      strcat(fileresprobmorprev,digit); /* Tvar to be done */
   /* Read guess parameters */    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   /* Reads comments: lines beginning with '#' */    strcat(fileresprobmorprev,fileres);
   while((c=getc(ficpar))=='#' && c!= EOF){    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     ungetc(c,ficpar);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     fgets(line, MAXLINE, ficpar);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     puts(line);    }
     fputs(line,ficparo);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   }   
   ungetc(c,ficpar);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
      pstamp(ficresprobmorprev);
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     for(i=1; i <=nlstate; i++)    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=1; j <=nlstate+ndeath-1; j++){    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fscanf(ficpar,"%1d%1d",&i1,&j1);      fprintf(ficresprobmorprev," p.%-d SE",j);
       fprintf(ficparo,"%1d%1d",i1,j1);      for(i=1; i<=nlstate;i++)
       if(mle==1)        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
         printf("%1d%1d",i,j);    }  
       fprintf(ficlog,"%1d%1d",i,j);    fprintf(ficresprobmorprev,"\n");
       for(k=1; k<=ncovmodel;k++){    fprintf(ficgp,"\n# Routine varevsij");
         fscanf(ficpar," %lf",&param[i][j][k]);    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
         if(mle==1){    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
           printf(" %lf",param[i][j][k]);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           fprintf(ficlog," %lf",param[i][j][k]);  /*   } */
         }    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         else    pstamp(ficresvij);
           fprintf(ficlog," %lf",param[i][j][k]);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
         fprintf(ficparo," %lf",param[i][j][k]);    if(popbased==1)
       }      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
       fscanf(ficpar,"\n");    else
       if(mle==1)      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
         printf("\n");    fprintf(ficresvij,"# Age");
       fprintf(ficlog,"\n");    for(i=1; i<=nlstate;i++)
       fprintf(ficparo,"\n");      for(j=1; j<=nlstate;j++)
     }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
      fprintf(ficresvij,"\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  
     xp=vector(1,npar);
   p=param[1][1];    dnewm=matrix(1,nlstate,1,npar);
      doldm=matrix(1,nlstate,1,nlstate);
   /* Reads comments: lines beginning with '#' */    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     puts(line);    gpp=vector(nlstate+1,nlstate+ndeath);
     fputs(line,ficparo);    gmp=vector(nlstate+1,nlstate+ndeath);
   }    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   ungetc(c,ficpar);    
     if(estepm < stepm){
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      printf ("Problem %d lower than %d\n",estepm, stepm);
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    }
   for(i=1; i <=nlstate; i++){    else  hstepm=estepm;   
     for(j=1; j <=nlstate+ndeath-1; j++){    /* For example we decided to compute the life expectancy with the smallest unit */
       fscanf(ficpar,"%1d%1d",&i1,&j1);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       printf("%1d%1d",i,j);       nhstepm is the number of hstepm from age to agelim 
       fprintf(ficparo,"%1d%1d",i1,j1);       nstepm is the number of stepm from age to agelin. 
       for(k=1; k<=ncovmodel;k++){       Look at function hpijx to understand why (it is linked to memory size questions) */
         fscanf(ficpar,"%le",&delti3[i][j][k]);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         printf(" %le",delti3[i][j][k]);       survival function given by stepm (the optimization length). Unfortunately it
         fprintf(ficparo," %le",delti3[i][j][k]);       means that if the survival funtion is printed every two years of age and if
       }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       fscanf(ficpar,"\n");       results. So we changed our mind and took the option of the best precision.
       printf("\n");    */
       fprintf(ficparo,"\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     }    agelim = AGESUP;
   }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   delti=delti3[1][1];      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   /* Reads comments: lines beginning with '#' */      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   while((c=getc(ficpar))=='#' && c!= EOF){      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
     ungetc(c,ficpar);      gp=matrix(0,nhstepm,1,nlstate);
     fgets(line, MAXLINE, ficpar);      gm=matrix(0,nhstepm,1,nlstate);
     puts(line);  
     fputs(line,ficparo);  
   }      for(theta=1; theta <=npar; theta++){
   ungetc(c,ficpar);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
            xp[i] = x[i] + (i==theta ?delti[theta]:0);
   matcov=matrix(1,npar,1,npar);        }
   for(i=1; i <=npar; i++){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     fscanf(ficpar,"%s",&str);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     if(mle==1)  
       printf("%s",str);        if (popbased==1) {
     fprintf(ficlog,"%s",str);          if(mobilav ==0){
     fprintf(ficparo,"%s",str);            for(i=1; i<=nlstate;i++)
     for(j=1; j <=i; j++){              prlim[i][i]=probs[(int)age][i][ij];
       fscanf(ficpar," %le",&matcov[i][j]);          }else{ /* mobilav */ 
       if(mle==1){            for(i=1; i<=nlstate;i++)
         printf(" %.5le",matcov[i][j]);              prlim[i][i]=mobaverage[(int)age][i][ij];
         fprintf(ficlog," %.5le",matcov[i][j]);          }
       }        }
       else    
         fprintf(ficlog," %.5le",matcov[i][j]);        for(j=1; j<= nlstate; j++){
       fprintf(ficparo," %.5le",matcov[i][j]);          for(h=0; h<=nhstepm; h++){
     }            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     fscanf(ficpar,"\n");              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     if(mle==1)          }
       printf("\n");        }
     fprintf(ficlog,"\n");        /* This for computing probability of death (h=1 means
     fprintf(ficparo,"\n");           computed over hstepm matrices product = hstepm*stepm months) 
   }           as a weighted average of prlim.
   for(i=1; i <=npar; i++)        */
     for(j=i+1;j<=npar;j++)        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       matcov[i][j]=matcov[j][i];          for(i=1,gpp[j]=0.; i<= nlstate; i++)
                gpp[j] += prlim[i][i]*p3mat[i][j][1];
   if(mle==1)        }    
     printf("\n");        /* end probability of death */
   fprintf(ficlog,"\n");  
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
     /*-------- Rewriting paramater file ----------*/        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
      strcpy(rfileres,"r");    /* "Rparameterfile */        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/   
      strcat(rfileres,".");    /* */        if (popbased==1) {
      strcat(rfileres,optionfilext);    /* Other files have txt extension */          if(mobilav ==0){
     if((ficres =fopen(rfileres,"w"))==NULL) {            for(i=1; i<=nlstate;i++)
       printf("Problem writing new parameter file: %s\n", fileres);goto end;              prlim[i][i]=probs[(int)age][i][ij];
       fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;          }else{ /* mobilav */ 
     }            for(i=1; i<=nlstate;i++)
     fprintf(ficres,"#%s\n",version);              prlim[i][i]=mobaverage[(int)age][i][ij];
              }
     /*-------- data file ----------*/        }
     if((fic=fopen(datafile,"r"))==NULL)    {  
       printf("Problem with datafile: %s\n", datafile);goto end;        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;          for(h=0; h<=nhstepm; h++){
     }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
     n= lastobs;          }
     severity = vector(1,maxwav);        }
     outcome=imatrix(1,maxwav+1,1,n);        /* This for computing probability of death (h=1 means
     num=ivector(1,n);           computed over hstepm matrices product = hstepm*stepm months) 
     moisnais=vector(1,n);           as a weighted average of prlim.
     annais=vector(1,n);        */
     moisdc=vector(1,n);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
     andc=vector(1,n);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
     agedc=vector(1,n);           gmp[j] += prlim[i][i]*p3mat[i][j][1];
     cod=ivector(1,n);        }    
     weight=vector(1,n);        /* end probability of death */
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */  
     mint=matrix(1,maxwav,1,n);        for(j=1; j<= nlstate; j++) /* vareij */
     anint=matrix(1,maxwav,1,n);          for(h=0; h<=nhstepm; h++){
     s=imatrix(1,maxwav+1,1,n);            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
     adl=imatrix(1,maxwav+1,1,n);              }
     tab=ivector(1,NCOVMAX);  
     ncodemax=ivector(1,8);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     i=1;        }
     while (fgets(line, MAXLINE, fic) != NULL)    {  
       if ((i >= firstobs) && (i <=lastobs)) {      } /* End theta */
          
         for (j=maxwav;j>=1;j--){      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  
           strcpy(line,stra);      for(h=0; h<=nhstepm; h++) /* veij */
           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);          for(theta=1; theta <=npar; theta++)
         }            trgradg[h][j][theta]=gradg[h][theta][j];
          
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);  
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      for(i=1;i<=nlstate;i++)
         for (j=ncovcol;j>=1;j--){        for(j=1;j<=nlstate;j++)
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);          vareij[i][j][(int)age] =0.;
         }  
         num[i]=atol(stra);      for(h=0;h<=nhstepm;h++){
                for(k=0;k<=nhstepm;k++){
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           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;}*/          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
         i=i+1;            for(j=1;j<=nlstate;j++)
       }              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
     }        }
     /* printf("ii=%d", ij);      }
        scanf("%d",i);*/    
   imx=i-1; /* Number of individuals */      /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
   /* for (i=1; i<=imx; i++){      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      for(j=nlstate+1;j<=nlstate+ndeath;j++)
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;        for(i=nlstate+1;i<=nlstate+ndeath;i++)
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;          varppt[j][i]=doldmp[j][i];
     }*/      /* end ppptj */
    /*  for (i=1; i<=imx; i++){      /*  x centered again */
      if (s[4][i]==9)  s[4][i]=-1;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
      printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     
        if (popbased==1) {
   /* Calculation of the number of parameter from char model*/        if(mobilav ==0){
   Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */          for(i=1; i<=nlstate;i++)
   Tprod=ivector(1,15);            prlim[i][i]=probs[(int)age][i][ij];
   Tvaraff=ivector(1,15);        }else{ /* mobilav */ 
   Tvard=imatrix(1,15,1,2);          for(i=1; i<=nlstate;i++)
   Tage=ivector(1,15);                  prlim[i][i]=mobaverage[(int)age][i][ij];
            }
   if (strlen(model) >1){      }
     j=0, j1=0, k1=1, k2=1;               
     j=nbocc(model,'+');      /* This for computing probability of death (h=1 means
     j1=nbocc(model,'*');         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
     cptcovn=j+1;         as a weighted average of prlim.
     cptcovprod=j1;      */
          for(j=nlstate+1;j<=nlstate+ndeath;j++){
     strcpy(modelsav,model);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       printf("Error. Non available option model=%s ",model);      }    
       fprintf(ficlog,"Error. Non available option model=%s ",model);      /* end probability of death */
       goto end;  
     }      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
          for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     for(i=(j+1); i>=1;i--){        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
       cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */        for(i=1; i<=nlstate;i++){
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyze it */          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        }
       /*scanf("%d",i);*/      } 
       if (strchr(strb,'*')) {  /* Model includes a product */      fprintf(ficresprobmorprev,"\n");
         cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/  
         if (strcmp(strc,"age")==0) { /* Vn*age */      fprintf(ficresvij,"%.0f ",age );
           cptcovprod--;      for(i=1; i<=nlstate;i++)
           cutv(strb,stre,strd,'V');        for(j=1; j<=nlstate;j++){
           Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
           cptcovage++;        }
             Tage[cptcovage]=i;      fprintf(ficresvij,"\n");
             /*printf("stre=%s ", stre);*/      free_matrix(gp,0,nhstepm,1,nlstate);
         }      free_matrix(gm,0,nhstepm,1,nlstate);
         else if (strcmp(strd,"age")==0) { /* or age*Vn */      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
           cptcovprod--;      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
           cutv(strb,stre,strc,'V');      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           Tvar[i]=atoi(stre);    } /* End age */
           cptcovage++;    free_vector(gpp,nlstate+1,nlstate+ndeath);
           Tage[cptcovage]=i;    free_vector(gmp,nlstate+1,nlstate+ndeath);
         }    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
         else {  /* Age is not in the model */    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
           cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/    fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
           Tvar[i]=ncovcol+k1;    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
           cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
           Tprod[k1]=i;  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
           Tvard[k1][1]=atoi(strc); /* m*/  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
           Tvard[k1][2]=atoi(stre); /* n */  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
           Tvar[cptcovn+k2]=Tvard[k1][1];    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
           Tvar[cptcovn+k2+1]=Tvard[k1][2];    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
           for (k=1; k<=lastobs;k++)    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 2 ",subdirf(fileresprobmorprev));
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
           k1++;    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);
           k2=k2+2;    /*  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);
         }  */
       }  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
       else { /* no more sum */    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/  
        /*  scanf("%d",i);*/    free_vector(xp,1,npar);
       cutv(strd,strc,strb,'V');    free_matrix(doldm,1,nlstate,1,nlstate);
       Tvar[i]=atoi(strc);    free_matrix(dnewm,1,nlstate,1,npar);
       }    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       strcpy(modelsav,stra);      free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         scanf("%d",i);*/    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     } /* end of loop + */    fclose(ficresprobmorprev);
   } /* end model */    fflush(ficgp);
      fflush(fichtm); 
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);  }  /* end varevsij */
   printf("cptcovprod=%d ", cptcovprod);  
   fprintf(ficlog,"cptcovprod=%d ", cptcovprod);  /************ Variance of prevlim ******************/
   scanf("%d ",i);*/  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
     fclose(fic);  {
     /* Variance of prevalence limit */
     /*  if(mle==1){*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     if (weightopt != 1) { /* Maximisation without weights*/    double **newm;
       for(i=1;i<=n;i++) weight[i]=1.0;    double **dnewm,**doldm;
     }    int i, j, nhstepm, hstepm;
     /*-calculation of age at interview from date of interview and age at death -*/    int k, cptcode;
     agev=matrix(1,maxwav,1,imx);    double *xp;
     double *gp, *gm;
     for (i=1; i<=imx; i++) {    double **gradg, **trgradg;
       for(m=2; (m<= maxwav); m++) {    double age,agelim;
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){    int theta;
          anint[m][i]=9999;    
          s[m][i]=-1;    pstamp(ficresvpl);
        }    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;    fprintf(ficresvpl,"# Age");
       }    for(i=1; i<=nlstate;i++)
     }        fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
     for (i=1; i<=imx; i++)  {  
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    xp=vector(1,npar);
       for(m=1; (m<= maxwav); m++){    dnewm=matrix(1,nlstate,1,npar);
         if(s[m][i] >0){    doldm=matrix(1,nlstate,1,nlstate);
           if (s[m][i] >= nlstate+1) {    
             if(agedc[i]>0)    hstepm=1*YEARM; /* Every year of age */
               if(moisdc[i]!=99 && andc[i]!=9999)    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
                 agev[m][i]=agedc[i];    agelim = AGESUP;
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
            else {      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
               if (andc[i]!=9999){      if (stepm >= YEARM) hstepm=1;
               printf("Warning negative age at death: %d line:%d\n",num[i],i);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
               fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);      gradg=matrix(1,npar,1,nlstate);
               agev[m][i]=-1;      gp=vector(1,nlstate);
               }      gm=vector(1,nlstate);
             }  
           }      for(theta=1; theta <=npar; theta++){
           else if(s[m][i] !=9){ /* Should no more exist */        for(i=1; i<=npar; i++){ /* Computes gradient */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
             if(mint[m][i]==99 || anint[m][i]==9999)        }
               agev[m][i]=1;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
             else if(agev[m][i] <agemin){        for(i=1;i<=nlstate;i++)
               agemin=agev[m][i];          gp[i] = prlim[i][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/      
             }        for(i=1; i<=npar; i++) /* Computes gradient */
             else if(agev[m][i] >agemax){          xp[i] = x[i] - (i==theta ?delti[theta]:0);
               agemax=agev[m][i];        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/        for(i=1;i<=nlstate;i++)
             }          gm[i] = prlim[i][i];
             /*agev[m][i]=anint[m][i]-annais[i];*/  
             /*   agev[m][i] = age[i]+2*m;*/        for(i=1;i<=nlstate;i++)
           }          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
           else { /* =9 */      } /* End theta */
             agev[m][i]=1;  
             s[m][i]=-1;      trgradg =matrix(1,nlstate,1,npar);
           }  
         }      for(j=1; j<=nlstate;j++)
         else /*= 0 Unknown */        for(theta=1; theta <=npar; theta++)
           agev[m][i]=1;          trgradg[j][theta]=gradg[theta][j];
       }  
          for(i=1;i<=nlstate;i++)
     }        varpl[i][(int)age] =0.;
     for (i=1; i<=imx; i++)  {      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       for(m=1; (m<= maxwav); m++){      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
         if (s[m][i] > (nlstate+ndeath)) {      for(i=1;i<=nlstate;i++)
           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);          varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
           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);    
           goto end;      fprintf(ficresvpl,"%.0f ",age );
         }      for(i=1; i<=nlstate;i++)
       }        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
     }      fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      free_vector(gm,1,nlstate);
  fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     free_vector(severity,1,maxwav);    } /* End age */
     free_imatrix(outcome,1,maxwav+1,1,n);  
     free_vector(moisnais,1,n);    free_vector(xp,1,npar);
     free_vector(annais,1,n);    free_matrix(doldm,1,nlstate,1,npar);
     /* free_matrix(mint,1,maxwav,1,n);    free_matrix(dnewm,1,nlstate,1,nlstate);
        free_matrix(anint,1,maxwav,1,n);*/  
     free_vector(moisdc,1,n);  }
     free_vector(andc,1,n);  
   /************ Variance of one-step probabilities  ******************/
      void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
     wav=ivector(1,imx);  {
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    int i, j=0,  i1, k1, l1, t, tj;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    int k2, l2, j1,  z1;
        int k=0,l, cptcode;
     /* Concatenates waves */    int first=1, first1, first2;
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
       Tcode=ivector(1,100);    double *gp, *gm;
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    double **gradg, **trgradg;
       ncodemax[1]=1;    double **mu;
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);    double age,agelim, cov[NCOVMAX+1];
          double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
    codtab=imatrix(1,100,1,10);    int theta;
    h=0;    char fileresprob[FILENAMELENGTH];
    m=pow(2,cptcoveff);    char fileresprobcov[FILENAMELENGTH];
      char fileresprobcor[FILENAMELENGTH];
    for(k=1;k<=cptcoveff; k++){    double ***varpij;
      for(i=1; i <=(m/pow(2,k));i++){  
        for(j=1; j <= ncodemax[k]; j++){    strcpy(fileresprob,"prob"); 
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    strcat(fileresprob,fileres);
            h++;    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;      printf("Problem with resultfile: %s\n", fileresprob);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
          }    }
        }    strcpy(fileresprobcov,"probcov"); 
      }    strcat(fileresprobcov,fileres);
    }    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);      printf("Problem with resultfile: %s\n", fileresprobcov);
       codtab[1][2]=1;codtab[2][2]=2; */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
    /* for(i=1; i <=m ;i++){    }
       for(k=1; k <=cptcovn; k++){    strcpy(fileresprobcor,"probcor"); 
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);    strcat(fileresprobcor,fileres);
       }    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("\n");      printf("Problem with resultfile: %s\n", fileresprobcor);
       }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
       scanf("%d",i);*/    }
        printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
    /* Calculates basic frequencies. Computes observed prevalence at single age    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
        and prints on file fileres'p'. */    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
        printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
        fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    pstamp(ficresprob);
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprob,"# Age");
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    pstamp(ficresprobcov);
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
          fprintf(ficresprobcov,"# Age");
     /* For Powell, parameters are in a vector p[] starting at p[1]    pstamp(ficresprobcor);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficresprobcor,"# Age");
   
     if(mle==1){  
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    for(i=1; i<=nlstate;i++)
     }      for(j=1; j<=(nlstate+ndeath);j++){
            fprintf(ficresprob," p%1d-%1d (SE)",i,j);
     /*--------- results files --------------*/        fprintf(ficresprobcov," p%1d-%1d ",i,j);
     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(ficresprobcor," p%1d-%1d ",i,j);
        }  
    /* fprintf(ficresprob,"\n");
    jk=1;    fprintf(ficresprobcov,"\n");
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    fprintf(ficresprobcor,"\n");
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");   */
    fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    xp=vector(1,npar);
    for(i=1,jk=1; i <=nlstate; i++){    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
      for(k=1; k <=(nlstate+ndeath); k++){    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
        if (k != i)    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
          {    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
            printf("%d%d ",i,k);    first=1;
            fprintf(ficlog,"%d%d ",i,k);    fprintf(ficgp,"\n# Routine varprob");
            fprintf(ficres,"%1d%1d ",i,k);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
            for(j=1; j <=ncovmodel; j++){    fprintf(fichtm,"\n");
              printf("%f ",p[jk]);  
              fprintf(ficlog,"%f ",p[jk]);    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
              fprintf(ficres,"%f ",p[jk]);    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
              jk++;    file %s<br>\n",optionfilehtmcov);
            }    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
            printf("\n");  and drawn. It helps understanding how is the covariance between two incidences.\
            fprintf(ficlog,"\n");   They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
            fprintf(ficres,"\n");    fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
          }  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
      }  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>\
    if(mle==1){   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
      /* Computing hessian and covariance matrix */   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
      ftolhess=ftol; /* Usually correct */  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
      hesscov(matcov, p, npar, delti, ftolhess, func);  
    }    cov[1]=1;
    fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");    /* tj=cptcoveff; */
    printf("# Scales (for hessian or gradient estimation)\n");    tj = (int) pow(2,cptcoveff);
    fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
    for(i=1,jk=1; i <=nlstate; i++){    j1=0;
      for(j=1; j <=nlstate+ndeath; j++){    for(j1=1; j1<=tj;j1++){
        if (j!=i) {      /*for(i1=1; i1<=ncodemax[t];i1++){ */
          fprintf(ficres,"%1d%1d",i,j);      /*j1++;*/
          printf("%1d%1d",i,j);        if  (cptcovn>0) {
          fprintf(ficlog,"%1d%1d",i,j);          fprintf(ficresprob, "\n#********** Variable "); 
          for(k=1; k<=ncovmodel;k++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            printf(" %.5e",delti[jk]);          fprintf(ficresprob, "**********\n#\n");
            fprintf(ficlog," %.5e",delti[jk]);          fprintf(ficresprobcov, "\n#********** Variable "); 
            fprintf(ficres," %.5e",delti[jk]);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
            jk++;          fprintf(ficresprobcov, "**********\n#\n");
          }          
          printf("\n");          fprintf(ficgp, "\n#********** Variable "); 
          fprintf(ficlog,"\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
          fprintf(ficres,"\n");          fprintf(ficgp, "**********\n#\n");
        }          
      }          
    }          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
              for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    k=1;          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
    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)          fprintf(ficresprobcor, "\n#********** Variable ");    
      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");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
    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");          fprintf(ficresprobcor, "**********\n#");    
    for(i=1;i<=npar;i++){        }
      /*  if (k>nlstate) k=1;        
          i1=(i-1)/(ncovmodel*nlstate)+1;        gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
          fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
          printf("%s%d%d",alph[k],i1,tab[i]);*/        gp=vector(1,(nlstate)*(nlstate+ndeath));
      fprintf(ficres,"%3d",i);        gm=vector(1,(nlstate)*(nlstate+ndeath));
      if(mle==1)        for (age=bage; age<=fage; age ++){ 
        printf("%3d",i);          cov[2]=age;
      fprintf(ficlog,"%3d",i);          for (k=1; k<=cptcovn;k++) {
      for(j=1; j<=i;j++){            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];/* j1 1 2 3 4
        fprintf(ficres," %.5e",matcov[i][j]);                                                           * 1  1 1 1 1
        if(mle==1)                                                           * 2  2 1 1 1
          printf(" %.5e",matcov[i][j]);                                                           * 3  1 2 1 1
        fprintf(ficlog," %.5e",matcov[i][j]);                                                           */
      }            /* nbcode[1][1]=0 nbcode[1][2]=1;*/
      fprintf(ficres,"\n");          }
      if(mle==1)          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
        printf("\n");          for (k=1; k<=cptcovprod;k++)
      fprintf(ficlog,"\n");            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
      k++;          
    }      
              for(theta=1; theta <=npar; theta++){
    while((c=getc(ficpar))=='#' && c!= EOF){            for(i=1; i<=npar; i++)
      ungetc(c,ficpar);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
      fgets(line, MAXLINE, ficpar);            
      puts(line);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
      fputs(line,ficparo);            
    }            k=0;
    ungetc(c,ficpar);            for(i=1; i<= (nlstate); i++){
    estepm=0;              for(j=1; j<=(nlstate+ndeath);j++){
    fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);                k=k+1;
    if (estepm==0 || estepm < stepm) estepm=stepm;                gp[k]=pmmij[i][j];
    if (fage <= 2) {              }
      bage = ageminpar;            }
      fage = agemaxpar;            
    }            for(i=1; i<=npar; i++)
                  xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
    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);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
    fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);            k=0;
                for(i=1; i<=(nlstate); i++){
    while((c=getc(ficpar))=='#' && c!= EOF){              for(j=1; j<=(nlstate+ndeath);j++){
      ungetc(c,ficpar);                k=k+1;
      fgets(line, MAXLINE, ficpar);                gm[k]=pmmij[i][j];
      puts(line);              }
      fputs(line,ficparo);            }
    }       
    ungetc(c,ficpar);            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
                gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
    fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);          }
    fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
    fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
                for(theta=1; theta <=npar; theta++)
    while((c=getc(ficpar))=='#' && c!= EOF){              trgradg[j][theta]=gradg[theta][j];
      ungetc(c,ficpar);          
      fgets(line, MAXLINE, ficpar);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
      puts(line);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
      fputs(line,ficparo);  
    }          pmij(pmmij,cov,ncovmodel,x,nlstate);
    ungetc(c,ficpar);          
            k=0;
           for(i=1; i<=(nlstate); i++){
    dateprev1=anprev1+mprev1/12.+jprev1/365.;            for(j=1; j<=(nlstate+ndeath);j++){
    dateprev2=anprev2+mprev2/12.+jprev2/365.;              k=k+1;
               mu[k][(int) age]=pmmij[i][j];
   fscanf(ficpar,"pop_based=%d\n",&popbased);            }
   fprintf(ficparo,"pop_based=%d\n",popbased);            }
   fprintf(ficres,"pop_based=%d\n",popbased);            for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
              for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
   while((c=getc(ficpar))=='#' && c!= EOF){              varpij[i][j][(int)age] = doldm[i][j];
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);          /*printf("\n%d ",(int)age);
     puts(line);            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     fputs(line,ficparo);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   }            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
   ungetc(c,ficpar);            }*/
   
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);          fprintf(ficresprob,"\n%d ",(int)age);
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);          fprintf(ficresprobcov,"\n%d ",(int)age);
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);          fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
 while((c=getc(ficpar))=='#' && c!= EOF){            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
     ungetc(c,ficpar);          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
     fgets(line, MAXLINE, ficpar);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
     puts(line);            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
     fputs(line,ficparo);          }
   }          i=0;
   ungetc(c,ficpar);          for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);              i++;
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                /* printf(" k=%d l=%d i=%d j=%d\n",k,l,i,j);fflush(stdout); */
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
 /*------------ gnuplot -------------*/                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
   strcpy(optionfilegnuplot,optionfilefiname);              }
   strcat(optionfilegnuplot,".gp");            }
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {          }/* end of loop for state */
     printf("Problem with file %s",optionfilegnuplot);        } /* end of loop for age */
   }        free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
   fclose(ficgp);        free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);        free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
 /*--------- index.htm --------*/        free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         
   strcpy(optionfilehtm,optionfile);        /* Confidence intervalle of pij  */
   strcat(optionfilehtm,".htm");        /*
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {          fprintf(ficgp,"\nunset parametric;unset label");
     printf("Problem with %s \n",optionfilehtm), exit(0);          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
   }          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
 \n          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
 Total number of observations=%d <br>\n        */
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n  
 <hr  size=\"2\" color=\"#EC5E5E\">        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
  <ul><li><h4>Parameter files</h4>\n        first1=1;first2=2;
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n        for (k2=1; k2<=(nlstate);k2++){
  - Log file of the run: <a href=\"%s\">%s</a><br>\n          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
  - 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);            if(l2==k2) continue;
   fclose(fichtm);            j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                  if(l1==k1) continue;
 /*------------ free_vector  -------------*/                i=(k1-1)*(nlstate+ndeath)+l1;
  chdir(path);                if(i<=j) continue;
                  for (age=bage; age<=fage; age ++){ 
  free_ivector(wav,1,imx);                  if ((int)age %5==0){
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);                      v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
  free_ivector(num,1,n);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
  free_vector(agedc,1,n);                    mu1=mu[i][(int) age]/stepm*YEARM ;
  /*free_matrix(covar,1,NCOVMAX,1,n);*/                    mu2=mu[j][(int) age]/stepm*YEARM;
  fclose(ficparo);                    c12=cv12/sqrt(v1*v2);
  fclose(ficres);                    /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   /*--------------- Prevalence limit --------------*/                    if ((lc2 <0) || (lc1 <0) ){
                        if(first2==1){
   strcpy(filerespl,"pl");                        first1=0;
   strcat(filerespl,fileres);                      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);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {                      }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;                      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);
     fprintf(ficlog,"Problem with Prev limit resultfile: %s\n", filerespl);goto end;                      /* lc1=fabs(lc1); */ /* If we want to have them positive */
   }                      /* lc2=fabs(lc2); */
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);                    }
   fprintf(ficlog,"Computing prevalence limit: result on file '%s' \n", filerespl);  
   fprintf(ficrespl,"#Prevalence limit\n");                    /* Eigen vectors */
   fprintf(ficrespl,"#Age ");                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);                    /*v21=sqrt(1.-v11*v11); *//* error */
   fprintf(ficrespl,"\n");                    v21=(lc1-v1)/cv12*v11;
                      v12=-v21;
   prlim=matrix(1,nlstate,1,nlstate);                    v22=v11;
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                    tnalp=v21/v11;
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                    if(first1==1){
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      first1=0;
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                      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);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */                    }
   k=0;                    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);
   agebase=ageminpar;                    /*printf(fignu*/
   agelim=agemaxpar;                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
   ftolpl=1.e-10;                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
   i1=cptcoveff;                    if(first==1){
   if (cptcovn < 1){i1=1;}                      first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
   for(cptcov=1;cptcov<=i1;cptcov++){                      fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                      fprintf(ficgp,"\nset ter png small size 320, 240");
         k=k+1;                      fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/   :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
         fprintf(ficrespl,"\n#******");  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
         printf("\n#******");                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
         fprintf(ficlog,"\n#******");                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
         for(j=1;j<=cptcoveff;j++) {                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
           printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
           fprintf(ficlog," 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);
         }                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
         fprintf(ficrespl,"******\n");                      fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
         printf("******\n");                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         fprintf(ficlog,"******\n");                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                            }else{
         for (age=agebase; age<=agelim; age++){                      first=0;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
           fprintf(ficrespl,"%.0f",age );                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
           for(i=1; i<=nlstate;i++)                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
           fprintf(ficrespl," %.5f", prlim[i][i]);                      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(ficrespl,"\n");                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
         }                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
       }                    }/* if first */
     }                  } /* age mod 5 */
   fclose(ficrespl);                } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   /*------------- h Pij x at various ages ------------*/                first=1;
                } /*l12 */
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);            } /* k12 */
   if((ficrespij=fopen(filerespij,"w"))==NULL) {          } /*l1 */
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;        }/* k1 */
     fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;        /* } /* loop covariates */
   }    }
   printf("Computing pij: result on file '%s' \n", filerespij);    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
   fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
      free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
   stepsize=(int) (stepm+YEARM-1)/YEARM;    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
   /*if (stepm<=24) stepsize=2;*/    free_vector(xp,1,npar);
     fclose(ficresprob);
   agelim=AGESUP;    fclose(ficresprobcov);
   hstepm=stepsize*YEARM; /* Every year of age */    fclose(ficresprobcor);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    fflush(ficgp);
     fflush(fichtmcov);
   /* hstepm=1;   aff par mois*/  }
   
   k=0;  
   for(cptcov=1;cptcov<=i1;cptcov++){  /******************* Printing html file ***********/
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
       k=k+1;                    int lastpass, int stepm, int weightopt, char model[],\
         fprintf(ficrespij,"\n#****** ");                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
         for(j=1;j<=cptcoveff;j++)                    int popforecast, int estepm ,\
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                    double jprev1, double mprev1,double anprev1, \
         fprintf(ficrespij,"******\n");                    double jprev2, double mprev2,double anprev2){
            int jj1, k1, i1, cpt;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */     fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
           /*      nhstepm=nhstepm*YEARM; aff par mois*/     fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
           oldm=oldms;savm=savms;     fprintf(fichtm,"\
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);     - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
           fprintf(ficrespij,"# Age");             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
           for(i=1; i<=nlstate;i++)     fprintf(fichtm,"\
             for(j=1; j<=nlstate+ndeath;j++)   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
               fprintf(ficrespij," %1d-%1d",i,j);             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
           fprintf(ficrespij,"\n");     fprintf(fichtm,"\
            for (h=0; h<=nhstepm; h++){   - (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): \
             fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );     <a href=\"%s\">%s</a> <br>\n",
             for(i=1; i<=nlstate;i++)             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
               for(j=1; j<=nlstate+ndeath;j++)     fprintf(fichtm,"\
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);   - Population projections by age and states: \
             fprintf(ficrespij,"\n");     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
              }  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
           fprintf(ficrespij,"\n");  
         }   m=pow(2,cptcoveff);
     }   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   }  
    jj1=0;
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);   for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
   fclose(ficrespij);       jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
   /*---------- Forecasting ------------------*/         for (cpt=1; cpt<=cptcoveff;cpt++) 
   if((stepm == 1) && (strcmp(model,".")==0)){           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);       }
   }       /* Pij */
   else{       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> \
     erreur=108;  <img src=\"%s%d_1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
     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);       /* Quasi-incidences */
     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);       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); 
          /* Period (stable) prevalence in each health state */
   /*---------- Health expectancies and variances ------------*/         for(cpt=1; cpt<=nlstate;cpt++){
            fprintf(fichtm,"<br>- Convergence from each state (1 to %d) to period (stable) prevalence in state %d <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
   strcpy(filerest,"t");  <img src=\"%s%d_%d.png\">",nlstate, cpt, subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
   strcat(filerest,fileres);         }
   if((ficrest=fopen(filerest,"w"))==NULL) {       for(cpt=1; cpt<=nlstate;cpt++) {
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;          fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies in each alive state (1 to %d) : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
     fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;  <img src=\"%s%d%d.png\">",cpt,nlstate,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
   }       }
   printf("Computing Total LEs with variances: file '%s' \n", filerest);     } /* end i1 */
   fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest);   }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   strcpy(filerese,"e");  
   strcat(filerese,fileres);   fprintf(fichtm,"\
   if((ficreseij=fopen(filerese,"w"))==NULL) {  \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
     fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);  
   }   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
   fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);   fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
   strcpy(fileresv,"v");           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   strcat(fileresv,fileres);  
   if((ficresvij=fopen(fileresv,"w"))==NULL) {   fprintf(fichtm,"\
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
     fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
   }   fprintf(fichtm,"\
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);   - 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): \
   fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);     <a href=\"%s\">%s</a> <br>\n</li>",
   calagedate=-1;             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);   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): \
   k=0;     <a href=\"%s\">%s</a> <br>\n</li>",
   for(cptcov=1;cptcov<=i1;cptcov++){             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){   fprintf(fichtm,"\
       k=k+1;   - 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(ficrest,"\n#****** ");           estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
       for(j=1;j<=cptcoveff;j++)   fprintf(fichtm,"\
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   - 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(ficrest,"******\n");           estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
       fprintf(ficreseij,"\n#****** ");   - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
       for(j=1;j<=cptcoveff;j++)           subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficreseij,"******\n");  /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
       fprintf(ficresvij,"\n#****** ");  /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
       for(j=1;j<=cptcoveff;j++)  /*      <br>",fileres,fileres,fileres,fileres); */
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  /*  else  */
       fprintf(ficresvij,"******\n");  /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
       oldm=oldms;savm=savms;  
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);     m=pow(2,cptcoveff);
     if (cptcovn < 1) {m=1;ncodemax[1]=1;}
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  
       oldm=oldms;savm=savms;   jj1=0;
       varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0);   for(k1=1; k1<=m;k1++){
       if(popbased==1){     for(i1=1; i1<=ncodemax[k1];i1++){
         varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased);       jj1++;
        }       if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
           for (cpt=1; cpt<=cptcoveff;cpt++) 
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
       fprintf(ficrest,"\n");       }
        for(cpt=1; cpt<=nlstate;cpt++) {
       epj=vector(1,nlstate+1);         fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
       for(age=bage; age <=fage ;age++){  prevalence (with 95%% confidence interval) in state (%d): %s%d_%d.png <br>\
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  <img src=\"%s%d_%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
         if (popbased==1) {       }
           for(i=1; i<=nlstate;i++)       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
             prlim[i][i]=probs[(int)age][i][k];  health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
         }  true period expectancies (those weighted with period prevalences are also\
           drawn in addition to the population based expectancies computed using\
         fprintf(ficrest," %4.0f",age);   observed and cahotic prevalences: %s%d.png<br>\
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {     } /* end i1 */
             epj[j] += prlim[i][i]*eij[i][j][(int)age];   }/* End k1 */
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/   fprintf(fichtm,"</ul>");
           }   fflush(fichtm);
           epj[nlstate+1] +=epj[j];  }
         }  
   /******************* Gnuplot file **************/
         for(i=1, vepp=0.;i <=nlstate;i++)  void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
           for(j=1;j <=nlstate;j++)  
             vepp += vareij[i][j][(int)age];    char dirfileres[132],optfileres[132];
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));    int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
         for(j=1;j <=nlstate;j++){    int ng=0;
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
         }  /*     printf("Problem with file %s",optionfilegnuplot); */
         fprintf(ficrest,"\n");  /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
       }  /*   } */
     }  
   }    /*#ifdef windows */
 free_matrix(mint,1,maxwav,1,n);    fprintf(ficgp,"cd \"%s\" \n",pathc);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);      /*#endif */
     free_vector(weight,1,n);    m=pow(2,cptcoveff);
   fclose(ficreseij);  
   fclose(ficresvij);    strcpy(dirfileres,optionfilefiname);
   fclose(ficrest);    strcpy(optfileres,"vpl");
   fclose(ficpar);   /* 1eme*/
   free_vector(epj,1,nlstate+1);    fprintf(ficgp,"\n# 1st: Period (stable) prevalence with CI: 'vpl' files\n");
      for (cpt=1; cpt<= nlstate ; cpt ++) {
   /*------- Variance limit prevalence------*/        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);
   strcpy(fileresvpl,"vpl");       fprintf(ficgp,"\n#set out \"v%s%d_%d.png\" \n",optionfilefiname,cpt,k1);
   strcat(fileresvpl,fileres);       fprintf(ficgp,"set xlabel \"Age\" \n\
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {  set ylabel \"Probability\" \n\
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);  set ter png small size 320, 240\n\
     exit(0);  plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   }  
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);       for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
   k=0;         else        fprintf(ficgp," \%%*lf (\%%*lf)");
   for(cptcov=1;cptcov<=i1;cptcov++){       }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       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);
       k=k+1;       for (i=1; i<= nlstate ; i ++) {
       fprintf(ficresvpl,"\n#****** ");         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
       for(j=1;j<=cptcoveff;j++)         else fprintf(ficgp," \%%*lf (\%%*lf)");
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       } 
       fprintf(ficresvpl,"******\n");       fprintf(ficgp,"\" t\"95\%% CI\" w l lt 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
             for (i=1; i<= nlstate ; i ++) {
       varpl=matrix(1,nlstate,(int) bage, (int) fage);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
       oldm=oldms;savm=savms;         else fprintf(ficgp," \%%*lf (\%%*lf)");
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);       }  
     }       fprintf(ficgp,"\" t\"\" w l lt 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
  }     }
     }
   fclose(ficresvpl);    /*2 eme*/
     fprintf(ficgp,"\n# 2nd: Total life expectancy with CI: 't' files\n");
   /*---------- End : free ----------------*/    for (k1=1; k1<= m ; k1 ++) { 
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      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);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      for (i=1; i<= nlstate+1 ; i ++) {
          k=2*i;
          fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        for (j=1; j<= nlstate+1 ; j ++) {
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          else fprintf(ficgp," \%%*lf (\%%*lf)");
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);        }   
          if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
   free_matrix(matcov,1,npar,1,npar);        else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
   free_vector(delti,1,npar);        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
   free_matrix(agev,1,maxwav,1,imx);        for (j=1; j<= nlstate+1 ; j ++) {
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
   fprintf(fichtm,"\n</body>");        }   
   fclose(fichtm);        fprintf(ficgp,"\" t\"\" w l lt 0,");
   fclose(ficgp);        fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
          for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
   if(erreur >0){          else fprintf(ficgp," \%%*lf (\%%*lf)");
     printf("End of Imach with error or warning %d\n",erreur);        }   
     fprintf(ficlog,"End of Imach with error or warning %d\n",erreur);        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l lt 0");
   }else{        else fprintf(ficgp,"\" t\"\" w l lt 0,");
    printf("End of Imach\n");      }
    fprintf(ficlog,"End of Imach\n");    }
   }    
   printf("See log file on %s\n",filelog);    /*3eme*/
   fclose(ficlog);    
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */    for (k1=1; k1<= m ; k1 ++) { 
        for (cpt=1; cpt<= nlstate ; cpt ++) {
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/        /*       k=2+nlstate*(2*cpt-2); */
   /*printf("Total time was %d uSec.\n", total_usecs);*/        k=2+(nlstate+1)*(cpt-1);
   /*------ End -----------*/        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small size 320, 240\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
  end:        /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
 #ifdef windows          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
   /* chdir(pathcd);*/          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
 #endif          fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
  /*system("wgnuplot graph.plt");*/          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
  /*system("../gp37mgw/wgnuplot graph.plt");*/          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
  /*system("cd ../gp37mgw");*/          
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/        */
  strcpy(plotcmd,GNUPLOTPROGRAM);        for (i=1; i< nlstate ; i ++) {
  strcat(plotcmd," ");          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);
  strcat(plotcmd,optionfilegnuplot);          /*      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);*/
  system(plotcmd);          
         } 
 #ifdef windows        fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
   while (z[0] != 'q') {      }
     /* chdir(path); */    }
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");    
     scanf("%s",z);    /* CV preval stable (period) */
     if (z[0] == 'c') system("./imach");    for (k1=1; k1<= m ; k1 ++) { /* For each multivariate if any */
     else if (z[0] == 'e') system(optionfilehtm);      for (cpt=1; cpt<=nlstate ; cpt ++) { /* For each life state */
     else if (z[0] == 'g') system(plotcmd);        k=3;
     else if (z[0] == 'q') exit(0);        fprintf(ficgp,"\n#\n#\n#CV preval stable (period): 'pij' files, cov=%d state=%d",k1, cpt);
   }        fprintf(ficgp,"\nset out \"%s%d_%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
 #endif        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
 }  set ter png small size 320, 240\n\
   unset log y\n\
   plot [%.f:%.f]  ", ageminpar, agemaxpar);
         for (i=1; i<= nlstate ; i ++){
           if(i==1)
             fprintf(ficgp,"\"%s\"",subdirf2(fileres,"pij"));
           else
             fprintf(ficgp,", '' ");
           l=(nlstate+ndeath)*(i-1)+1;
           fprintf(ficgp," u ($1==%d ? ($3):1/0):($%d/($%d",k1,k+l+(cpt-1),k+l);
           for (j=1; j<= (nlstate-1) ; j ++)
             fprintf(ficgp,"+$%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 or gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error or 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("gnuplot command might not be in your path: %s, err=%d\n", plotcmd, outcmd);
       printf("\n Trying if gnuplot resides on the same directory that IMaCh\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(" Successul, please wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit results with your browser, g to graph again and q for exit: ");
       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.1.51  
changed lines
  Added in v.1.155


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