Diff for /imach/src/imach.c between versions 1.41.2.1 and 1.194

version 1.41.2.1, 2003/06/12 10:43:20 version 1.194, 2015/08/18 13:32:00
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.194  2015/08/18 13:32:00  brouard
      Summary:  Adding error when the covariance matrix doesn't contain the exact number of lines required by the model line.
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    Revision 1.193  2015/08/04 07:17:42  brouard
   first survey ("cross") where individuals from different ages are    Summary: 0.98q4
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.192  2015/07/16 16:49:02  brouard
   second wave of interviews ("longitudinal") which measure each change    Summary: Fixing some outputs
   (if any) in individual health status.  Health expectancies are  
   computed from the time spent in each health state according to a    Revision 1.191  2015/07/14 10:00:33  brouard
   model. More health states you consider, more time is necessary to reach the    Summary: Some fixes
   Maximum Likelihood of the parameters involved in the model.  The  
   simplest model is the multinomial logistic model where pij is the    Revision 1.190  2015/05/05 08:51:13  brouard
   probability to be observed in state j at the second wave    Summary: Adding digits in output parameters (7 digits instead of 6)
   conditional to be observed in state i at the first wave. Therefore  
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Fix 1+age+.
   '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 1.189  2015/04/30 14:45:16  brouard
   where the markup *Covariates have to be included here again* invites    Summary: 0.98q2
   you to do it.  More covariates you add, slower the  
   convergence.    Revision 1.188  2015/04/30 08:27:53  brouard
     *** empty log message ***
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.187  2015/04/29 09:11:15  brouard
   identical for each individual. Also, if a individual missed an    *** empty log message ***
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.186  2015/04/23 12:01:52  brouard
     Summary: V1*age is working now, version 0.98q1
   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    Some codes had been disabled in order to simplify and Vn*age was
   split into an exact number (nh*stepm) of unobserved intermediate    working in the optimization phase, ie, giving correct MLE parameters,
   states. This elementary transition (by month or quarter trimester,    but, as usual, outputs were not correct and program core dumped.
   semester or year) is model as a multinomial logistic.  The hPx  
   matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.185  2015/03/11 13:26:42  brouard
   and the contribution of each individual to the likelihood is simply    Summary: Inclusion of compile and links command line for Intel Compiler
   hPijx.  
     Revision 1.184  2015/03/11 11:52:39  brouard
   Also this programme outputs the covariance matrix of the parameters but also    Summary: Back from Windows 8. Intel Compiler
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.183  2015/03/10 20:34:32  brouard
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Summary: 0.98q0, trying with directest, mnbrak fixed
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    We use directest instead of original Powell test; probably no
   from the European Union.    incidence on the results, but better justifications;
   It is copyrighted identically to a GNU software product, ie programme and    We fixed Numerical Recipes mnbrak routine which was wrong and gave
   software can be distributed freely for non commercial use. Latest version    wrong results.
   can be accessed at http://euroreves.ined.fr/imach .  
   **********************************************************************/    Revision 1.182  2015/02/12 08:19:57  brouard
      Summary: Trying to keep directest which seems simpler and more general
 #include <math.h>    Author: Nicolas Brouard
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.181  2015/02/11 23:22:24  brouard
 #include <unistd.h>    Summary: Comments on Powell added
   
 #define MAXLINE 256    Author:
 #define GNUPLOTPROGRAM "wgnuplot"  
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    Revision 1.180  2015/02/11 17:33:45  brouard
 #define FILENAMELENGTH 80    Summary: Finishing move from main to function (hpijx and prevalence_limit)
 /*#define DEBUG*/  
     Revision 1.179  2015/01/04 09:57:06  brouard
 /*#define windows*/    Summary: back to OS/X
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */  
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    Revision 1.178  2015/01/04 09:35:48  brouard
     *** empty log message ***
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.177  2015/01/03 18:40:56  brouard
     Summary: Still testing ilc32 on OSX
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.176  2015/01/03 16:45:04  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    *** empty log message ***
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.175  2015/01/03 16:33:42  brouard
 #define YEARM 12. /* Number of months per year */    *** empty log message ***
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.174  2015/01/03 16:15:49  brouard
     Summary: Still in cross-compilation
   
 int erreur; /* Error number */    Revision 1.173  2015/01/03 12:06:26  brouard
 int nvar;    Summary: trying to detect cross-compilation
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.172  2014/12/27 12:07:47  brouard
 int nlstate=2; /* Number of live states */    Summary: Back from Visual Studio and Intel, options for compiling for Windows XP
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.171  2014/12/23 13:26:59  brouard
 int popbased=0;    Summary: Back from Visual C
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Still problem with utsname.h on Windows
 int maxwav; /* Maxim number of waves */  
 int jmin, jmax; /* min, max spacing between 2 waves */    Revision 1.170  2014/12/23 11:17:12  brouard
 int mle, weightopt;    Summary: Cleaning some \%% back to %%
 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 */    The escape was mandatory for a specific compiler (which one?), but too many warnings.
 double jmean; /* Mean space between 2 waves */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.169  2014/12/22 23:08:31  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Summary: 0.98p
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficgp,*ficresprob,*ficpop;    Outputs some informations on compiler used, OS etc. Testing on different platforms.
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Revision 1.168  2014/12/22 15:17:42  brouard
  FILE  *ficresvij;    Summary: update
   char fileresv[FILENAMELENGTH];  
  FILE  *ficresvpl;    Revision 1.167  2014/12/22 13:50:56  brouard
   char fileresvpl[FILENAMELENGTH];    Summary: Testing uname and compiler version and if compiled 32 or 64
   
 #define NR_END 1    Testing on Linux 64
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.166  2014/12/22 11:40:47  brouard
     *** empty log message ***
 #define NRANSI  
 #define ITMAX 200    Revision 1.165  2014/12/16 11:20:36  brouard
     Summary: After compiling on Visual C
 #define TOL 2.0e-4  
     * imach.c (Module): Merging 1.61 to 1.162
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10    Revision 1.164  2014/12/16 10:52:11  brouard
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Summary: Merging with Visual C after suppressing some warnings for unused variables. Also fixing Saito's bug 0.98Xn
   
 #define GOLD 1.618034    * imach.c (Module): Merging 1.61 to 1.162
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.163  2014/12/16 10:30:11  brouard
     * imach.c (Module): Merging 1.61 to 1.162
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.162  2014/09/25 11:43:39  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Summary: temporary backup 0.99!
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.1  2014/09/16 11:06:58  brouard
 #define rint(a) floor(a+0.5)    Summary: With some code (wrong) for nlopt
   
 static double sqrarg;    Author:
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.161  2014/09/15 20:41:41  brouard
     Summary: Problem with macro SQR on Intel compiler
 int imx;  
 int stepm;    Revision 1.160  2014/09/02 09:24:05  brouard
 /* Stepm, step in month: minimum step interpolation*/    *** empty log message ***
   
 int estepm;    Revision 1.159  2014/09/01 10:34:10  brouard
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    Summary: WIN32
     Author: Brouard
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.158  2014/08/27 17:11:51  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    *** empty log message ***
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.157  2014/08/27 16:26:55  brouard
     Summary: Preparing windows Visual studio version
 double *weight;    Author: Brouard
 int **s; /* Status */  
 double *agedc, **covar, idx;    In order to compile on Visual studio, time.h is now correct and time_t
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    and tm struct should be used. difftime should be used but sometimes I
     just make the differences in raw time format (time(&now).
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Trying to suppress #ifdef LINUX
 double ftolhess; /* Tolerance for computing hessian */    Add xdg-open for __linux in order to open default browser.
   
 /**************** split *************************/    Revision 1.156  2014/08/25 20:10:10  brouard
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    *** empty log message ***
 {  
    char *s;                             /* pointer */    Revision 1.155  2014/08/25 18:32:34  brouard
    int  l1, l2;                         /* length counters */    Summary: New compile, minor changes
     Author: Brouard
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.154  2014/06/20 17:32:08  brouard
 #ifdef windows    Summary: Outputs now all graphs of convergence to period prevalence
    s = strrchr( path, '\\' );           /* find last / */  
 #else    Revision 1.153  2014/06/20 16:45:46  brouard
    s = strrchr( path, '/' );            /* find last / */    Summary: If 3 live state, convergence to period prevalence on same graph
 #endif    Author: Brouard
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.152  2014/06/18 17:54:09  brouard
       extern char       *getwd( );    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.151  2014/06/18 16:43:30  brouard
 #else    *** empty log message ***
       extern char       *getcwd( );  
     Revision 1.150  2014/06/18 16:42:35  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
 #endif    Author: brouard
          return( GLOCK_ERROR_GETCWD );  
       }    Revision 1.149  2014/06/18 15:51:14  brouard
       strcpy( name, path );             /* we've got it */    Summary: Some fixes in parameter files errors
    } else {                             /* strip direcotry from path */    Author: Nicolas Brouard
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.148  2014/06/17 17:38:48  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Summary: Nothing new
       strcpy( name, s );                /* save file name */    Author: Brouard
       strncpy( dirc, path, l1 - l2 );   /* now the directory */  
       dirc[l1-l2] = 0;                  /* add zero */    Just a new packaging for OS/X version 0.98nS
    }  
    l1 = strlen( dirc );                 /* length of directory */    Revision 1.147  2014/06/16 10:33:11  brouard
 #ifdef windows    *** empty log message ***
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
 #else    Revision 1.146  2014/06/16 10:20:28  brouard
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    Summary: Merge
 #endif    Author: Brouard
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Merge, before building revised version.
    strcpy(ext,s);                       /* save extension */  
    l1= strlen( name);    Revision 1.145  2014/06/10 21:23:15  brouard
    l2= strlen( s)+1;    Summary: Debugging with valgrind
    strncpy( finame, name, l1-l2);    Author: Nicolas Brouard
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    Lot of changes in order to output the results with some covariates
 }    After the Edimburgh REVES conference 2014, it seems mandatory to
     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.
     Also, decodemodel has been improved. Tricode is still not
 void replace(char *s, char*t)    optimal. nbcode should be improved. Documentation has been added in
 {    the source code.
   int i;  
   int lg=20;    Revision 1.143  2014/01/26 09:45:38  brouard
   i=0;    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
     (s[i] = t[i]);    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.142  2014/01/26 03:57:36  brouard
 }    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
   
 int nbocc(char *s, char occ)    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 {  
   int i,j=0;    Revision 1.141  2014/01/26 02:42:01  brouard
   int lg=20;    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   i=0;  
   lg=strlen(s);    Revision 1.140  2011/09/02 10:37:54  brouard
   for(i=0; i<= lg; i++) {    Summary: times.h is ok with mingw32 now.
   if  (s[i] == occ ) j++;  
   }    Revision 1.139  2010/06/14 07:50:17  brouard
   return j;    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 }    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   
 void cutv(char *u,char *v, char*t, char occ)    Revision 1.138  2010/04/30 18:19:40  brouard
 {    *** empty log message ***
   int i,lg,j,p=0;  
   i=0;    Revision 1.137  2010/04/29 18:11:38  brouard
   for(j=0; j<=strlen(t)-1; j++) {    (Module): Checking covariates for more complex models
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    than V1+V2. A lot of change to be done. Unstable.
   }  
     Revision 1.136  2010/04/26 20:30:53  brouard
   lg=strlen(t);    (Module): merging some libgsl code. Fixing computation
   for(j=0; j<p; j++) {    of likelione (using inter/intrapolation if mle = 0) in order to
     (u[j] = t[j]);    get same likelihood as if mle=1.
   }    Some cleaning of code and comments added.
      u[p]='\0';  
     Revision 1.135  2009/10/29 15:33:14  brouard
    for(j=0; j<= lg; j++) {    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }    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.
   
 /********************** nrerror ********************/    Revision 1.133  2009/07/06 10:21:25  brouard
     just nforces
 void nrerror(char error_text[])  
 {    Revision 1.132  2009/07/06 08:22:05  brouard
   fprintf(stderr,"ERREUR ...\n");    Many tings
   fprintf(stderr,"%s\n",error_text);  
   exit(1);    Revision 1.131  2009/06/20 16:22:47  brouard
 }    Some dimensions resccaled
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    Revision 1.130  2009/05/26 06:44:34  brouard
 {    (Module): Max Covariate is now set to 20 instead of 8. A
   double *v;    lot of cleaning with variables initialized to 0. Trying to make
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;    Revision 1.129  2007/08/31 13:49:27  lievre
 }    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   
 /************************ free vector ******************/    Revision 1.128  2006/06/30 13:02:05  brouard
 void free_vector(double*v, int nl, int nh)    (Module): Clarifications on computing e.j
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.127  2006/04/28 18:11:50  brouard
 }    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 /************************ivector *******************************/    loop. Now we define nhstepma in the age loop.
 int *ivector(long nl,long nh)    (Module): In order to speed up (in case of numerous covariates) we
 {    compute health expectancies (without variances) in a first step
   int *v;    and then all the health expectancies with variances or standard
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    deviation (needs data from the Hessian matrices) which slows the
   if (!v) nrerror("allocation failure in ivector");    computation.
   return v-nl+NR_END;    In the future we should be able to stop the program is only health
 }    expectancies and graph are needed without standard deviations.
   
 /******************free ivector **************************/    Revision 1.126  2006/04/28 17:23:28  brouard
 void free_ivector(int *v, long nl, long nh)    (Module): Yes the sum of survivors was wrong since
 {    imach-114 because nhstepm was no more computed in the age
   free((FREE_ARG)(v+nl-NR_END));    loop. Now we define nhstepma in the age loop.
 }    Version 0.98h
   
 /******************* imatrix *******************************/    Revision 1.125  2006/04/04 15:20:31  lievre
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Errors in calculation of health expectancies. Age was not initialized.
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    Forecasting file added.
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Revision 1.124  2006/03/22 17:13:53  lievre
   int **m;    Parameters are printed with %lf instead of %f (more numbers after the comma).
      The log-likelihood is printed in the log file
   /* allocate pointers to rows */  
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    Revision 1.123  2006/03/20 10:52:43  brouard
   if (!m) nrerror("allocation failure 1 in matrix()");    * imach.c (Module): <title> changed, corresponds to .htm file
   m += NR_END;    name. <head> headers where missing.
   m -= nrl;  
      * imach.c (Module): Weights can have a decimal point as for
      English (a comma might work with a correct LC_NUMERIC environment,
   /* allocate rows and set pointers to them */    otherwise the weight is truncated).
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    Modification of warning when the covariates values are not 0 or
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    1.
   m[nrl] += NR_END;    Version 0.98g
   m[nrl] -= ncl;  
      Revision 1.122  2006/03/20 09:45:41  brouard
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    (Module): Weights can have a decimal point as for
      English (a comma might work with a correct LC_NUMERIC environment,
   /* return pointer to array of pointers to rows */    otherwise the weight is truncated).
   return m;    Modification of warning when the covariates values are not 0 or
 }    1.
     Version 0.98g
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Revision 1.121  2006/03/16 17:45:01  lievre
       int **m;    * imach.c (Module): Comments concerning covariates added
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */    * imach.c (Module): refinements in the computation of lli if
 {    status=-2 in order to have more reliable computation if stepm is
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    not 1 month. Version 0.98f
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Revision 1.120  2006/03/16 15:10:38  lievre
     (Module): refinements in the computation of lli if
 /******************* matrix *******************************/    status=-2 in order to have more reliable computation if stepm is
 double **matrix(long nrl, long nrh, long ncl, long nch)    not 1 month. Version 0.98f
 {  
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    Revision 1.119  2006/03/15 17:42:26  brouard
   double **m;    (Module): Bug if status = -2, the loglikelihood was
     computed as likelihood omitting the logarithm. Version O.98e
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    Revision 1.118  2006/03/14 18:20:07  brouard
   m += NR_END;    (Module): varevsij Comments added explaining the second
   m -= nrl;    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    (Module): Function pstamp added
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    (Module): Version 0.98d
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.117  2006/03/14 17:16:22  brouard
     (Module): varevsij Comments added explaining the second
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    table of variances if popbased=1 .
   return m;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 }    (Module): Function pstamp added
     (Module): Version 0.98d
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    Revision 1.116  2006/03/06 10:29:27  brouard
 {    (Module): Variance-covariance wrong links and
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    varian-covariance of ej. is needed (Saito).
   free((FREE_ARG)(m+nrl-NR_END));  
 }    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
 /******************* ma3x *******************************/  
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    Revision 1.114  2006/02/26 12:57:58  brouard
 {    (Module): Some improvements in processing parameter
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    filename with strsep.
   double ***m;  
     Revision 1.113  2006/02/24 14:20:24  brouard
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    (Module): Memory leaks checks with valgrind and:
   if (!m) nrerror("allocation failure 1 in matrix()");    datafile was not closed, some imatrix were not freed and on matrix
   m += NR_END;    allocation too.
   m -= nrl;  
     Revision 1.112  2006/01/30 09:55:26  brouard
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.111  2006/01/25 20:38:18  brouard
   m[nrl] -= ncl;    (Module): Lots of cleaning and bugs added (Gompertz)
     (Module): Comments can be added in data file. Missing date values
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    can be a simple dot '.'.
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    Revision 1.110  2006/01/25 00:51:50  brouard
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    (Module): Lots of cleaning and bugs added (Gompertz)
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;    Revision 1.109  2006/01/24 19:37:15  brouard
   for (j=ncl+1; j<=nch; j++)    (Module): Comments (lines starting with a #) are allowed in data.
     m[nrl][j]=m[nrl][j-1]+nlay;  
      Revision 1.108  2006/01/19 18:05:42  lievre
   for (i=nrl+1; i<=nrh; i++) {    Gnuplot problem appeared...
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    To be fixed
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;    Revision 1.107  2006/01/19 16:20:37  brouard
   }    Test existence of gnuplot in imach path
   return m;  
 }    Revision 1.106  2006/01/19 13:24:36  brouard
     Some cleaning and links added in html output
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    Revision 1.105  2006/01/05 20:23:19  lievre
 {    *** empty log message ***
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.104  2005/09/30 16:11:43  lievre
   free((FREE_ARG)(m+nrl-NR_END));    (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
 /***************** f1dim *************************/    (instead of missing=-1 in earlier versions) and his/her
 extern int ncom;    contributions to the likelihood is 1 - Prob of dying from last
 extern double *pcom,*xicom;    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 extern double (*nrfunc)(double []);    the healthy state at last known wave). Version is 0.98
    
 double f1dim(double x)    Revision 1.103  2005/09/30 15:54:49  lievre
 {    (Module): sump fixed, loop imx fixed, and simplifications.
   int j;  
   double f;    Revision 1.102  2004/09/15 17:31:30  brouard
   double *xt;    Add the possibility to read data file including tab characters.
    
   xt=vector(1,ncom);    Revision 1.101  2004/09/15 10:38:38  brouard
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    Fix on curr_time
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);    Revision 1.100  2004/07/12 18:29:06  brouard
   return f;    Add version for Mac OS X. Just define UNIX in Makefile
 }  
     Revision 1.99  2004/06/05 08:57:40  brouard
 /*****************brent *************************/    *** empty log message ***
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {    Revision 1.98  2004/05/16 15:05:56  brouard
   int iter;    New version 0.97 . First attempt to estimate force of mortality
   double a,b,d,etemp;    directly from the data i.e. without the need of knowing the health
   double fu,fv,fw,fx;    state at each age, but using a Gompertz model: log u =a + b*age .
   double ftemp;    This is the basic analysis of mortality and should be done before any
   double p,q,r,tol1,tol2,u,v,w,x,xm;    other analysis, in order to test if the mortality estimated from the
   double e=0.0;    cross-longitudinal survey is different from the mortality estimated
      from other sources like vital statistic data.
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);    The same imach parameter file can be used but the option for mle should be -3.
   x=w=v=bx;  
   fw=fv=fx=(*f)(x);    Agnès, who wrote this part of the code, tried to keep most of the
   for (iter=1;iter<=ITMAX;iter++) {    former routines in order to include the new code within the former code.
     xm=0.5*(a+b);  
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    The output is very simple: only an estimate of the intercept and of
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    the slope with 95% confident intervals.
     printf(".");fflush(stdout);  
 #ifdef DEBUG    Current limitations:
     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);    A) Even if you enter covariates, i.e. with the
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 #endif    B) There is no computation of Life Expectancy nor Life Table.
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  
       *xmin=x;    Revision 1.97  2004/02/20 13:25:42  lievre
       return fx;    Version 0.96d. Population forecasting command line is (temporarily)
     }    suppressed.
     ftemp=fu;  
     if (fabs(e) > tol1) {    Revision 1.96  2003/07/15 15:38:55  brouard
       r=(x-w)*(fx-fv);    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
       q=(x-v)*(fx-fw);    rewritten within the same printf. Workaround: many printfs.
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);    Revision 1.95  2003/07/08 07:54:34  brouard
       if (q > 0.0) p = -p;    * imach.c (Repository):
       q=fabs(q);    (Repository): Using imachwizard code to output a more meaningful covariance
       etemp=e;    matrix (cov(a12,c31) instead of numbers.
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    Revision 1.94  2003/06/27 13:00:02  brouard
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    Just cleaning
       else {  
         d=p/q;    Revision 1.93  2003/06/25 16:33:55  brouard
         u=x+d;    (Module): On windows (cygwin) function asctime_r doesn't
         if (u-a < tol2 || b-u < tol2)    exist so I changed back to asctime which exists.
           d=SIGN(tol1,xm-x);    (Module): Version 0.96b
       }  
     } else {    Revision 1.92  2003/06/25 16:30:45  brouard
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    (Module): On windows (cygwin) function asctime_r doesn't
     }    exist so I changed back to asctime which exists.
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  
     fu=(*f)(u);    Revision 1.91  2003/06/25 15:30:29  brouard
     if (fu <= fx) {    * imach.c (Repository): Duplicated warning errors corrected.
       if (u >= x) a=x; else b=x;    (Repository): Elapsed time after each iteration is now output. It
       SHFT(v,w,x,u)    helps to forecast when convergence will be reached. Elapsed time
         SHFT(fv,fw,fx,fu)    is stamped in powell.  We created a new html file for the graphs
         } else {    concerning matrix of covariance. It has extension -cov.htm.
           if (u < x) a=u; else b=u;  
           if (fu <= fw || w == x) {    Revision 1.90  2003/06/24 12:34:15  brouard
             v=w;    (Module): Some bugs corrected for windows. Also, when
             w=u;    mle=-1 a template is output in file "or"mypar.txt with the design
             fv=fw;    of the covariance matrix to be input.
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {    Revision 1.89  2003/06/24 12:30:52  brouard
             v=u;    (Module): Some bugs corrected for windows. Also, when
             fv=fu;    mle=-1 a template is output in file "or"mypar.txt with the design
           }    of the covariance matrix to be input.
         }  
   }    Revision 1.88  2003/06/23 17:54:56  brouard
   nrerror("Too many iterations in brent");    * 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.
   *xmin=x;  
   return fx;    Revision 1.87  2003/06/18 12:26:01  brouard
 }    Version 0.96
   
 /****************** mnbrak ***********************/    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    routine fileappend.
             double (*func)(double))  
 {    Revision 1.85  2003/06/17 13:12:43  brouard
   double ulim,u,r,q, dum;    * imach.c (Repository): Check when date of death was earlier that
   double fu;    current date of interview. It may happen when the death was just
      prior to the death. In this case, dh was negative and likelihood
   *fa=(*func)(*ax);    was wrong (infinity). We still send an "Error" but patch by
   *fb=(*func)(*bx);    assuming that the date of death was just one stepm after the
   if (*fb > *fa) {    interview.
     SHFT(dum,*ax,*bx,dum)    (Repository): Because some people have very long ID (first column)
       SHFT(dum,*fb,*fa,dum)    we changed int to long in num[] and we added a new lvector for
       }    memory allocation. But we also truncated to 8 characters (left
   *cx=(*bx)+GOLD*(*bx-*ax);    truncation)
   *fc=(*func)(*cx);    (Repository): No more line truncation errors.
   while (*fb > *fc) {  
     r=(*bx-*ax)*(*fb-*fc);    Revision 1.84  2003/06/13 21:44:43  brouard
     q=(*bx-*cx)*(*fb-*fa);    * imach.c (Repository): Replace "freqsummary" at a correct
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    place. It differs from routine "prevalence" which may be called
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    many times. Probs is memory consuming and must be used with
     ulim=(*bx)+GLIMIT*(*cx-*bx);    parcimony.
     if ((*bx-u)*(u-*cx) > 0.0) {    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {    Revision 1.83  2003/06/10 13:39:11  lievre
       fu=(*func)(u);    *** empty log message ***
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    Revision 1.82  2003/06/05 15:57:20  brouard
           SHFT(*fb,*fc,fu,(*func)(u))    Add log in  imach.c and  fullversion number is now printed.
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  */
       u=ulim;  /*
       fu=(*func)(u);     Interpolated Markov Chain
     } else {  
       u=(*cx)+GOLD*(*cx-*bx);    Short summary of the programme:
       fu=(*func)(u);    
     }    This program computes Healthy Life Expectancies from
     SHFT(*ax,*bx,*cx,u)    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
       SHFT(*fa,*fb,*fc,fu)    first survey ("cross") where individuals from different ages are
       }    interviewed on their health status or degree of disability (in the
 }    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
 /*************** linmin ************************/    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
 int ncom;    model. More health states you consider, more time is necessary to reach the
 double *pcom,*xicom;    Maximum Likelihood of the parameters involved in the model.  The
 double (*nrfunc)(double []);    simplest model is the multinomial logistic model where pij is the
      probability to be observed in state j at the second wave
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    conditional to be observed in state i at the first wave. Therefore
 {    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   double brent(double ax, double bx, double cx,    'age' is age and 'sex' is a covariate. If you want to have a more
                double (*f)(double), double tol, double *xmin);    complex model than "constant and age", you should modify the program
   double f1dim(double x);    where the markup *Covariates have to be included here again* invites
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    you to do it.  More covariates you add, slower the
               double *fc, double (*func)(double));    convergence.
   int j;  
   double xx,xmin,bx,ax;    The advantage of this computer programme, compared to a simple
   double fx,fb,fa;    multinomial logistic model, is clear when the delay between waves is not
      identical for each individual. Also, if a individual missed an
   ncom=n;    intermediate interview, the information is lost, but taken into
   pcom=vector(1,n);    account using an interpolation or extrapolation.  
   xicom=vector(1,n);  
   nrfunc=func;    hPijx is the probability to be observed in state i at age x+h
   for (j=1;j<=n;j++) {    conditional to the observed state i at age x. The delay 'h' can be
     pcom[j]=p[j];    split into an exact number (nh*stepm) of unobserved intermediate
     xicom[j]=xi[j];    states. This elementary transition (by month, quarter,
   }    semester or year) is modelled as a multinomial logistic.  The hPx
   ax=0.0;    matrix is simply the matrix product of nh*stepm elementary matrices
   xx=1.0;    and the contribution of each individual to the likelihood is simply
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    hPijx.
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG    Also this programme outputs the covariance matrix of the parameters but also
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    of the life expectancies. It also computes the period (stable) prevalence. 
 #endif    
   for (j=1;j<=n;j++) {    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
     xi[j] *= xmin;             Institut national d'études démographiques, Paris.
     p[j] += xi[j];    This software have been partly granted by Euro-REVES, a concerted action
   }    from the European Union.
   free_vector(xicom,1,n);    It is copyrighted identically to a GNU software product, ie programme and
   free_vector(pcom,1,n);    software can be distributed freely for non commercial use. Latest version
 }    can be accessed at http://euroreves.ined.fr/imach .
   
 /*************** powell ************************/    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
             double (*func)(double []))    
 {    **********************************************************************/
   void linmin(double p[], double xi[], int n, double *fret,  /*
               double (*func)(double []));    main
   int i,ibig,j;    read parameterfile
   double del,t,*pt,*ptt,*xit;    read datafile
   double fp,fptt;    concatwav
   double *xits;    freqsummary
   pt=vector(1,n);    if (mle >= 1)
   ptt=vector(1,n);      mlikeli
   xit=vector(1,n);    print results files
   xits=vector(1,n);    if mle==1 
   *fret=(*func)(p);       computes hessian
   for (j=1;j<=n;j++) pt[j]=p[j];    read end of parameter file: agemin, agemax, bage, fage, estepm
   for (*iter=1;;++(*iter)) {        begin-prev-date,...
     fp=(*fret);    open gnuplot file
     ibig=0;    open html file
     del=0.0;    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
     for (i=1;i<=n;i++)                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
       printf(" %d %.12f",i, p[i]);      freexexit2 possible for memory heap.
     printf("\n");  
     for (i=1;i<=n;i++) {    h Pij x                         | pij_nom  ficrestpij
       for (j=1;j<=n;j++) xit[j]=xi[j][i];     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
       fptt=(*fret);         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
 #ifdef DEBUG         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
       printf("fret=%lf \n",*fret);  
 #endif         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
       printf("%d",i);fflush(stdout);         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
       linmin(p,xit,n,fret,func);    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
       if (fabs(fptt-(*fret)) > del) {     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
         del=fabs(fptt-(*fret));     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
         ibig=i;  
       }    forecasting if prevfcast==1 prevforecast call prevalence()
 #ifdef DEBUG    health expectancies
       printf("%d %.12e",i,(*fret));    Variance-covariance of DFLE
       for (j=1;j<=n;j++) {    prevalence()
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);     movingaverage()
         printf(" x(%d)=%.12e",j,xit[j]);    varevsij() 
       }    if popbased==1 varevsij(,popbased)
       for(j=1;j<=n;j++)    total life expectancies
         printf(" p=%.12e",p[j]);    Variance of period (stable) prevalence
       printf("\n");   end
 #endif  */
     }  
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  /* #define DEBUG */
 #ifdef DEBUG  /* #define DEBUGBRENT */
       int k[2],l;  #define POWELL /* Instead of NLOPT */
       k[0]=1;  #define POWELLF1F3 /* Skip test */
       k[1]=-1;  /* #define POWELLORIGINAL /\* Don't use Directest to decide new direction but original Powell test *\/ */
       printf("Max: %.12e",(*func)(p));  /* #define MNBRAKORIGINAL /\* Don't use mnbrak fix *\/ */
       for (j=1;j<=n;j++)  
         printf(" %.12e",p[j]);  #include <math.h>
       printf("\n");  #include <stdio.h>
       for(l=0;l<=1;l++) {  #include <stdlib.h>
         for (j=1;j<=n;j++) {  #include <string.h>
           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]);  #ifdef _WIN32
         }  #include <io.h>
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  #include <windows.h>
       }  #include <tchar.h>
 #endif  #else
   #include <unistd.h>
   #endif
       free_vector(xit,1,n);  
       free_vector(xits,1,n);  #include <limits.h>
       free_vector(ptt,1,n);  #include <sys/types.h>
       free_vector(pt,1,n);  
       return;  #if defined(__GNUC__)
     }  #include <sys/utsname.h> /* Doesn't work on Windows */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  #endif
     for (j=1;j<=n;j++) {  
       ptt[j]=2.0*p[j]-pt[j];  #include <sys/stat.h>
       xit[j]=p[j]-pt[j];  #include <errno.h>
       pt[j]=p[j];  /* extern int errno; */
     }  
     fptt=(*func)(ptt);  /* #ifdef LINUX */
     if (fptt < fp) {  /* #include <time.h> */
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  /* #include "timeval.h" */
       if (t < 0.0) {  /* #else */
         linmin(p,xit,n,fret,func);  /* #include <sys/time.h> */
         for (j=1;j<=n;j++) {  /* #endif */
           xi[j][ibig]=xi[j][n];  
           xi[j][n]=xit[j];  #include <time.h>
         }  
 #ifdef DEBUG  #ifdef GSL
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  #include <gsl/gsl_errno.h>
         for(j=1;j<=n;j++)  #include <gsl/gsl_multimin.h>
           printf(" %.12e",xit[j]);  #endif
         printf("\n");  
 #endif  
       }  #ifdef NLOPT
     }  #include <nlopt.h>
   }  typedef struct {
 }    double (* function)(double [] );
   } myfunc_data ;
 /**** Prevalence limit ****************/  #endif
   
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  /* #include <libintl.h> */
 {  /* #define _(String) gettext (String) */
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  
      matrix by transitions matrix until convergence is reached */  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   
   int i, ii,j,k;  #define GNUPLOTPROGRAM "gnuplot"
   double min, max, maxmin, maxmax,sumnew=0.;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   double **matprod2();  #define FILENAMELENGTH 132
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   double agefin, delaymax=50 ; /* Max number of years to converge */  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
   for (ii=1;ii<=nlstate+ndeath;ii++)  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
     for (j=1;j<=nlstate+ndeath;j++){  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  #define NINTERVMAX 8
   #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
    cov[1]=1.;  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
    #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  #define MAXN 20000
     newm=savm;  #define YEARM 12. /**< Number of months per year */
     /* Covariates have to be included here again */  #define AGESUP 130
      cov[2]=agefin;  #define AGEBASE 40
    #define AGEOVERFLOW 1.e20
       for (k=1; k<=cptcovn;k++) {  #define AGEGOMP 10 /**< Minimal age for Gompertz adjustment */
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  #ifdef _WIN32
         /*      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]]);*/  #define DIRSEPARATOR '\\'
       }  #define CHARSEPARATOR "\\"
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  #define ODIRSEPARATOR '/'
       for (k=1; k<=cptcovprod;k++)  #else
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  #define DIRSEPARATOR '/'
   #define CHARSEPARATOR "/"
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  #define ODIRSEPARATOR '\\'
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  #endif
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/  
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  /* $Id$ */
   /* $State$ */
     savm=oldm;  
     oldm=newm;  char version[]="Imach version 0.98q5, August 2015,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015";
     maxmax=0.;  char fullversion[]="$Revision$ $Date$"; 
     for(j=1;j<=nlstate;j++){  char strstart[80];
       min=1.;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       max=0.;  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       for(i=1; i<=nlstate; i++) {  int nagesqr=0, nforce=0; /* nagesqr=1 if model is including age*age, number of forces */
         sumnew=0;  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
         prlim[i][j]= newm[i][j]/(1-sumnew);  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
         max=FMAX(max,prlim[i][j]);  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
         min=FMIN(min,prlim[i][j]);  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
       }  int cptcovprodnoage=0; /**< Number of covariate products without age */   
       maxmin=max-min;  int cptcoveff=0; /* Total number of covariates to vary for printing results */
       maxmax=FMAX(maxmax,maxmin);  int cptcov=0; /* Working variable */
     }  int npar=NPARMAX;
     if(maxmax < ftolpl){  int nlstate=2; /* Number of live states */
       return prlim;  int ndeath=1; /* Number of dead states */
     }  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   }  int popbased=0;
 }  
   int *wav; /* Number of waves for this individuual 0 is possible */
 /*************** transition probabilities ***************/  int maxwav=0; /* Maxim number of waves */
   int jmin=0, jmax=0; /* min, max spacing between 2 waves */
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
 {  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
   double s1, s2;                     to the likelihood and the sum of weights (done by funcone)*/
   /*double t34;*/  int mle=1, weightopt=0;
   int i,j,j1, nc, ii, jj;  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 */
     for(i=1; i<= nlstate; i++){  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
     for(j=1; j<i;j++){             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  int countcallfunc=0;  /* Count the number of calls to func */
         /*s2 += param[i][j][nc]*cov[nc];*/  double jmean=1; /* Mean space between 2 waves */
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  double **matprod2(); /* test */
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  double **oldm, **newm, **savm; /* Working pointers to matrices */
       }  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       ps[i][j]=s2;  /*FILE *fic ; */ /* Used in readdata only */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     }  FILE *ficlog, *ficrespow;
     for(j=i+1; j<=nlstate+ndeath;j++){  int globpr=0; /* Global variable for printing or not */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  double fretone; /* Only one call to likelihood */
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  long ipmx=0; /* Number of contributions */
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  double sw; /* Sum of weights */
       }  char filerespow[FILENAMELENGTH];
       ps[i][j]=s2;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     }  FILE *ficresilk;
   }  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
     /*ps[3][2]=1;*/  FILE *ficresprobmorprev;
   FILE *fichtm, *fichtmcov; /* Html File */
   for(i=1; i<= nlstate; i++){  FILE *ficreseij;
      s1=0;  char filerese[FILENAMELENGTH];
     for(j=1; j<i; j++)  FILE *ficresstdeij;
       s1+=exp(ps[i][j]);  char fileresstde[FILENAMELENGTH];
     for(j=i+1; j<=nlstate+ndeath; j++)  FILE *ficrescveij;
       s1+=exp(ps[i][j]);  char filerescve[FILENAMELENGTH];
     ps[i][i]=1./(s1+1.);  FILE  *ficresvij;
     for(j=1; j<i; j++)  char fileresv[FILENAMELENGTH];
       ps[i][j]= exp(ps[i][j])*ps[i][i];  FILE  *ficresvpl;
     for(j=i+1; j<=nlstate+ndeath; j++)  char fileresvpl[FILENAMELENGTH];
       ps[i][j]= exp(ps[i][j])*ps[i][i];  char title[MAXLINE];
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   } /* end i */  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  char command[FILENAMELENGTH];
     for(jj=1; jj<= nlstate+ndeath; jj++){  int  outcmd=0;
       ps[ii][jj]=0;  
       ps[ii][ii]=1;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     }  
   }  char filelog[FILENAMELENGTH]; /* Log file */
   char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  char popfile[FILENAMELENGTH];
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
    }  
     printf("\n ");  /* struct timeval start_time, end_time, curr_time, last_time, forecast_time; */
     }  /* struct timezone tzp; */
     printf("\n ");printf("%lf ",cov[2]);*/  /* extern int gettimeofday(); */
 /*  struct tm tml, *gmtime(), *localtime();
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  
   goto end;*/  extern time_t time();
     return ps;  
 }  struct tm start_time, end_time, curr_time, last_time, forecast_time;
   time_t  rstart_time, rend_time, rcurr_time, rlast_time, rforecast_time; /* raw time */
 /**************** Product of 2 matrices ******************/  struct tm tm;
   
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  char strcurr[80], strfor[80];
 {  
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  char *endptr;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  long lval;
   /* in, b, out are matrice of pointers which should have been initialized  double dval;
      before: only the contents of out is modified. The function returns  
      a pointer to pointers identical to out */  #define NR_END 1
   long i, j, k;  #define FREE_ARG char*
   for(i=nrl; i<= nrh; i++)  #define FTOL 1.0e-10
     for(k=ncolol; k<=ncoloh; k++)  
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  #define NRANSI 
         out[i][k] +=in[i][j]*b[j][k];  #define ITMAX 200 
   
   return out;  #define TOL 2.0e-4 
 }  
   #define CGOLD 0.3819660 
   #define ZEPS 1.0e-10 
 /************* Higher Matrix Product ***************/  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  #define GOLD 1.618034 
 {  #define GLIMIT 100.0 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  #define TINY 1.0e-20 
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  static double maxarg1,maxarg2;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
      (typically every 2 years instead of every month which is too big).  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
      Model is determined by parameters x and covariates have to be    
      included manually here.  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   #define rint(a) floor(a+0.5)
      */  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/myutils_8h-source.html */
   #define mytinydouble 1.0e-16
   int i, j, d, h, k;  /* #define DEQUAL(a,b) (fabs((a)-(b))<mytinydouble) */
   double **out, cov[NCOVMAX];  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/mynrutils_8h-source.html */
   double **newm;  /* static double dsqrarg; */
   /* #define DSQR(a) (DEQUAL((dsqrarg=(a)),0.0) ? 0.0 : dsqrarg*dsqrarg) */
   /* Hstepm could be zero and should return the unit matrix */  static double sqrarg;
   for (i=1;i<=nlstate+ndeath;i++)  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
     for (j=1;j<=nlstate+ndeath;j++){  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
       oldm[i][j]=(i==j ? 1.0 : 0.0);  int agegomp= AGEGOMP;
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }  int imx; 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  int stepm=1;
   for(h=1; h <=nhstepm; h++){  /* Stepm, step in month: minimum step interpolation*/
     for(d=1; d <=hstepm; d++){  
       newm=savm;  int estepm;
       /* Covariates have to be included here again */  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
       cov[1]=1.;  
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  int m,nb;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  long *num;
       for (k=1; k<=cptcovage;k++)  int firstpass=0, lastpass=4,*cod, *Tage,*cens;
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  int *ncodemax;  /* ncodemax[j]= Number of modalities of the j th
       for (k=1; k<=cptcovprod;k++)                     covariate for which somebody answered excluding 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];                     undefined. Usually 2: 0 and 1. */
   int *ncodemaxwundef;  /* ncodemax[j]= Number of modalities of the j th
                                covariate for which somebody answered including 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/                               undefined. Usually 3: -1, 0 and 1. */
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  double **pmmij, ***probs;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  double *ageexmed,*agecens;
       savm=oldm;  double dateintmean=0;
       oldm=newm;  
     }  double *weight;
     for(i=1; i<=nlstate+ndeath; i++)  int **s; /* Status */
       for(j=1;j<=nlstate+ndeath;j++) {  double *agedc;
         po[i][j][h]=newm[i][j];  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);                    * covar=matrix(0,NCOVMAX,1,n); 
          */                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*age; */
       }  double  idx; 
   } /* end h */  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
   return po;  int *Ndum; /** Freq of modality (tricode */
 }  int **codtab; /**< codtab=imatrix(1,100,1,10); */
   int **Tvard, *Tprod, cptcovprod, *Tvaraff;
   double *lsurv, *lpop, *tpop;
 /*************** log-likelihood *************/  
 double func( double *x)  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
 {  double ftolhess; /**< Tolerance for computing hessian */
   int i, ii, j, k, mi, d, kk;  
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  /**************** split *************************/
   double **out;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   double sw; /* Sum of weights */  {
   double lli; /* Individual log likelihood */    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   long ipmx;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   /*extern weight */    */ 
   /* We are differentiating ll according to initial status */    char  *ss;                            /* pointer */
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    int   l1=0, l2=0;                             /* length counters */
   /*for(i=1;i<imx;i++)  
     printf(" %d\n",s[4][i]);    l1 = strlen(path );                   /* length of path */
   */    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   cov[1]=1.;    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     if ( ss == NULL ) {                   /* no directory, so determine current directory */
   for(k=1; k<=nlstate; k++) ll[k]=0.;      strcpy( name, path );               /* we got the fullname name because no directory */
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     for(mi=1; mi<= wav[i]-1; mi++){      /* get current working directory */
       for (ii=1;ii<=nlstate+ndeath;ii++)      /*    extern  char* getcwd ( char *buf , int len);*/
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  #ifdef WIN32
       for(d=0; d<dh[mi][i]; d++){      if (_getcwd( dirc, FILENAME_MAX ) == NULL ) {
         newm=savm;  #else
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;          if (getcwd(dirc, FILENAME_MAX) == NULL) {
         for (kk=1; kk<=cptcovage;kk++) {  #endif
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];        return( GLOCK_ERROR_GETCWD );
         }      }
              /* got dirc from getcwd*/
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      printf(" DIRC = %s \n",dirc);
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    } else {                              /* strip direcotry from path */
         savm=oldm;      ss++;                               /* after this, the filename */
         oldm=newm;      l2 = strlen( ss );                  /* length of filename */
              if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
              strcpy( name, ss );         /* save file name */
       } /* end mult */      strncpy( dirc, path, l1 - l2 );     /* now the directory */
            dirc[l1-l2] = '\0';                 /* add zero */
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      printf(" DIRC2 = %s \n",dirc);
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    }
       ipmx +=1;    /* We add a separator at the end of dirc if not exists */
       sw += weight[i];    l1 = strlen( dirc );                  /* length of directory */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    if( dirc[l1-1] != DIRSEPARATOR ){
     } /* end of wave */      dirc[l1] =  DIRSEPARATOR;
   } /* end of individual */      dirc[l1+1] = 0; 
       printf(" DIRC3 = %s \n",dirc);
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    }
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    ss = strrchr( name, '.' );            /* find last / */
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */    if (ss >0){
   return -l;      ss++;
 }      strcpy(ext,ss);                     /* save extension */
       l1= strlen( name);
       l2= strlen(ss)+1;
 /*********** Maximum Likelihood Estimation ***************/      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    }
 {  
   int i,j, iter;    return( 0 );                          /* we're done */
   double **xi,*delti;  }
   double fret;  
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)  /******************************************/
     for (j=1;j<=npar;j++)  
       xi[i][j]=(i==j ? 1.0 : 0.0);  void replace_back_to_slash(char *s, char*t)
   printf("Powell\n");  {
   powell(p,xi,npar,ftol,&iter,&fret,func);    int i;
     int lg=0;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    i=0;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    lg=strlen(t);
     for(i=0; i<= lg; i++) {
 }      (s[i] = t[i]);
       if (t[i]== '\\') s[i]='/';
 /**** Computes Hessian and covariance matrix ***/    }
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  }
 {  
   double  **a,**y,*x,pd;  char *trimbb(char *out, char *in)
   double **hess;  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
   int i, j,jk;    char *s;
   int *indx;    s=out;
     while (*in != '\0'){
   double hessii(double p[], double delta, int theta, double delti[]);      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
   double hessij(double p[], double delti[], int i, int j);        in++;
   void lubksb(double **a, int npar, int *indx, double b[]) ;      }
   void ludcmp(double **a, int npar, int *indx, double *d) ;      *out++ = *in++;
     }
   hess=matrix(1,npar,1,npar);    *out='\0';
     return s;
   printf("\nCalculation of the hessian matrix. Wait...\n");  }
   for (i=1;i<=npar;i++){  
     printf("%d",i);fflush(stdout);  /* char *substrchaine(char *out, char *in, char *chain) */
     hess[i][i]=hessii(p,ftolhess,i,delti);  /* { */
     /*printf(" %f ",p[i]);*/  /*   /\* Substract chain 'chain' from 'in', return and output 'out' *\/ */
     /*printf(" %lf ",hess[i][i]);*/  /*   char *s, *t; */
   }  /*   t=in;s=out; */
    /*   while ((*in != *chain) && (*in != '\0')){ */
   for (i=1;i<=npar;i++) {  /*     *out++ = *in++; */
     for (j=1;j<=npar;j++)  {  /*   } */
       if (j>i) {  
         printf(".%d%d",i,j);fflush(stdout);  /*   /\* *in matches *chain *\/ */
         hess[i][j]=hessij(p,delti,i,j);  /*   while ((*in++ == *chain++) && (*in != '\0')){ */
         hess[j][i]=hess[i][j];      /*     printf("*in = %c, *out= %c *chain= %c \n", *in, *out, *chain);  */
         /*printf(" %lf ",hess[i][j]);*/  /*   } */
       }  /*   in--; chain--; */
     }  /*   while ( (*in != '\0')){ */
   }  /*     printf("Bef *in = %c, *out= %c *chain= %c \n", *in, *out, *chain);  */
   printf("\n");  /*     *out++ = *in++; */
   /*     printf("Aft *in = %c, *out= %c *chain= %c \n", *in, *out, *chain);  */
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  /*   } */
    /*   *out='\0'; */
   a=matrix(1,npar,1,npar);  /*   out=s; */
   y=matrix(1,npar,1,npar);  /*   return out; */
   x=vector(1,npar);  /* } */
   indx=ivector(1,npar);  char *substrchaine(char *out, char *in, char *chain)
   for (i=1;i<=npar;i++)  {
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    /* Substract chain 'chain' from 'in', return and output 'out' */
   ludcmp(a,npar,indx,&pd);    /* in="V1+V1*age+age*age+V2", chain="age*age" */
   
   for (j=1;j<=npar;j++) {    char *strloc;
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;    strcpy (out, in); 
     lubksb(a,npar,indx,x);    strloc = strstr(out, chain); /* strloc points to out at age*age+V2 */
     for (i=1;i<=npar;i++){    printf("Bef strloc=%s chain=%s out=%s \n", strloc, chain, out);
       matcov[i][j]=x[i];    if(strloc != NULL){ 
     }      /* will affect out */ /* strloc+strlenc(chain)=+V2 */ /* Will also work in Unicode */
   }      memmove(strloc,strloc+strlen(chain), strlen(strloc+strlen(chain))+1);
       /* strcpy (strloc, strloc +strlen(chain));*/
   printf("\n#Hessian matrix#\n");    }
   for (i=1;i<=npar;i++) {    printf("Aft strloc=%s chain=%s in=%s out=%s \n", strloc, chain, in, out);
     for (j=1;j<=npar;j++) {    return out;
       printf("%.3e ",hess[i][j]);  }
     }  
     printf("\n");  
   }  char *cutl(char *blocc, char *alocc, char *in, char occ)
   {
   /* Recompute Inverse */    /* cuts string in into blocc and alocc where blocc ends before FIRST occurence of char 'occ' 
   for (i=1;i<=npar;i++)       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];       gives blocc="abcdef" and alocc="ghi2j".
   ludcmp(a,npar,indx,&pd);       If occ is not found blocc is null and alocc is equal to in. Returns blocc
     */
   /*  printf("\n#Hessian matrix recomputed#\n");    char *s, *t;
     t=in;s=in;
   for (j=1;j<=npar;j++) {    while ((*in != occ) && (*in != '\0')){
     for (i=1;i<=npar;i++) x[i]=0;      *alocc++ = *in++;
     x[j]=1;    }
     lubksb(a,npar,indx,x);    if( *in == occ){
     for (i=1;i<=npar;i++){      *(alocc)='\0';
       y[i][j]=x[i];      s=++in;
       printf("%.3e ",y[i][j]);    }
     }   
     printf("\n");    if (s == t) {/* occ not found */
   }      *(alocc-(in-s))='\0';
   */      in=s;
     }
   free_matrix(a,1,npar,1,npar);    while ( *in != '\0'){
   free_matrix(y,1,npar,1,npar);      *blocc++ = *in++;
   free_vector(x,1,npar);    }
   free_ivector(indx,1,npar);  
   free_matrix(hess,1,npar,1,npar);    *blocc='\0';
     return t;
   }
 }  char *cutv(char *blocc, char *alocc, char *in, char occ)
   {
 /*************** hessian matrix ****************/    /* cuts string in into blocc and alocc where blocc ends before LAST occurence of char 'occ' 
 double hessii( double x[], double delta, int theta, double delti[])       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
 {       gives blocc="abcdef2ghi" and alocc="j".
   int i;       If occ is not found blocc is null and alocc is equal to in. Returns alocc
   int l=1, lmax=20;    */
   double k1,k2;    char *s, *t;
   double p2[NPARMAX+1];    t=in;s=in;
   double res;    while (*in != '\0'){
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;      while( *in == occ){
   double fx;        *blocc++ = *in++;
   int k=0,kmax=10;        s=in;
   double l1;      }
       *blocc++ = *in++;
   fx=func(x);    }
   for (i=1;i<=npar;i++) p2[i]=x[i];    if (s == t) /* occ not found */
   for(l=0 ; l <=lmax; l++){      *(blocc-(in-s))='\0';
     l1=pow(10,l);    else
     delts=delt;      *(blocc-(in-s)-1)='\0';
     for(k=1 ; k <kmax; k=k+1){    in=s;
       delt = delta*(l1*k);    while ( *in != '\0'){
       p2[theta]=x[theta] +delt;      *alocc++ = *in++;
       k1=func(p2)-fx;    }
       p2[theta]=x[theta]-delt;  
       k2=func(p2)-fx;    *alocc='\0';
       /*res= (k1-2.0*fx+k2)/delt/delt; */    return s;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  }
        
 #ifdef DEBUG  int nbocc(char *s, char occ)
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);  {
 #endif    int i,j=0;
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    int lg=20;
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    i=0;
         k=kmax;    lg=strlen(s);
       }    for(i=0; i<= lg; i++) {
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    if  (s[i] == occ ) j++;
         k=kmax; l=lmax*10.;    }
       }    return j;
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  }
         delts=delt;  
       }  /* void cutv(char *u,char *v, char*t, char occ) */
     }  /* { */
   }  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
   delti[theta]=delts;  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
   return res;  /*      gives u="abcdef2ghi" and v="j" *\/ */
    /*   int i,lg,j,p=0; */
 }  /*   i=0; */
   /*   lg=strlen(t); */
 double hessij( double x[], double delti[], int thetai,int thetaj)  /*   for(j=0; j<=lg-1; j++) { */
 {  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   int i;  /*   } */
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;  /*   for(j=0; j<p; j++) { */
   double p2[NPARMAX+1];  /*     (u[j] = t[j]); */
   int k;  /*   } */
   /*      u[p]='\0'; */
   fx=func(x);  
   for (k=1; k<=2; k++) {  /*    for(j=0; j<= lg; j++) { */
     for (i=1;i<=npar;i++) p2[i]=x[i];  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
     p2[thetai]=x[thetai]+delti[thetai]/k;  /*   } */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  /* } */
     k1=func(p2)-fx;  
    #ifdef _WIN32
     p2[thetai]=x[thetai]+delti[thetai]/k;  char * strsep(char **pp, const char *delim)
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  {
     k2=func(p2)-fx;    char *p, *q;
             
     p2[thetai]=x[thetai]-delti[thetai]/k;    if ((p = *pp) == NULL)
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      return 0;
     k3=func(p2)-fx;    if ((q = strpbrk (p, delim)) != NULL)
      {
     p2[thetai]=x[thetai]-delti[thetai]/k;      *pp = q + 1;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      *q = '\0';
     k4=func(p2)-fx;    }
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    else
 #ifdef DEBUG      *pp = 0;
     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);    return p;
 #endif  }
   }  #endif
   return res;  
 }  /********************** nrerror ********************/
   
 /************** Inverse of matrix **************/  void nrerror(char error_text[])
 void ludcmp(double **a, int n, int *indx, double *d)  {
 {    fprintf(stderr,"ERREUR ...\n");
   int i,imax,j,k;    fprintf(stderr,"%s\n",error_text);
   double big,dum,sum,temp;    exit(EXIT_FAILURE);
   double *vv;  }
    /*********************** vector *******************/
   vv=vector(1,n);  double *vector(int nl, int nh)
   *d=1.0;  {
   for (i=1;i<=n;i++) {    double *v;
     big=0.0;    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     for (j=1;j<=n;j++)    if (!v) nrerror("allocation failure in vector");
       if ((temp=fabs(a[i][j])) > big) big=temp;    return v-nl+NR_END;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  }
     vv[i]=1.0/big;  
   }  /************************ free vector ******************/
   for (j=1;j<=n;j++) {  void free_vector(double*v, int nl, int nh)
     for (i=1;i<j;i++) {  {
       sum=a[i][j];    free((FREE_ARG)(v+nl-NR_END));
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  }
       a[i][j]=sum;  
     }  /************************ivector *******************************/
     big=0.0;  int *ivector(long nl,long nh)
     for (i=j;i<=n;i++) {  {
       sum=a[i][j];    int *v;
       for (k=1;k<j;k++)    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
         sum -= a[i][k]*a[k][j];    if (!v) nrerror("allocation failure in ivector");
       a[i][j]=sum;    return v-nl+NR_END;
       if ( (dum=vv[i]*fabs(sum)) >= big) {  }
         big=dum;  
         imax=i;  /******************free ivector **************************/
       }  void free_ivector(int *v, long nl, long nh)
     }  {
     if (j != imax) {    free((FREE_ARG)(v+nl-NR_END));
       for (k=1;k<=n;k++) {  }
         dum=a[imax][k];  
         a[imax][k]=a[j][k];  /************************lvector *******************************/
         a[j][k]=dum;  long *lvector(long nl,long nh)
       }  {
       *d = -(*d);    long *v;
       vv[imax]=vv[j];    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     }    if (!v) nrerror("allocation failure in ivector");
     indx[j]=imax;    return v-nl+NR_END;
     if (a[j][j] == 0.0) a[j][j]=TINY;  }
     if (j != n) {  
       dum=1.0/(a[j][j]);  /******************free lvector **************************/
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  void free_lvector(long *v, long nl, long nh)
     }  {
   }    free((FREE_ARG)(v+nl-NR_END));
   free_vector(vv,1,n);  /* Doesn't work */  }
 ;  
 }  /******************* imatrix *******************************/
   int **imatrix(long nrl, long nrh, long ncl, long nch) 
 void lubksb(double **a, int n, int *indx, double b[])       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
 {  { 
   int i,ii=0,ip,j;    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   double sum;    int **m; 
      
   for (i=1;i<=n;i++) {    /* allocate pointers to rows */ 
     ip=indx[i];    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     sum=b[ip];    if (!m) nrerror("allocation failure 1 in matrix()"); 
     b[ip]=b[i];    m += NR_END; 
     if (ii)    m -= nrl; 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];    
     else if (sum) ii=i;    
     b[i]=sum;    /* allocate rows and set pointers to them */ 
   }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
   for (i=n;i>=1;i--) {    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     sum=b[i];    m[nrl] += NR_END; 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    m[nrl] -= ncl; 
     b[i]=sum/a[i][i];    
   }    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
 }    
     /* return pointer to array of pointers to rows */ 
 /************ Frequencies ********************/    return m; 
 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)  } 
 {  /* Some frequencies */  
    /****************** free_imatrix *************************/
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  void free_imatrix(m,nrl,nrh,ncl,nch)
   double ***freq; /* Frequencies */        int **m;
   double *pp;        long nch,ncl,nrh,nrl; 
   double pos, k2, dateintsum=0,k2cpt=0;       /* free an int matrix allocated by imatrix() */ 
   FILE *ficresp;  { 
   char fileresp[FILENAMELENGTH];    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
      free((FREE_ARG) (m+nrl-NR_END)); 
   pp=vector(1,nlstate);  } 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   strcpy(fileresp,"p");  /******************* matrix *******************************/
   strcat(fileresp,fileres);  double **matrix(long nrl, long nrh, long ncl, long nch)
   if((ficresp=fopen(fileresp,"w"))==NULL) {  {
     printf("Problem with prevalence resultfile: %s\n", fileresp);    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     exit(0);    double **m;
   }  
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   j1=0;    if (!m) nrerror("allocation failure 1 in matrix()");
      m += NR_END;
   j=cptcoveff;    m -= nrl;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  
      m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   for(k1=1; k1<=j;k1++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     for(i1=1; i1<=ncodemax[k1];i1++){    m[nrl] += NR_END;
       j1++;    m[nrl] -= ncl;
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);  
         scanf("%d", i);*/    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       for (i=-1; i<=nlstate+ndeath; i++)      return m;
         for (jk=-1; jk<=nlstate+ndeath; jk++)      /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
           for(m=agemin; m <= agemax+3; m++)  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
             freq[i][jk][m]=0;  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
           */
       dateintsum=0;  }
       k2cpt=0;  
       for (i=1; i<=imx; i++) {  /*************************free matrix ************************/
         bool=1;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         if  (cptcovn>0) {  {
           for (z1=1; z1<=cptcoveff; z1++)    free((FREE_ARG)(m[nrl]+ncl-NR_END));
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])    free((FREE_ARG)(m+nrl-NR_END));
               bool=0;  }
         }  
         if (bool==1) {  /******************* ma3x *******************************/
           for(m=firstpass; m<=lastpass; m++){  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
             k2=anint[m][i]+(mint[m][i]/12.);  {
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
               if(agev[m][i]==0) agev[m][i]=agemax+1;    double ***m;
               if(agev[m][i]==1) agev[m][i]=agemax+2;  
               if (m<lastpass) {    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    if (!m) nrerror("allocation failure 1 in matrix()");
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    m += NR_END;
               }    m -= nrl;
                
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
                 dateintsum=dateintsum+k2;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
                 k2cpt++;    m[nrl] += NR_END;
               }    m[nrl] -= ncl;
             }  
           }    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         }  
       }    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
            if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
       if  (cptcovn>0) {    for (j=ncl+1; j<=nch; j++) 
         fprintf(ficresp, "\n#********** Variable ");      m[nrl][j]=m[nrl][j-1]+nlay;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    
         fprintf(ficresp, "**********\n#");    for (i=nrl+1; i<=nrh; i++) {
       }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       for(i=1; i<=nlstate;i++)      for (j=ncl+1; j<=nch; j++) 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        m[i][j]=m[i][j-1]+nlay;
       fprintf(ficresp, "\n");    }
          return m; 
       for(i=(int)agemin; i <= (int)agemax+3; i++){    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
         if(i==(int)agemax+3)             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
           printf("Total");    */
         else  }
           printf("Age %d", i);  
         for(jk=1; jk <=nlstate ; jk++){  /*************************free ma3x ************************/
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
             pp[jk] += freq[jk][m][i];  {
         }    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
         for(jk=1; jk <=nlstate ; jk++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
           for(m=-1, pos=0; m <=0 ; m++)    free((FREE_ARG)(m+nrl-NR_END));
             pos += freq[jk][m][i];  }
           if(pp[jk]>=1.e-10)  
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  /*************** function subdirf ***********/
           else  char *subdirf(char fileres[])
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  {
         }    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
         for(jk=1; jk <=nlstate ; jk++){    strcat(tmpout,"/"); /* Add to the right */
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    strcat(tmpout,fileres);
             pp[jk] += freq[jk][m][i];    return tmpout;
         }  }
   
         for(jk=1,pos=0; jk <=nlstate ; jk++)  /*************** function subdirf2 ***********/
           pos += pp[jk];  char *subdirf2(char fileres[], char *preop)
         for(jk=1; jk <=nlstate ; jk++){  {
           if(pos>=1.e-5)    
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    /* Caution optionfilefiname is hidden */
           else    strcpy(tmpout,optionfilefiname);
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    strcat(tmpout,"/");
           if( i <= (int) agemax){    strcat(tmpout,preop);
             if(pos>=1.e-5){    strcat(tmpout,fileres);
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    return tmpout;
               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]);*/  
             }  /*************** function subdirf3 ***********/
             else  char *subdirf3(char fileres[], char *preop, char *preop2)
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  {
           }    
         }    /* Caution optionfilefiname is hidden */
            strcpy(tmpout,optionfilefiname);
         for(jk=-1; jk <=nlstate+ndeath; jk++)    strcat(tmpout,"/");
           for(m=-1; m <=nlstate+ndeath; m++)    strcat(tmpout,preop);
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    strcat(tmpout,preop2);
         if(i <= (int) agemax)    strcat(tmpout,fileres);
           fprintf(ficresp,"\n");    return tmpout;
         printf("\n");  }
       }  
     }  char *asc_diff_time(long time_sec, char ascdiff[])
   }  {
   dateintmean=dateintsum/k2cpt;    long sec_left, days, hours, minutes;
      days = (time_sec) / (60*60*24);
   fclose(ficresp);    sec_left = (time_sec) % (60*60*24);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    hours = (sec_left) / (60*60) ;
   free_vector(pp,1,nlstate);    sec_left = (sec_left) %(60*60);
      minutes = (sec_left) /60;
   /* End of Freq */    sec_left = (sec_left) % (60);
 }    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     return ascdiff;
 /************ Prevalence ********************/  }
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)  
 {  /* Some frequencies */  /***************** f1dim *************************/
    extern int ncom; 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  extern double *pcom,*xicom;
   double ***freq; /* Frequencies */  extern double (*nrfunc)(double []); 
   double *pp;   
   double pos, k2;  double f1dim(double x) 
   { 
   pp=vector(1,nlstate);    int j; 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    double f;
      double *xt; 
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);   
   j1=0;    xt=vector(1,ncom); 
      for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   j=cptcoveff;    f=(*nrfunc)(xt); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    free_vector(xt,1,ncom); 
      return f; 
  for(k1=1; k1<=j;k1++){  } 
     for(i1=1; i1<=ncodemax[k1];i1++){  
       j1++;  /*****************brent *************************/
    double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
       for (i=-1; i<=nlstate+ndeath; i++)    {
         for (jk=-1; jk<=nlstate+ndeath; jk++)      /* Given a function f, and given a bracketing triplet of abscissas ax, bx, cx (such that bx is
           for(m=agemin; m <= agemax+3; m++)     * between ax and cx, and f(bx) is less than both f(ax) and f(cx) ), this routine isolates
             freq[i][jk][m]=0;     * the minimum to a fractional precision of about tol using Brent’s method. The abscissa of
           * the minimum is returned as xmin, and the minimum function value is returned as brent , the
       for (i=1; i<=imx; i++) {     * returned function value. 
         bool=1;    */
         if  (cptcovn>0) {    int iter; 
           for (z1=1; z1<=cptcoveff; z1++)    double a,b,d,etemp;
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])    double fu=0,fv,fw,fx;
               bool=0;    double ftemp=0.;
         }    double p,q,r,tol1,tol2,u,v,w,x,xm; 
         if (bool==1) {    double e=0.0; 
           for(m=firstpass; m<=lastpass; m++){   
             k2=anint[m][i]+(mint[m][i]/12.);    a=(ax < cx ? ax : cx); 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    b=(ax > cx ? ax : cx); 
               if(agev[m][i]==0) agev[m][i]=agemax+1;    x=w=v=bx; 
               if(agev[m][i]==1) agev[m][i]=agemax+2;    fw=fv=fx=(*f)(x); 
               if (m<lastpass)    for (iter=1;iter<=ITMAX;iter++) { 
                 if (calagedate>0) freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];      xm=0.5*(a+b); 
               else      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
                freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];      printf(".");fflush(stdout);
             }      fprintf(ficlog,".");fflush(ficlog);
           }  #ifdef DEBUGBRENT
         }      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);
         for(i=(int)agemin; i <= (int)agemax+3; i++){      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
           for(jk=1; jk <=nlstate ; jk++){  #endif
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
               pp[jk] += freq[jk][m][i];        *xmin=x; 
           }        return fx; 
           for(jk=1; jk <=nlstate ; jk++){      } 
             for(m=-1, pos=0; m <=0 ; m++)      ftemp=fu;
             pos += freq[jk][m][i];      if (fabs(e) > tol1) { 
         }        r=(x-w)*(fx-fv); 
                q=(x-v)*(fx-fw); 
          for(jk=1; jk <=nlstate ; jk++){        p=(x-v)*q-(x-w)*r; 
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        q=2.0*(q-r); 
              pp[jk] += freq[jk][m][i];        if (q > 0.0) p = -p; 
          }        q=fabs(q); 
                  etemp=e; 
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        e=d; 
         if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
          for(jk=1; jk <=nlstate ; jk++){                    d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
            if( i <= (int) agemax){        else { 
              if(pos>=1.e-5){          d=p/q; 
                probs[i][jk][j1]= pp[jk]/pos;          u=x+d; 
              }          if (u-a < tol2 || b-u < tol2) 
            }            d=SIGN(tol1,xm-x); 
          }        } 
                } else { 
         }        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     }      } 
   }      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*f)(u); 
        if (fu <= fx) { 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        if (u >= x) a=x; else b=x; 
   free_vector(pp,1,nlstate);        SHFT(v,w,x,u) 
          SHFT(fv,fw,fx,fu) 
 }  /* End of Freq */      } else { 
         if (u < x) a=u; else b=u; 
 /************* Waves Concatenation ***************/        if (fu <= fw || w == x) { 
           v=w; 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          w=u; 
 {          fv=fw; 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          fw=fu; 
      Death is a valid wave (if date is known).        } else if (fu <= fv || v == x || v == w) { 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i          v=u; 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          fv=fu; 
      and mw[mi+1][i]. dh depends on stepm.        } 
      */      } 
     } 
   int i, mi, m;    nrerror("Too many iterations in brent"); 
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    *xmin=x; 
      double sum=0., jmean=0.;*/    return fx; 
   } 
   int j, k=0,jk, ju, jl;  
   double sum=0.;  /****************** mnbrak ***********************/
   jmin=1e+5;  
   jmax=-1;  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   jmean=0.;              double (*func)(double)) 
   for(i=1; i<=imx; i++){  { /* Given a function func , and given distinct initial points ax and bx , this routine searches in
     mi=0;  the downhill direction (defined by the function as evaluated at the initial points) and returns
     m=firstpass;  new points ax , bx , cx that bracket a minimum of the function. Also returned are the function
     while(s[m][i] <= nlstate){  values at the three points, fa, fb , and fc such that fa > fb and fb < fc.
       if(s[m][i]>=1)     */
         mw[++mi][i]=m;    double ulim,u,r,q, dum;
       if(m >=lastpass)    double fu; 
         break;  
       else    double scale=10.;
         m++;    int iterscale=0;
     }/* end while */  
     if (s[m][i] > nlstate){    *fa=(*func)(*ax); /*  xta[j]=pcom[j]+(*ax)*xicom[j]; fa=f(xta[j])*/
       mi++;     /* Death is another wave */    *fb=(*func)(*bx); /*  xtb[j]=pcom[j]+(*bx)*xicom[j]; fb=f(xtb[j]) */
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */  
       mw[mi][i]=m;    /* while(*fb != *fb){ /\* *ax should be ok, reducing distance to *ax *\/ */
     }    /*   printf("Warning mnbrak *fb = %lf, *bx=%lf *ax=%lf *fa==%lf iter=%d\n",*fb, *bx, *ax, *fa, iterscale++); */
     /*   *bx = *ax - (*ax - *bx)/scale; */
     wav[i]=mi;    /*   *fb=(*func)(*bx);  /\*  xtb[j]=pcom[j]+(*bx)*xicom[j]; fb=f(xtb[j]) *\/ */
     if(mi==0)    /* } */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  
   }    if (*fb > *fa) { 
       SHFT(dum,*ax,*bx,dum) 
   for(i=1; i<=imx; i++){      SHFT(dum,*fb,*fa,dum) 
     for(mi=1; mi<wav[i];mi++){    } 
       if (stepm <=0)    *cx=(*bx)+GOLD*(*bx-*ax); 
         dh[mi][i]=1;    *fc=(*func)(*cx); 
       else{  #ifdef DEBUG
         if (s[mw[mi+1][i]][i] > nlstate) {    printf("mnbrak0 *fb=%.12e *fc=%.12e\n",*fb,*fc);
           if (agedc[i] < 2*AGESUP) {    fprintf(ficlog,"mnbrak0 *fb=%.12e *fc=%.12e\n",*fb,*fc);
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);  #endif
           if(j==0) j=1;  /* Survives at least one month after exam */    while (*fb > *fc) { /* Declining a,b,c with fa> fb > fc */
           k=k+1;      r=(*bx-*ax)*(*fb-*fc); 
           if (j >= jmax) jmax=j;      q=(*bx-*cx)*(*fb-*fa); 
           if (j <= jmin) jmin=j;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
           sum=sum+j;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); /* Minimum abscissa of a parabolic estimated from (a,fa), (b,fb) and (c,fc). */
           /*if (j<0) printf("j=%d num=%d \n",j,i); */      ulim=(*bx)+GLIMIT*(*cx-*bx); /* Maximum abscissa where function should be evaluated */
           }      if ((*bx-u)*(u-*cx) > 0.0) { /* if u_p is between b and c */
         }        fu=(*func)(u); 
         else{  #ifdef DEBUG
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        /* f(x)=A(x-u)**2+f(u) */
           k=k+1;        double A, fparabu; 
           if (j >= jmax) jmax=j;        A= (*fb - *fa)/(*bx-*ax)/(*bx+*ax-2*u);
           else if (j <= jmin)jmin=j;        fparabu= *fa - A*(*ax-u)*(*ax-u);
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */        printf("mnbrak (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf, fparabu=%.12f)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu, fparabu);
           sum=sum+j;        fprintf(ficlog, "mnbrak (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf, fparabu=%.12f)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu, fparabu);
         }        /* And thus,it can be that fu > *fc even if fparabu < *fc */
         jk= j/stepm;        /* mnbrak (*ax=7.666299858533, *fa=299039.693133272231), (*bx=8.595447774979, *fb=298976.598289369489),
         jl= j -jk*stepm;          (*cx=10.098840694817, *fc=298946.631474258087),  (*u=9.852501168332, fu=298948.773013752128, fparabu=298945.434711494134) */
         ju= j -(jk+1)*stepm;        /* In that case, there is no bracket in the output! Routine is wrong with many consequences.*/
         if(jl <= -ju)  #endif 
           dh[mi][i]=jk;  #ifdef MNBRAKORIGINAL
         else  #else
           dh[mi][i]=jk+1;  /*       if (fu > *fc) { */
         if(dh[mi][i]==0)  /* #ifdef DEBUG */
           dh[mi][i]=1; /* At least one step */  /*       printf("mnbrak4  fu > fc \n"); */
       }  /*       fprintf(ficlog, "mnbrak4 fu > fc\n"); */
     }  /* #endif */
   }  /*      /\* SHFT(u,*cx,*cx,u) /\\* ie a=c, c=u and u=c; in that case, next SHFT(a,b,c,u) will give a=b=b, b=c=u, c=u=c and *\\/  *\/ */
   jmean=sum/k;  /*      /\* SHFT(*fa,*fc,fu,*fc) /\\* (b, u, c) is a bracket while test fb > fc will be fu > fc  will exit *\\/ *\/ */
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);  /*      dum=u; /\* Shifting c and u *\/ */
  }  /*      u = *cx; */
 /*********** Tricode ****************************/  /*      *cx = dum; */
 void tricode(int *Tvar, int **nbcode, int imx)  /*      dum = fu; */
 {  /*      fu = *fc; */
   int Ndum[20],ij=1, k, j, i;  /*      *fc =dum; */
   int cptcode=0;  /*       } else { /\* end *\/ */
   cptcoveff=0;  /* #ifdef DEBUG */
    /*       printf("mnbrak3  fu < fc \n"); */
   for (k=0; k<19; k++) Ndum[k]=0;  /*       fprintf(ficlog, "mnbrak3 fu < fc\n"); */
   for (k=1; k<=7; k++) ncodemax[k]=0;  /* #endif */
   /*      dum=u; /\* Shifting c and u *\/ */
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {  /*      u = *cx; */
     for (i=1; i<=imx; i++) {  /*      *cx = dum; */
       ij=(int)(covar[Tvar[j]][i]);  /*      dum = fu; */
       Ndum[ij]++;  /*      fu = *fc; */
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/  /*      *fc =dum; */
       if (ij > cptcode) cptcode=ij;  /*       } */
     }  #ifdef DEBUG
         printf("mnbrak34  fu < or >= fc \n");
     for (i=0; i<=cptcode; i++) {        fprintf(ficlog, "mnbrak34 fu < fc\n");
       if(Ndum[i]!=0) ncodemax[j]++;  #endif
     }        dum=u; /* Shifting c and u */
     ij=1;        u = *cx;
         *cx = dum;
         dum = fu;
     for (i=1; i<=ncodemax[j]; i++) {        fu = *fc;
       for (k=0; k<=19; k++) {        *fc =dum;
         if (Ndum[k] != 0) {  #endif
           nbcode[Tvar[j]][ij]=k;      } else if ((*cx-u)*(u-ulim) > 0.0) { /* u is after c but before ulim */
            #ifdef DEBUG
           ij++;        printf("mnbrak2  u after c but before ulim\n");
         }        fprintf(ficlog, "mnbrak2 u after c but before ulim\n");
         if (ij > ncodemax[j]) break;  #endif
       }          fu=(*func)(u); 
     }        if (fu < *fc) { 
   }    #ifdef DEBUG
         printf("mnbrak2  u after c but before ulim AND fu < fc\n");
  for (k=0; k<19; k++) Ndum[k]=0;        fprintf(ficlog, "mnbrak2 u after c but before ulim AND fu <fc \n");
   #endif
  for (i=1; i<=ncovmodel-2; i++) {          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       ij=Tvar[i];          SHFT(*fb,*fc,fu,(*func)(u)) 
       Ndum[ij]++;        } 
     }      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { /* u outside ulim (verifying that ulim is beyond c) */
   #ifdef DEBUG
  ij=1;        printf("mnbrak2  u outside ulim (verifying that ulim is beyond c)\n");
  for (i=1; i<=10; i++) {        fprintf(ficlog, "mnbrak2 u outside ulim (verifying that ulim is beyond c)\n");
    if((Ndum[i]!=0) && (i<=ncovcol)){  #endif
      Tvaraff[ij]=i;        u=ulim; 
      ij++;        fu=(*func)(u); 
    }      } else { /* u could be left to b (if r > q parabola has a maximum) */
  }  #ifdef DEBUG
          printf("mnbrak2  u could be left to b (if r > q parabola has a maximum)\n");
     cptcoveff=ij-1;        fprintf(ficlog, "mnbrak2  u could be left to b (if r > q parabola has a maximum)\n");
 }  #endif
         u=(*cx)+GOLD*(*cx-*bx); 
 /*********** Health Expectancies ****************/        fu=(*func)(u); 
       } /* end tests */
 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 )      SHFT(*ax,*bx,*cx,u) 
       SHFT(*fa,*fb,*fc,fu) 
 {  #ifdef DEBUG
   /* Health expectancies */        printf("mnbrak2 (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu);
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;        fprintf(ficlog, "mnbrak2 (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu);
   double age, agelim, hf;  #endif
   double ***p3mat,***varhe;    } /* end while; ie return (a, b, c, fa, fb, fc) such that a < b < c with f(a) > f(b) and fb < f(c) */
   double **dnewm,**doldm;  } 
   double *xp;  
   double **gp, **gm;  /*************** linmin ************************/
   double ***gradg, ***trgradg;  /* Given an n -dimensional point p[1..n] and an n -dimensional direction xi[1..n] , moves and
   int theta;  resets p to where the function func(p) takes on a minimum along the direction xi from p ,
   and replaces xi by the actual vector displacement that p was moved. Also returns as fret
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);  the value of func at the returned location p . This is actually all accomplished by calling the
   xp=vector(1,npar);  routines mnbrak and brent .*/
   dnewm=matrix(1,nlstate*2,1,npar);  int ncom; 
   doldm=matrix(1,nlstate*2,1,nlstate*2);  double *pcom,*xicom;
    double (*nrfunc)(double []); 
   fprintf(ficreseij,"# Health expectancies\n");   
   fprintf(ficreseij,"# Age");  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for(i=1; i<=nlstate;i++)  { 
     for(j=1; j<=nlstate;j++)    double brent(double ax, double bx, double cx, 
       fprintf(ficreseij," %1d-%1d (SE)",i,j);                 double (*f)(double), double tol, double *xmin); 
   fprintf(ficreseij,"\n");    double f1dim(double x); 
     void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   if(estepm < stepm){                double *fc, double (*func)(double)); 
     printf ("Problem %d lower than %d\n",estepm, stepm);    int j; 
   }    double xx,xmin,bx,ax; 
   else  hstepm=estepm;      double fx,fb,fa;
   /* We compute the life expectancy from trapezoids spaced every estepm months  
    * This is mainly to measure the difference between two models: for example    double scale=10., axs, xxs, xxss; /* Scale added for infinity */
    * 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    ncom=n; 
    * progression inbetween and thus overestimating or underestimating according    pcom=vector(1,n); 
    * to the curvature of the survival function. If, for the same date, we    xicom=vector(1,n); 
    * estimate the model with stepm=1 month, we can keep estepm to 24 months    nrfunc=func; 
    * to compare the new estimate of Life expectancy with the same linear    for (j=1;j<=n;j++) { 
    * hypothesis. A more precise result, taking into account a more precise      pcom[j]=p[j]; 
    * curvature will be obtained if estepm is as small as stepm. */      xicom[j]=xi[j]; 
     } 
   /* 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.    /* axs=0.0; */
      nhstepm is the number of hstepm from age to agelim    /* xxss=1; /\* 1 and using scale *\/ */
      nstepm is the number of stepm from age to agelin.    xxs=1;
      Look at hpijx to understand the reason of that which relies in memory size    /* do{ */
      and note for a fixed period like estepm months */      ax=0.;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the      xx= xxs;
      survival function given by stepm (the optimization length). Unfortunately it      mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  /* Outputs: xtx[j]=pcom[j]+(*xx)*xicom[j]; fx=f(xtx[j]) */
      means that if the survival funtion is printed only each two years of age and if      /* brackets with inputs ax=0 and xx=1, but points, pcom=p, and directions values, xicom=xi, are sent via f1dim(x) */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same      /* xt[x,j]=pcom[j]+x*xicom[j]  f(ax) = f(xt(a,j=1,n)) = f(p(j) + 0 * xi(j)) and  f(xx) = f(xt(x, j=1,n)) = f(p(j) + 1 * xi(j))   */
      results. So we changed our mind and took the option of the best precision.      /* Outputs: fa=f(p(j)) and fx=f(p(j) + xxs * xi(j) ) and f(bx)= f(p(j)+ bx* xi(j)) */
   */      /* Given input ax=axs and xx=xxs, xx might be too far from ax to get a finite f(xx) */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */      /* Searches on line, outputs (ax, xx, bx) such that fx < min(fa and fb) */
       /* Find a bracket a,x,b in direction n=xi ie xicom, order may change. Scale is [0:xxs*xi[j]] et non plus  [0:xi[j]]*/
   agelim=AGESUP;    /*   if (fx != fx){ */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    /*    xxs=xxs/scale; /\* Trying a smaller xx, closer to initial ax=0 *\/ */
     /* nhstepm age range expressed in number of stepm */    /*    printf("\nLinmin NAN : input [axs=%lf:xxs=%lf], mnbrak outputs fx=%lf <(fb=%lf and fa=%lf) with xx=%lf in [ax=%lf:bx=%lf] \n",  axs, xxs, fx,fb, fa, xx, ax, bx); */
     nstepm=(int) rint((agelim-age)*YEARM/stepm);    /*   } */
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */    /* }while(fx != fx); */
     /* if (stepm >= YEARM) hstepm=1;*/  
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  #ifdef DEBUGLINMIN
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    printf("\nLinmin after mnbrak: ax=%12.7f xx=%12.7f bx=%12.7f fa=%12.2f fx=%12.2f fb=%12.2f\n",  ax,xx,bx,fa,fx,fb);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);  #endif
     gp=matrix(0,nhstepm,1,nlstate*2);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); /* Giving a bracketting triplet (ax, xx, bx), find a minimum, xmin, according to f1dim, *fret(xmin),*/
     gm=matrix(0,nhstepm,1,nlstate*2);    /* fa = f(p[j] + ax * xi[j]), fx = f(p[j] + xx * xi[j]), fb = f(p[j] + bx * xi[j]) */
     /* fmin = f(p[j] + xmin * xi[j]) */
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    /* P+lambda n in that direction (lambdamin), with TOL between abscisses */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    /* f1dim(xmin): for (j=1;j<=ncom;j++) xt[j]=pcom[j]+xmin*xicom[j]; */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);    #ifdef DEBUG
      printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */  #endif
   #ifdef DEBUGLINMIN
     /* Computing Variances of health expectancies */    printf("linmin end ");
   #endif
      for(theta=1; theta <=npar; theta++){    for (j=1;j<=n;j++) { 
       for(i=1; i<=npar; i++){      /* printf(" before xi[%d]=%12.8f", j,xi[j]); */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      xi[j] *= xmin; /* xi rescaled by xmin: if xmin=-1.237 and xi=(1,0,...,0) xi=(-1.237,0,...,0) */
       }      /* if(xxs <1.0) */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        /*   printf(" after xi[%d]=%12.8f, xmin=%12.8f, ax=%12.8f, xx=%12.8f, bx=%12.8f, xxs=%12.8f", j,xi[j], xmin, ax, xx, bx,xxs ); */
        p[j] += xi[j]; /* Parameters values are updated accordingly */
       cptj=0;    } 
       for(j=1; j<= nlstate; j++){    /* printf("\n"); */
         for(i=1; i<=nlstate; i++){  #ifdef DEBUGLINMIN
           cptj=cptj+1;    printf("Comparing last *frec(xmin=%12.8f)=%12.8f from Brent and frec(0.)=%12.8f \n", xmin, *fret, (*func)(p));
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){    for (j=1;j<=n;j++) { 
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;      printf(" xi[%d]= %12.7f p[%d]= %12.7f",j,xi[j],j,p[j]);
           }      if(j % ncovmodel == 0)
         }        printf("\n");
       }    }
        #endif
          free_vector(xicom,1,n); 
       for(i=1; i<=npar; i++)    free_vector(pcom,1,n); 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  } 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
        
       cptj=0;  /*************** powell ************************/
       for(j=1; j<= nlstate; j++){  /*
         for(i=1;i<=nlstate;i++){  Minimization of a function func of n variables. Input consists of an initial starting point
           cptj=cptj+1;  p[1..n] ; an initial matrix xi[1..n][1..n] , whose columns contain the initial set of di-
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){  rections (usually the n unit vectors); and ftol , the fractional tolerance in the function value
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;  such that failure to decrease by more than this amount on one iteration signals doneness. On
           }  output, p is set to the best point found, xi is the then-current direction set, fret is the returned
         }  function value at p , and iter is the number of iterations taken. The routine linmin is used.
       }   */
        void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
                  double (*func)(double [])) 
   { 
       for(j=1; j<= nlstate*2; j++)    void linmin(double p[], double xi[], int n, double *fret, 
         for(h=0; h<=nhstepm-1; h++){                double (*func)(double [])); 
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    int i,ibig,j; 
         }    double del,t,*pt,*ptt,*xit;
     double directest;
      }    double fp,fptt;
        double *xits;
 /* End theta */    int niterf, itmp;
   
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);    pt=vector(1,n); 
     ptt=vector(1,n); 
      for(h=0; h<=nhstepm-1; h++)    xit=vector(1,n); 
       for(j=1; j<=nlstate*2;j++)    xits=vector(1,n); 
         for(theta=1; theta <=npar; theta++)    *fret=(*func)(p); 
         trgradg[h][j][theta]=gradg[h][theta][j];    for (j=1;j<=n;j++) pt[j]=p[j]; 
       rcurr_time = time(NULL);  
     for (*iter=1;;++(*iter)) { 
      for(i=1;i<=nlstate*2;i++)      fp=(*fret); /* From former iteration or initial value */
       for(j=1;j<=nlstate*2;j++)      ibig=0; 
         varhe[i][j][(int)age] =0.;      del=0.0; 
       rlast_time=rcurr_time;
     for(h=0;h<=nhstepm-1;h++){      /* (void) gettimeofday(&curr_time,&tzp); */
       for(k=0;k<=nhstepm-1;k++){      rcurr_time = time(NULL);  
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);      curr_time = *localtime(&rcurr_time);
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, rcurr_time-rlast_time, rcurr_time-rstart_time);fflush(stdout);
         for(i=1;i<=nlstate*2;i++)      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret,rcurr_time-rlast_time, rcurr_time-rstart_time); fflush(ficlog);
           for(j=1;j<=nlstate*2;j++)  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tm_sec-start_time.tm_sec); */
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;      for (i=1;i<=n;i++) {
       }        printf(" %d %.12f",i, p[i]);
     }        fprintf(ficlog," %d %.12lf",i, p[i]);
         fprintf(ficrespow," %.12lf", p[i]);
            }
     /* Computing expectancies */      printf("\n");
     for(i=1; i<=nlstate;i++)      fprintf(ficlog,"\n");
       for(j=1; j<=nlstate;j++)      fprintf(ficrespow,"\n");fflush(ficrespow);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){      if(*iter <=3){
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;        tml = *localtime(&rcurr_time);
                  strcpy(strcurr,asctime(&tml));
 /* 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]);*/        rforecast_time=rcurr_time; 
         itmp = strlen(strcurr);
         }        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
           strcurr[itmp-1]='\0';
     fprintf(ficreseij,"%3.0f",age );        printf("\nConsidering the time needed for the last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
     cptj=0;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
     for(i=1; i<=nlstate;i++)        for(niterf=10;niterf<=30;niterf+=10){
       for(j=1; j<=nlstate;j++){          rforecast_time=rcurr_time+(niterf-*iter)*(rcurr_time-rlast_time);
         cptj++;          forecast_time = *localtime(&rforecast_time);
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );          strcpy(strfor,asctime(&forecast_time));
       }          itmp = strlen(strfor);
     fprintf(ficreseij,"\n");          if(strfor[itmp-1]=='\n')
              strfor[itmp-1]='\0';
     free_matrix(gm,0,nhstepm,1,nlstate*2);          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(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
     free_matrix(gp,0,nhstepm,1,nlstate*2);          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(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);        }
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);      }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for (i=1;i<=n;i++) { /* For each direction i */
   }        for (j=1;j<=n;j++) xit[j]=xi[j][i]; /* Directions stored from previous iteration with previous scales */
   free_vector(xp,1,npar);        fptt=(*fret); 
   free_matrix(dnewm,1,nlstate*2,1,npar);  #ifdef DEBUG
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);            printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);            fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
 }  #endif
             printf("%d",i);fflush(stdout); /* print direction (parameter) i */
 /************ Variance ******************/        fprintf(ficlog,"%d",i);fflush(ficlog);
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)        linmin(p,xit,n,fret,func); /* Point p[n]. xit[n] has been loaded for direction i as input.*/
 {                                      /* Outputs are fret(new point p) p is updated and xit rescaled */
   /* Variance of health expectancies */        if (fabs(fptt-(*fret)) > del) { /* We are keeping the max gain on each of the n directions */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          /* because that direction will be replaced unless the gain del is small */
   double **newm;          /* in comparison with the 'probable' gain, mu^2, with the last average direction. */
   double **dnewm,**doldm;          /* Unless the n directions are conjugate some gain in the determinant may be obtained */
   int i, j, nhstepm, hstepm, h, nstepm ;          /* with the new direction. */
   int k, cptcode;          del=fabs(fptt-(*fret)); 
   double *xp;          ibig=i; 
   double **gp, **gm;        } 
   double ***gradg, ***trgradg;  #ifdef DEBUG
   double ***p3mat;        printf("%d %.12e",i,(*fret));
   double age,agelim, hf;        fprintf(ficlog,"%d %.12e",i,(*fret));
   int theta;        for (j=1;j<=n;j++) {
           xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
    fprintf(ficresvij,"# Covariances of life expectancies\n");          printf(" x(%d)=%.12e",j,xit[j]);
   fprintf(ficresvij,"# Age");          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   for(i=1; i<=nlstate;i++)        }
     for(j=1; j<=nlstate;j++)        for(j=1;j<=n;j++) {
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);          printf(" p(%d)=%.12e",j,p[j]);
   fprintf(ficresvij,"\n");          fprintf(ficlog," p(%d)=%.12e",j,p[j]);
         }
   xp=vector(1,npar);        printf("\n");
   dnewm=matrix(1,nlstate,1,npar);        fprintf(ficlog,"\n");
   doldm=matrix(1,nlstate,1,nlstate);  #endif
        } /* end loop on each direction i */
   if(estepm < stepm){      /* Convergence test will use last linmin estimation (fret) and compare former iteration (fp) */ 
     printf ("Problem %d lower than %d\n",estepm, stepm);      /* But p and xit have been updated at the end of linmin, *fret corresponds to new p, xit  */
   }      /* New value of last point Pn is not computed, P(n-1) */
   else  hstepm=estepm;        if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) { /* Did we reach enough precision? */
   /* For example we decided to compute the life expectancy with the smallest unit */        /* We could compare with a chi^2. chisquare(0.95,ddl=1)=3.84 */
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.        /* By adding age*age in a model, the new -2LL should be lower and the difference follows a */
      nhstepm is the number of hstepm from age to agelim        /* a chisquare statistics with 1 degree. To be significant at the 95% level, it should have */
      nstepm is the number of stepm from age to agelin.        /* decreased of more than 3.84  */
      Look at hpijx to understand the reason of that which relies in memory size        /* By adding age*age and V1*age the gain (-2LL) should be more than 5.99 (ddl=2) */
      and note for a fixed period like k years */        /* By using V1+V2+V3, the gain should be  7.82, compared with basic 1+age. */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        /* By adding 10 parameters more the gain should be 18.31 */
      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        /* Starting the program with initial values given by a former maximization will simply change */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same        /* the scales of the directions and the directions, because the are reset to canonical directions */
      results. So we changed our mind and took the option of the best precision.        /* Thus the first calls to linmin will give new points and better maximizations until fp-(*fret) is */
   */        /* under the tolerance value. If the tolerance is very small 1.e-9, it could last long.  */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */  #ifdef DEBUG
   agelim = AGESUP;        int k[2],l;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        k[0]=1;
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        k[1]=-1;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */        printf("Max: %.12e",(*func)(p));
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficlog,"Max: %.12e",(*func)(p));
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        for (j=1;j<=n;j++) {
     gp=matrix(0,nhstepm,1,nlstate);          printf(" %.12e",p[j]);
     gm=matrix(0,nhstepm,1,nlstate);          fprintf(ficlog," %.12e",p[j]);
         }
     for(theta=1; theta <=npar; theta++){        printf("\n");
       for(i=1; i<=npar; i++){ /* Computes gradient */        fprintf(ficlog,"\n");
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        for(l=0;l<=1;l++) {
       }          for (j=1;j<=n;j++) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              ptt[j]=p[j]+(p[j]-pt[j])*k[l];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
             fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       if (popbased==1) {          }
         for(i=1; i<=nlstate;i++)          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           prlim[i][i]=probs[(int)age][i][ij];          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       }        }
    #endif
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){  
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        free_vector(xit,1,n); 
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        free_vector(xits,1,n); 
         }        free_vector(ptt,1,n); 
       }        free_vector(pt,1,n); 
            return; 
       for(i=1; i<=npar; i++) /* Computes gradient */      } /* enough precision */ 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        for (j=1;j<=n;j++) { /* Computes the extrapolated point P_0 + 2 (P_n-P_0) */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        ptt[j]=2.0*p[j]-pt[j]; 
          xit[j]=p[j]-pt[j]; 
       if (popbased==1) {        pt[j]=p[j]; 
         for(i=1; i<=nlstate;i++)      } 
           prlim[i][i]=probs[(int)age][i][ij];      fptt=(*func)(ptt); /* f_3 */
       }  #ifdef POWELLF1F3
   #else
       for(j=1; j<= nlstate; j++){      if (fptt < fp) { /* If extrapolated point is better, decide if we keep that new direction or not */
         for(h=0; h<=nhstepm; h++){  #endif
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        /* (x1 f1=fp), (x2 f2=*fret), (x3 f3=fptt), (xm fm) */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        /* From x1 (P0) distance of x2 is at h and x3 is 2h */
         }        /* Let f"(x2) be the 2nd derivative equal everywhere.  */
       }        /* Then the parabolic through (x1,f1), (x2,f2) and (x3,f3) */
         /* will reach at f3 = fm + h^2/2 f"m  ; f" = (f1 -2f2 +f3 ) / h**2 */
       for(j=1; j<= nlstate; j++)        /* Conditional for using this new direction is that mu^2 = (f1-2f2+f3)^2 /2 < del */
         for(h=0; h<=nhstepm; h++){        /* t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  #ifdef NRCORIGINAL
         }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)- del*SQR(fp-fptt); /* Original Numerical Recipes in C*/
     } /* End theta */  #else
         t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del); /* Intel compiler doesn't work on one line; bug reported */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        t= t- del*SQR(fp-fptt);
   #endif
     for(h=0; h<=nhstepm; h++)        directest = fp-2.0*(*fret)+fptt - 2.0 * del; /* If del was big enough we change it for a new direction */
       for(j=1; j<=nlstate;j++)  #ifdef DEBUG
         for(theta=1; theta <=npar; theta++)        printf("t1= %.12lf, t2= %.12lf, t=%.12lf  directest=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t,directest);
           trgradg[h][j][theta]=gradg[h][theta][j];        fprintf(ficlog,"t1= %.12lf, t2= %.12lf, t=%.12lf directest=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t,directest);
         printf("t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */               (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
     for(i=1;i<=nlstate;i++)        fprintf(ficlog,"t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
       for(j=1;j<=nlstate;j++)               (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
         vareij[i][j][(int)age] =0.;        printf("tt= %.12lf, t=%.12lf\n",2.0*(fp-2.0*(*fret)+fptt)*(fp-(*fret)-del)*(fp-(*fret)-del)-del*(fp-fptt)*(fp-fptt),t);
         fprintf(ficlog, "tt= %.12lf, t=%.12lf\n",2.0*(fp-2.0*(*fret)+fptt)*(fp-(*fret)-del)*(fp-(*fret)-del)-del*(fp-fptt)*(fp-fptt),t);
     for(h=0;h<=nhstepm;h++){  #endif
       for(k=0;k<=nhstepm;k++){  #ifdef POWELLORIGINAL
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);        if (t < 0.0) { /* Then we use it for new direction */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  #else
         for(i=1;i<=nlstate;i++)        if (directest*t < 0.0) { /* Contradiction between both tests */
           for(j=1;j<=nlstate;j++)          printf("directest= %.12lf, t= %.12lf, f1= %.12lf,f2= %.12lf,f3= %.12lf, del= %.12lf\n",directest, t, fp,(*fret),fptt,del);
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;          printf("f1-2f2+f3= %.12lf, f1-f2-del= %.12lf, f1-f3= %.12lf\n",fp-2.0*(*fret)+fptt, fp -(*fret) -del, fp-fptt);
       }          fprintf(ficlog,"directest= %.12lf, t= %.12lf, f1= %.12lf,f2= %.12lf,f3= %.12lf, del= %.12lf\n",directest, t, fp,(*fret),fptt, del);
     }          fprintf(ficlog,"f1-2f2+f3= %.12lf, f1-f2-del= %.12lf, f1-f3= %.12lf\n",fp-2.0*(*fret)+fptt, fp -(*fret) -del, fp-fptt);
         } 
     fprintf(ficresvij,"%.0f ",age );        if (directest < 0.0) { /* Then we use it for new direction */
     for(i=1; i<=nlstate;i++)  #endif
       for(j=1; j<=nlstate;j++){  #ifdef DEBUGLINMIN
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);          printf("Before linmin in direction P%d-P0\n",n);
       }          for (j=1;j<=n;j++) { 
     fprintf(ficresvij,"\n");            printf("Before xit[%d]= %12.7f p[%d]= %12.7f",j,xit[j],j,p[j]);
     free_matrix(gp,0,nhstepm,1,nlstate);            if(j % ncovmodel == 0)
     free_matrix(gm,0,nhstepm,1,nlstate);              printf("\n");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);          }
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);  #endif
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          linmin(p,xit,n,fret,func); /* computes minimum on the extrapolated direction: changes p and rescales xit.*/
   } /* End age */  #ifdef DEBUGLINMIN
            for (j=1;j<=n;j++) { 
   free_vector(xp,1,npar);            printf("After xit[%d]= %12.7f p[%d]= %12.7f",j,xit[j],j,p[j]);
   free_matrix(doldm,1,nlstate,1,npar);            if(j % ncovmodel == 0)
   free_matrix(dnewm,1,nlstate,1,nlstate);              printf("\n");
           }
 }  #endif
           for (j=1;j<=n;j++) { 
 /************ Variance of prevlim ******************/            xi[j][ibig]=xi[j][n]; /* Replace direction with biggest decrease by last direction n */
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)            xi[j][n]=xit[j];      /* and this nth direction by the by the average p_0 p_n */
 {          }
   /* Variance of prevalence limit */          printf("Gaining to use new average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          fprintf(ficlog,"Gaining to use new average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig);
   double **newm;  
   double **dnewm,**doldm;  #ifdef DEBUG
   int i, j, nhstepm, hstepm;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   int k, cptcode;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   double *xp;          for(j=1;j<=n;j++){
   double *gp, *gm;            printf(" %.12e",xit[j]);
   double **gradg, **trgradg;            fprintf(ficlog," %.12e",xit[j]);
   double age,agelim;          }
   int theta;          printf("\n");
              fprintf(ficlog,"\n");
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  #endif
   fprintf(ficresvpl,"# Age");        } /* end of t or directest negative */
   for(i=1; i<=nlstate;i++)  #ifdef POWELLF1F3
       fprintf(ficresvpl," %1d-%1d",i,i);  #else
   fprintf(ficresvpl,"\n");      } /* end if (fptt < fp)  */
   #endif
   xp=vector(1,npar);    } /* loop iteration */ 
   dnewm=matrix(1,nlstate,1,npar);  } 
   doldm=matrix(1,nlstate,1,nlstate);  
    /**** Prevalence limit (stable or period prevalence)  ****************/
   hstepm=1*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   agelim = AGESUP;  {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */       matrix by transitions matrix until convergence is reached */
     if (stepm >= YEARM) hstepm=1;    
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    int i, ii,j,k;
     gradg=matrix(1,npar,1,nlstate);    double min, max, maxmin, maxmax,sumnew=0.;
     gp=vector(1,nlstate);    /* double **matprod2(); */ /* test */
     gm=vector(1,nlstate);    double **out, cov[NCOVMAX+1], **pmij();
     double **newm;
     for(theta=1; theta <=npar; theta++){    double agefin, delaymax=50 ; /* Max number of years to converge */
       for(i=1; i<=npar; i++){ /* Computes gradient */    
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    for (ii=1;ii<=nlstate+ndeath;ii++)
       }      for (j=1;j<=nlstate+ndeath;j++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(i=1;i<=nlstate;i++)      }
         gp[i] = prlim[i][i];    
        cov[1]=1.;
       for(i=1; i<=npar; i++) /* Computes gradient */    
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       for(i=1;i<=nlstate;i++)      newm=savm;
         gm[i] = prlim[i][i];      /* Covariates have to be included here again */
       cov[2]=agefin;
       for(i=1;i<=nlstate;i++)      if(nagesqr==1)
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        cov[3]= agefin*agefin;;
     } /* End theta */      for (k=1; k<=cptcovn;k++) {
         cov[2+nagesqr+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
     trgradg =matrix(1,nlstate,1,npar);        /*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]]);*/
       }
     for(j=1; j<=nlstate;j++)      /*wrong? for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(theta=1; theta <=npar; theta++)      for (k=1; k<=cptcovage;k++) cov[2+nagesqr+Tage[k]]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]*cov[2];
         trgradg[j][theta]=gradg[theta][j];      for (k=1; k<=cptcovprod;k++) /* Useless */
         cov[2+nagesqr+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
     for(i=1;i<=nlstate;i++)      
       varpl[i][(int)age] =0.;      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
     for(i=1;i<=nlstate;i++)      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */      /* 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 */
     fprintf(ficresvpl,"%.0f ",age );      
     for(i=1; i<=nlstate;i++)      savm=oldm;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      oldm=newm;
     fprintf(ficresvpl,"\n");      maxmax=0.;
     free_vector(gp,1,nlstate);      for(j=1;j<=nlstate;j++){
     free_vector(gm,1,nlstate);        min=1.;
     free_matrix(gradg,1,npar,1,nlstate);        max=0.;
     free_matrix(trgradg,1,nlstate,1,npar);        for(i=1; i<=nlstate; i++) {
   } /* End age */          sumnew=0;
           for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   free_vector(xp,1,npar);          prlim[i][j]= newm[i][j]/(1-sumnew);
   free_matrix(doldm,1,nlstate,1,npar);          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
   free_matrix(dnewm,1,nlstate,1,nlstate);          max=FMAX(max,prlim[i][j]);
           min=FMIN(min,prlim[i][j]);
 }        }
         maxmin=max-min;
 /************ Variance of one-step probabilities  ******************/        maxmax=FMAX(maxmax,maxmin);
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)      } /* j loop */
 {      if(maxmax < ftolpl){
   int i, j, i1, k1, j1, z1;        return prlim;
   int k=0, cptcode;      }
   double **dnewm,**doldm;    } /* age loop */
   double *xp;    return prlim; /* should not reach here */
   double *gp, *gm;  }
   double **gradg, **trgradg;  
   double age,agelim, cov[NCOVMAX];  /*************** transition probabilities ***************/ 
   int theta;  
   char fileresprob[FILENAMELENGTH];  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   {
   strcpy(fileresprob,"prob");    /* According to parameters values stored in x and the covariate's values stored in cov,
   strcat(fileresprob,fileres);       computes the probability to be observed in state j being in state i by appying the
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {       model to the ncovmodel covariates (including constant and age).
     printf("Problem with resultfile: %s\n", fileresprob);       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
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);       ncth covariate in the global vector x is given by the formula:
         j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
   fprintf(ficresprob,"# Age");       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
   for(i=1; i<=nlstate;i++)       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
     for(j=1; j<=(nlstate+ndeath);j++)       Outputs ps[i][j] the probability to be observed in j being in j according to
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     */
     double s1, lnpijopii;
   fprintf(ficresprob,"\n");    /*double t34;*/
     int i,j, nc, ii, jj;
   
   xp=vector(1,npar);      for(i=1; i<= nlstate; i++){
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        for(j=1; j<i;j++){
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
              /*lnpijopii += param[i][j][nc]*cov[nc];*/
   cov[1]=1;            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   j=cptcoveff;  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          }
   j1=0;          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   for(k1=1; k1<=1;k1++){  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
     for(i1=1; i1<=ncodemax[k1];i1++){        }
     j1++;        for(j=i+1; j<=nlstate+ndeath;j++){
           for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
     if  (cptcovn>0) {            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
       fprintf(ficresprob, "\n#********** Variable ");            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
       fprintf(ficresprob, "**********\n#");          }
     }          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
            }
       for (age=bage; age<=fage; age ++){      }
         cov[2]=age;      
         for (k=1; k<=cptcovn;k++) {      for(i=1; i<= nlstate; i++){
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];        s1=0;
                  for(j=1; j<i; j++){
         }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         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]]];        for(j=i+1; j<=nlstate+ndeath; j++){
                  s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         gradg=matrix(1,npar,1,9);          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         trgradg=matrix(1,9,1,npar);        }
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));        ps[i][i]=1./(s1+1.);
            /* Computing other pijs */
         for(theta=1; theta <=npar; theta++){        for(j=1; j<i; j++)
           for(i=1; i<=npar; i++)          ps[i][j]= exp(ps[i][j])*ps[i][i];
             xp[i] = x[i] + (i==theta ?delti[theta]:0);        for(j=i+1; j<=nlstate+ndeath; j++)
                    ps[i][j]= exp(ps[i][j])*ps[i][i];
           pmij(pmmij,cov,ncovmodel,xp,nlstate);        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
                } /* end i */
           k=0;      
           for(i=1; i<= (nlstate+ndeath); i++){      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
             for(j=1; j<=(nlstate+ndeath);j++){        for(jj=1; jj<= nlstate+ndeath; jj++){
               k=k+1;          ps[ii][jj]=0;
               gp[k]=pmmij[i][j];          ps[ii][ii]=1;
             }        }
           }      }
                
           for(i=1; i<=npar; i++)      
             xp[i] = x[i] - (i==theta ?delti[theta]:0);      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
          /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
           k=0;      /*   } */
           for(i=1; i<=(nlstate+ndeath); i++){      /*   printf("\n "); */
             for(j=1; j<=(nlstate+ndeath);j++){      /* } */
               k=k+1;      /* printf("\n ");printf("%lf ",cov[2]);*/
               gm[k]=pmmij[i][j];      /*
             }        for(i=1; i<= npar; i++) printf("%f ",x[i]);
           }        goto end;*/
            return ps;
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)  }
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];    
         }  /**************** Product of 2 matrices ******************/
   
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
           for(theta=1; theta <=npar; theta++)  {
             trgradg[j][theta]=gradg[theta][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(...) */
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    /* in, b, out are matrice of pointers which should have been initialized 
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);       before: only the contents of out is modified. The function returns
               a pointer to pointers identical to out */
         pmij(pmmij,cov,ncovmodel,x,nlstate);    int i, j, k;
            for(i=nrl; i<= nrh; i++)
         k=0;      for(k=ncolol; k<=ncoloh; k++){
         for(i=1; i<=(nlstate+ndeath); i++){        out[i][k]=0.;
           for(j=1; j<=(nlstate+ndeath);j++){        for(j=ncl; j<=nch; j++)
             k=k+1;          out[i][k] +=in[i][j]*b[j][k];
             gm[k]=pmmij[i][j];      }
           }    return out;
         }  }
        
      /*printf("\n%d ",(int)age);  
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){  /************* Higher Matrix Product ***************/
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));  
      }*/  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   {
         fprintf(ficresprob,"\n%d ",(int)age);    /* Computes the transition matrix starting at age 'age' over 
        'nhstepm*hstepm*stepm' months (i.e. until
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));       nhstepm*hstepm matrices. 
         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 
     }       for the memory).
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));       Model is determined by parameters x and covariates have to be 
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));       included manually here. 
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);       */
   }  
   free_vector(xp,1,npar);    int i, j, d, h, k;
   fclose(ficresprob);    double **out, cov[NCOVMAX+1];
      double **newm;
 }    double agexact;
   
 /******************* Printing html file ***********/    /* Hstepm could be zero and should return the unit matrix */
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \    for (i=1;i<=nlstate+ndeath;i++)
  int lastpass, int stepm, int weightopt, char model[],\      for (j=1;j<=nlstate+ndeath;j++){
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \        oldm[i][j]=(i==j ? 1.0 : 0.0);
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\        po[i][j][0]=(i==j ? 1.0 : 0.0);
  char version[], int popforecast, int estepm ){      }
   int jj1, k1, i1, cpt;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   FILE *fichtm;    for(h=1; h <=nhstepm; h++){
   /*char optionfilehtm[FILENAMELENGTH];*/      for(d=1; d <=hstepm; d++){
         newm=savm;
   strcpy(optionfilehtm,optionfile);        /* Covariates have to be included here again */
   strcat(optionfilehtm,".htm");        cov[1]=1.;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        agexact=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
     printf("Problem with %s \n",optionfilehtm), exit(0);        cov[2]=agexact;
   }        if(nagesqr==1)
           cov[3]= agexact*agexact;
  fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n        for (k=1; k<=cptcovn;k++) 
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n          cov[2+nagesqr+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
 \n        for (k=1; k<=cptcovage;k++) /* Should start at cptcovn+1 */
 Total number of observations=%d <br>\n          /* cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n          cov[2+nagesqr+Tage[k]]=nbcode[Tvar[Tage[k]]][codtab[ij][Tvar[Tage[k]]]]*cov[2];
 <hr  size=\"2\" color=\"#EC5E5E\">        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
  <ul><li>Outputs files<br>\n          cov[2+nagesqr+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n  
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n  
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
  - Life expectancies by age and initial health status (estepm=%2d months): <a href=\"e%s\">e%s</a> <br>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot,fileres,fileres,fileres,fileres,fileres,fileres,estepm,fileres,fileres);                     pmij(pmmij,cov,ncovmodel,x,nlstate));
         savm=oldm;
  fprintf(fichtm,"\n        oldm=newm;
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n      }
   - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n      for(i=1; i<=nlstate+ndeath; i++)
  - Variances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n        for(j=1;j<=nlstate+ndeath;j++) {
  - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>\n          po[i][j][h]=newm[i][j];
  - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
         }
  if(popforecast==1) fprintf(fichtm,"\n      /*printf("h=%d ",h);*/
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n    } /* end h */
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n  /*     printf("\n H=%d \n",h); */
         <br>",fileres,fileres,fileres,fileres);    return po;
  else  }
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);  
 fprintf(fichtm," <li>Graphs</li><p>");  #ifdef NLOPT
     double  myfunc(unsigned n, const double *p1, double *grad, void *pd){
  m=cptcoveff;    double fret;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    double *xt;
     int j;
  jj1=0;    myfunc_data *d2 = (myfunc_data *) pd;
  for(k1=1; k1<=m;k1++){  /* xt = (p1-1); */
    for(i1=1; i1<=ncodemax[k1];i1++){    xt=vector(1,n); 
        jj1++;    for (j=1;j<=n;j++)   xt[j]=p1[j-1]; /* xt[1]=p1[0] */
        if (cptcovn > 0) {  
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    fret=(d2->function)(xt); /*  p xt[1]@8 is fine */
          for (cpt=1; cpt<=cptcoveff;cpt++)    /* fret=(*func)(xt); /\*  p xt[1]@8 is fine *\/ */
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);    printf("Function = %.12lf ",fret);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    for (j=1;j<=n;j++) printf(" %d %.8lf", j, xt[j]); 
        }    printf("\n");
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>   free_vector(xt,1,n);
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        return fret;
        for(cpt=1; cpt<nlstate;cpt++){  }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>  #endif
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
        }  /*************** log-likelihood *************/
     for(cpt=1; cpt<=nlstate;cpt++) {  double func( double *x)
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  {
 interval) in state (%d): v%s%d%d.gif <br>    int i, ii, j, k, mi, d, kk;
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
      }    double **out;
      for(cpt=1; cpt<=nlstate;cpt++) {    double sw; /* Sum of weights */
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    double lli; /* Individual log likelihood */
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    int s1, s2;
      }    double bbh, survp;
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    long ipmx;
 health expectancies in states (1) and (2): e%s%d.gif<br>    double agexact;
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);    /*extern weight */
 fprintf(fichtm,"\n</body>");    /* We are differentiating ll according to initial status */
    }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
    }    /*for(i=1;i<imx;i++) 
 fclose(fichtm);      printf(" %d\n",s[4][i]);
 }    */
   
 /******************* Gnuplot file **************/    ++countcallfunc;
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){  
     cov[1]=1.;
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;  
     for(k=1; k<=nlstate; k++) ll[k]=0.;
   strcpy(optionfilegnuplot,optionfilefiname);  
   strcat(optionfilegnuplot,".gp.txt");    if(mle==1){
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     printf("Problem with file %s",optionfilegnuplot);        /* Computes the values of the ncovmodel covariates of the model
   }           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
            Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
 #ifdef windows           to be observed in j being in i according to the model.
     fprintf(ficgp,"cd \"%s\" \n",pathc);         */
 #endif        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
 m=pow(2,cptcoveff);            cov[2+nagesqr+k]=covar[Tvar[k]][i];
          }
  /* 1eme*/        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
   for (cpt=1; cpt<= nlstate ; cpt ++) {           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
    for (k1=1; k1<= m ; k1 ++) {           has been calculated etc */
         for(mi=1; mi<= wav[i]-1; mi++){
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
 for (i=1; i<= nlstate ; i ++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   else fprintf(ficgp," \%%*lf (\%%*lf)");            }
 }          for(d=0; d<dh[mi][i]; d++){
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            newm=savm;
     for (i=1; i<= nlstate ; i ++) {            agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            cov[2]=agexact;
   else fprintf(ficgp," \%%*lf (\%%*lf)");            if(nagesqr==1)
 }              cov[3]= agexact*agexact;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            for (kk=1; kk<=cptcovage;kk++) {
      for (i=1; i<= nlstate ; i ++) {              cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact; /* Tage[kk] gives the data-covariate associated with age */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 }                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));            savm=oldm;
             oldm=newm;
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          } /* end mult */
    }        
   }          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   /*2 eme*/          /* But now since version 0.9 we anticipate for bias at large stepm.
            * If stepm is larger than one month (smallest stepm) and if the exact delay 
   for (k1=1; k1<= m ; k1 ++) {           * (in months) between two waves is not a multiple of stepm, we rounded to 
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",ageminpar,fage);           * the nearest (and in case of equal distance, to the lowest) interval but now
               * we keep into memory the bias bh[mi][i] and also the previous matrix product
     for (i=1; i<= nlstate+1 ; i ++) {           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
       k=2*i;           * probability in order to take into account the bias as a fraction of the way
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
       for (j=1; j<= nlstate+1 ; j ++) {           * -stepm/2 to stepm/2 .
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");           * For stepm=1 the results are the same as for previous versions of Imach.
   else fprintf(ficgp," \%%*lf (\%%*lf)");           * For stepm > 1 the results are less biased than in previous versions. 
 }             */
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");          s1=s[mw[mi][i]][i];
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);          s2=s[mw[mi+1][i]][i];
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);          bbh=(double)bh[mi][i]/(double)stepm; 
       for (j=1; j<= nlstate+1 ; j ++) {          /* bias bh is positive if real duration
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");           * is higher than the multiple of stepm and negative otherwise.
         else fprintf(ficgp," \%%*lf (\%%*lf)");           */
 }            /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
       fprintf(ficgp,"\" t\"\" w l 0,");          if( s2 > nlstate){ 
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            /* i.e. if s2 is a death state and if the date of death is known 
       for (j=1; j<= nlstate+1 ; j ++) {               then the contribution to the likelihood is the probability to 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");               die between last step unit time and current  step unit time, 
   else fprintf(ficgp," \%%*lf (\%%*lf)");               which is also equal to probability to die before dh 
 }                 minus probability to die before dh-stepm . 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");               In version up to 0.92 likelihood was computed
       else fprintf(ficgp,"\" t\"\" w l 0,");          as if date of death was unknown. Death was treated as any other
     }          health state: the date of the interview describes the actual state
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);          and not the date of a change in health state. The former idea was
   }          to consider that at each interview the state was recorded
            (healthy, disable or death) and IMaCh was corrected; but when we
   /*3eme*/          introduced the exact date of death then we should have modified
           the contribution of an exact death to the likelihood. This new
   for (k1=1; k1<= m ; k1 ++) {          contribution is smaller and very dependent of the step unit
     for (cpt=1; cpt<= nlstate ; cpt ++) {          stepm. It is no more the probability to die between last interview
       k=2+nlstate*(2*cpt-2);          and month of death but the probability to survive from last
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);          interview up to one month before death multiplied by the
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          probability to die within a month. Thanks to Chris
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          Jackson for correcting this bug.  Former versions increased
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          mortality artificially. The bad side is that we add another loop
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          which slows down the processing. The difference can be up to 10%
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          lower mortality.
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            */
           /* If, at the beginning of the maximization mostly, the
 */             cumulative probability or probability to be dead is
       for (i=1; i< nlstate ; i ++) {             constant (ie = 1) over time d, the difference is equal to
         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);             0.  out[s1][3] = savm[s1][3]: probability, being at state
              s1 at precedent wave, to be dead a month before current
       }             wave is equal to probability, being at state s1 at
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);             precedent wave, to be dead at mont of the current
     }             wave. Then the observed probability (that this person died)
     }             is null according to current estimated parameter. In fact,
               it should be very low but not zero otherwise the log go to
   /* CV preval stat */             infinity.
     for (k1=1; k1<= m ; k1 ++) {          */
     for (cpt=1; cpt<nlstate ; cpt ++) {  /* #ifdef INFINITYORIGINAL */
       k=3;  /*          lli=log(out[s1][s2] - savm[s1][s2]); */
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);  /* #else */
   /*        if ((out[s1][s2] - savm[s1][s2]) < mytinydouble)  */
       for (i=1; i< nlstate ; i ++)  /*          lli=log(mytinydouble); */
         fprintf(ficgp,"+$%d",k+i+1);  /*        else */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);  /*          lli=log(out[s1][s2] - savm[s1][s2]); */
        /* #endif */
       l=3+(nlstate+ndeath)*cpt;              lli=log(out[s1][s2] - savm[s1][s2]);
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);  
       for (i=1; i< nlstate ; i ++) {          } else if  (s2==-2) {
         l=3+(nlstate+ndeath)*cpt;            for (j=1,survp=0. ; j<=nlstate; j++) 
         fprintf(ficgp,"+$%d",l+i+1);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       }            /*survp += out[s1][j]; */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);              lli= log(survp);
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          }
     }          
   }            else if  (s2==-4) { 
              for (j=3,survp=0. ; j<=nlstate; j++)  
   /* proba elementaires */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
    for(i=1,jk=1; i <=nlstate; i++){            lli= log(survp); 
     for(k=1; k <=(nlstate+ndeath); k++){          } 
       if (k != i) {  
         for(j=1; j <=ncovmodel; j++){          else if  (s2==-5) { 
                    for (j=1,survp=0. ; j<=2; j++)  
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           jk++;            lli= log(survp); 
           fprintf(ficgp,"\n");          } 
         }          
       }          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(jk=1; jk <=m; jk++) {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);          /*if(lli ==000.0)*/
    i=1;          /*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); */
    for(k2=1; k2<=nlstate; k2++) {          ipmx +=1;
      k3=i;          sw += weight[i];
      for(k=1; k<=(nlstate+ndeath); k++) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
        if (k != k2){          /* if (lli < log(mytinydouble)){ */
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          /*   printf("Close to inf lli = %.10lf <  %.10lf i= %d mi= %d, s[%d][i]=%d s1=%d s2=%d\n", lli,log(mytinydouble), i, mi,mw[mi][i], s[mw[mi][i]][i], s1,s2); */
 ij=1;          /*   fprintf(ficlog,"Close to inf lli = %.10lf i= %d mi= %d, s[mw[mi][i]][i]=%d\n", lli, i, mi,s[mw[mi][i]][i]); */
         for(j=3; j <=ncovmodel; j++) {          /* } */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        } /* end of wave */
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);      } /* end of individual */
             ij++;    }  else if(mle==2){
           }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           else        for (k=1; k<=cptcovn;k++) cov[2+nagesqr+k]=covar[Tvar[k]][i];
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        for(mi=1; mi<= wav[i]-1; mi++){
         }          for (ii=1;ii<=nlstate+ndeath;ii++)
           fprintf(ficgp,")/(1");            for (j=1;j<=nlstate+ndeath;j++){
                      oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(k1=1; k1 <=nlstate; k1++){                savm[ii][j]=(ii==j ? 1.0 : 0.0);
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);            }
 ij=1;          for(d=0; d<=dh[mi][i]; d++){
           for(j=3; j <=ncovmodel; j++){            newm=savm;
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {            agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);            cov[2]=agexact;
             ij++;            if(nagesqr==1)
           }              cov[3]= agexact*agexact;
           else            for (kk=1; kk<=cptcovage;kk++) {
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);              cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact;
           }            }
           fprintf(ficgp,")");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);            savm=oldm;
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");            oldm=newm;
         i=i+ncovmodel;          } /* end mult */
        }        
      }          s1=s[mw[mi][i]][i];
    }          s2=s[mw[mi+1][i]][i];
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);          bbh=(double)bh[mi][i]/(double)stepm; 
    }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
              ipmx +=1;
   fclose(ficgp);          sw += weight[i];
 }  /* end gnuplot */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
       } /* end of individual */
 /*************** Moving average **************/    }  else if(mle==3){  /* exponential inter-extrapolation */
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+nagesqr+k]=covar[Tvar[k]][i];
   int i, cpt, cptcod;        for(mi=1; mi<= wav[i]-1; mi++){
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)          for (ii=1;ii<=nlstate+ndeath;ii++)
       for (i=1; i<=nlstate;i++)            for (j=1;j<=nlstate+ndeath;j++){
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           mobaverage[(int)agedeb][i][cptcod]=0.;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
                }
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){          for(d=0; d<dh[mi][i]; d++){
       for (i=1; i<=nlstate;i++){            newm=savm;
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
           for (cpt=0;cpt<=4;cpt++){            cov[2]=agexact;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];            if(nagesqr==1)
           }              cov[3]= agexact*agexact;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;            for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact;
       }            }
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                             1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 }            savm=oldm;
             oldm=newm;
           } /* end mult */
 /************** Forecasting ******************/        
 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){          s1=s[mw[mi][i]][i];
            s2=s[mw[mi+1][i]][i];
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;          bbh=(double)bh[mi][i]/(double)stepm; 
   int *popage;          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 */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;          ipmx +=1;
   double *popeffectif,*popcount;          sw += weight[i];
   double ***p3mat;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   char fileresf[FILENAMELENGTH];        } /* end of wave */
       } /* end of individual */
  agelim=AGESUP;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+nagesqr+k]=covar[Tvar[k]][i];
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
              for (j=1;j<=nlstate+ndeath;j++){
   strcpy(fileresf,"f");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   strcat(fileresf,fileres);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   if((ficresf=fopen(fileresf,"w"))==NULL) {            }
     printf("Problem with forecast resultfile: %s\n", fileresf);          for(d=0; d<dh[mi][i]; d++){
   }            newm=savm;
   printf("Computing forecasting: result on file '%s' \n", fileresf);            agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
             cov[2]=agexact;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            if(nagesqr==1)
               cov[3]= agexact*agexact;
   if (mobilav==1) {            for (kk=1; kk<=cptcovage;kk++) {
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);              cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact;
     movingaverage(agedeb, fage, ageminpar, mobaverage);            }
   }          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   stepsize=(int) (stepm+YEARM-1)/YEARM;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   if (stepm<=12) stepsize=1;            savm=oldm;
              oldm=newm;
   agelim=AGESUP;          } /* end mult */
          
   hstepm=1;          s1=s[mw[mi][i]][i];
   hstepm=hstepm/stepm;          s2=s[mw[mi+1][i]][i];
   yp1=modf(dateintmean,&yp);          if( s2 > nlstate){ 
   anprojmean=yp;            lli=log(out[s1][s2] - savm[s1][s2]);
   yp2=modf((yp1*12),&yp);          }else{
   mprojmean=yp;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   yp1=modf((yp2*30.5),&yp);          }
   jprojmean=yp;          ipmx +=1;
   if(jprojmean==0) jprojmean=1;          sw += weight[i];
   if(mprojmean==0) jprojmean=1;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);        } /* end of wave */
        } /* end of individual */
   for(cptcov=1;cptcov<=i2;cptcov++){    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       k=k+1;        for (k=1; k<=cptcovn;k++) cov[2+nagesqr+k]=covar[Tvar[k]][i];
       fprintf(ficresf,"\n#******");        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1;j<=cptcoveff;j++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            for (j=1;j<=nlstate+ndeath;j++){
       }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       fprintf(ficresf,"******\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       fprintf(ficresf,"# StartingAge FinalAge");            }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);          for(d=0; d<dh[mi][i]; d++){
                  newm=savm;
                  agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {            cov[2]=agexact;
         fprintf(ficresf,"\n");            if(nagesqr==1)
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);                cov[3]= agexact*agexact;
             for (kk=1; kk<=cptcovage;kk++) {
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){              cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            }
           nhstepm = nhstepm/hstepm;          
                      out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           oldm=oldms;savm=savms;            savm=oldm;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              oldm=newm;
                  } /* end mult */
           for (h=0; h<=nhstepm; h++){        
             if (h==(int) (calagedate+YEARM*cpt)) {          s1=s[mw[mi][i]][i];
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);          s2=s[mw[mi+1][i]][i];
             }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
             for(j=1; j<=nlstate+ndeath;j++) {          ipmx +=1;
               kk1=0.;kk2=0;          sw += weight[i];
               for(i=1; i<=nlstate;i++) {                        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
                 if (mobilav==1)          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];        } /* end of wave */
                 else {      } /* end of individual */
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    } /* End of if */
                 }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
                    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
               }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
               if (h==(int)(calagedate+12*cpt)){    return -l;
                 fprintf(ficresf," %.3f", kk1);  }
                          
               }  /*************** log-likelihood *************/
             }  double funcone( double *x)
           }  {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* Same as likeli but slower because of a lot of printf and if */
         }    int i, ii, j, k, mi, d, kk;
       }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     }    double **out;
   }    double lli; /* Individual log likelihood */
            double llt;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    int s1, s2;
     double bbh, survp;
   fclose(ficresf);    double agexact;
 }    /*extern weight */
 /************** Forecasting ******************/    /* We are differentiating ll according to initial status */
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
      /*for(i=1;i<imx;i++) 
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      printf(" %d\n",s[4][i]);
   int *popage;    */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    cov[1]=1.;
   double *popeffectif,*popcount;  
   double ***p3mat,***tabpop,***tabpopprev;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   char filerespop[FILENAMELENGTH];  
     for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for (k=1; k<=cptcovn;k++) cov[2+nagesqr+k]=covar[Tvar[k]][i];
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(mi=1; mi<= wav[i]-1; mi++){
   agelim=AGESUP;        for (ii=1;ii<=nlstate+ndeath;ii++)
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;          for (j=1;j<=nlstate+ndeath;j++){
              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
            }
          for(d=0; d<dh[mi][i]; d++){
   strcpy(filerespop,"pop");          newm=savm;
   strcat(filerespop,fileres);          agexact=agev[mw[mi][i]][i]+d*stepm/YEARM;
   if((ficrespop=fopen(filerespop,"w"))==NULL) {          cov[2]=agexact;
     printf("Problem with forecast resultfile: %s\n", filerespop);          if(nagesqr==1)
   }            cov[3]= agexact*agexact;
   printf("Computing forecasting: result on file '%s' \n", filerespop);          for (kk=1; kk<=cptcovage;kk++) {
             cov[Tage[kk]+2+nagesqr]=covar[Tvar[Tage[kk]]][i]*agexact;
   if (cptcoveff==0) ncodemax[cptcoveff]=1;          }
   
   if (mobilav==1) {          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     movingaverage(agedeb, fage, ageminpar, mobaverage);                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   }          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
           /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
   stepsize=(int) (stepm+YEARM-1)/YEARM;          savm=oldm;
   if (stepm<=12) stepsize=1;          oldm=newm;
          } /* end mult */
   agelim=AGESUP;        
          s1=s[mw[mi][i]][i];
   hstepm=1;        s2=s[mw[mi+1][i]][i];
   hstepm=hstepm/stepm;        bbh=(double)bh[mi][i]/(double)stepm; 
          /* bias is positive if real duration
   if (popforecast==1) {         * is higher than the multiple of stepm and negative otherwise.
     if((ficpop=fopen(popfile,"r"))==NULL) {         */
       printf("Problem with population file : %s\n",popfile);exit(0);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     }          lli=log(out[s1][s2] - savm[s1][s2]);
     popage=ivector(0,AGESUP);        } else if  (s2==-2) {
     popeffectif=vector(0,AGESUP);          for (j=1,survp=0. ; j<=nlstate; j++) 
     popcount=vector(0,AGESUP);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
              lli= log(survp);
     i=1;          }else if (mle==1){
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
            } else if(mle==2){
     imx=i;          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<imx;i++) popeffectif[popage[i]]=popcount[i];        } else if(mle==3){  /* exponential inter-extrapolation */
   }          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
         } else if (mle==4){  /* mle=4 no inter-extrapolation */
   for(cptcov=1;cptcov<=i2;cptcov++){          lli=log(out[s1][s2]); /* Original formula */
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        } else{  /* mle=0 back to 1 */
       k=k+1;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       fprintf(ficrespop,"\n#******");          /*lli=log(out[s1][s2]); */ /* Original formula */
       for(j=1;j<=cptcoveff;j++) {        } /* End of if */
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        ipmx +=1;
       }        sw += weight[i];
       fprintf(ficrespop,"******\n");        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficrespop,"# Age");        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);        if(globpr){
       if (popforecast==1)  fprintf(ficrespop," [Population]");          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
         %11.6f %11.6f %11.6f ", \
       for (cpt=0; cpt<=0;cpt++) {                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);                    2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
                  for(k=1,llt=0.,l=0.; k<=nlstate; k++){
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){            llt +=ll[k]*gipmx/gsw;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
           nhstepm = nhstepm/hstepm;          }
                    fprintf(ficresilk," %10.6f\n", -llt);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        }
           oldm=oldms;savm=savms;      } /* end of wave */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      } /* end of individual */
            for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
           for (h=0; h<=nhstepm; h++){    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
             if (h==(int) (calagedate+YEARM*cpt)) {    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    if(globpr==0){ /* First time we count the contributions and weights */
             }      gipmx=ipmx;
             for(j=1; j<=nlstate+ndeath;j++) {      gsw=sw;
               kk1=0.;kk2=0;    }
               for(i=1; i<=nlstate;i++) {                  return -l;
                 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];  /*************** function likelione ***********/
                 }  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
               }  {
               if (h==(int)(calagedate+12*cpt)){    /* This routine should help understanding what is done with 
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;       the selection of individuals/waves and
                   /*fprintf(ficrespop," %.3f", kk1);       to check the exact contribution to the likelihood.
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/       Plotting could be done.
               }     */
             }    int k;
             for(i=1; i<=nlstate;i++){  
               kk1=0.;    if(*globpri !=0){ /* Just counts and sums, no printings */
                 for(j=1; j<=nlstate;j++){      strcpy(fileresilk,"ilk"); 
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];      strcat(fileresilk,fileres);
                 }      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];        printf("Problem with resultfile: %s\n", fileresilk);
             }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
           }      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(k=1; k<=nlstate; k++) 
         }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       }      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
      }
   /******/  
     *fretone=(*funcone)(p);
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    if(*globpri !=0){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        fclose(ficresilk);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      fflush(fichtm); 
           nhstepm = nhstepm/hstepm;    } 
              return;
           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++){  /*********** Maximum Likelihood Estimation ***************/
             if (h==(int) (calagedate+YEARM*cpt)) {  
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
             }  {
             for(j=1; j<=nlstate+ndeath;j++) {    int i,j, iter=0;
               kk1=0.;kk2=0;    double **xi;
               for(i=1; i<=nlstate;i++) {                  double fret;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        double fretone; /* Only one call to likelihood */
               }    /*  char filerespow[FILENAMELENGTH];*/
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);  
             }  #ifdef NLOPT
           }    int creturn;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    nlopt_opt opt;
         }    /* double lb[9] = { -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL }; /\* lower bounds *\/ */
       }    double *lb;
    }    double minf; /* the minimum objective value, upon return */
   }    double * p1; /* Shifted parameters from 0 instead of 1 */
      myfunc_data dinst, *d = &dinst;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  #endif
   
   if (popforecast==1) {  
     free_ivector(popage,0,AGESUP);    xi=matrix(1,npar,1,npar);
     free_vector(popeffectif,0,AGESUP);    for (i=1;i<=npar;i++)
     free_vector(popcount,0,AGESUP);      for (j=1;j<=npar;j++)
   }        xi[i][j]=(i==j ? 1.0 : 0.0);
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    strcpy(filerespow,"pow"); 
   fclose(ficrespop);    strcat(filerespow,fileres);
 }    if((ficrespow=fopen(filerespow,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", filerespow);
 /***********************************************/      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
 /**************** Main Program *****************/    }
 /***********************************************/    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     for (i=1;i<=nlstate;i++)
 int main(int argc, char *argv[])      for(j=1;j<=nlstate+ndeath;j++)
 {        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     fprintf(ficrespow,"\n");
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;  #ifdef POWELL
   double agedeb, agefin,hf;    powell(p,xi,npar,ftol,&iter,&fret,func);
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;  #endif
   
   double fret;  #ifdef NLOPT
   double **xi,tmp,delta;  #ifdef NEWUOA
     opt = nlopt_create(NLOPT_LN_NEWUOA,npar);
   double dum; /* Dummy variable */  #else
   double ***p3mat;    opt = nlopt_create(NLOPT_LN_BOBYQA,npar);
   int *indx;  #endif
   char line[MAXLINE], linepar[MAXLINE];    lb=vector(0,npar-1);
   char title[MAXLINE];    for (i=0;i<npar;i++) lb[i]= -HUGE_VAL;
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    nlopt_set_lower_bounds(opt, lb);
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    nlopt_set_initial_step1(opt, 0.1);
      
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    p1= (p+1); /*  p *(p+1)@8 and p *(p1)@8 are equal p1[0]=p[1] */
     d->function = func;
   char filerest[FILENAMELENGTH];    printf(" Func %.12lf \n",myfunc(npar,p1,NULL,d));
   char fileregp[FILENAMELENGTH];    nlopt_set_min_objective(opt, myfunc, d);
   char popfile[FILENAMELENGTH];    nlopt_set_xtol_rel(opt, ftol);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];    if ((creturn=nlopt_optimize(opt, p1, &minf)) < 0) {
   int firstobs=1, lastobs=10;      printf("nlopt failed! %d\n",creturn); 
   int sdeb, sfin; /* Status at beginning and end */    }
   int c,  h , cpt,l;    else {
   int ju,jl, mi;      printf("found minimum after %d evaluations (NLOPT=%d)\n", countcallfunc ,NLOPT);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;      printf("found minimum at f(%g,%g) = %0.10g\n", p[0], p[1], minf);
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      iter=1; /* not equal */
   int mobilav=0,popforecast=0;    }
   int hstepm, nhstepm;    nlopt_destroy(opt);
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;  #endif
     free_matrix(xi,1,npar,1,npar);
   double bage, fage, age, agelim, agebase;    fclose(ficrespow);
   double ftolpl=FTOL;    printf("#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   double **prlim;    fprintf(ficlog,"#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   double *severity;    fprintf(ficres,"#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   double ***param; /* Matrix of parameters */  
   double  *p;  }
   double **matcov; /* Matrix of covariance */  
   double ***delti3; /* Scale */  /**** Computes Hessian and covariance matrix ***/
   double *delti; /* Scale */  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   double ***eij, ***vareij;  {
   double **varpl; /* Variances of prevalence limits by age */    double  **a,**y,*x,pd;
   double *epj, vepp;    double **hess;
   double kk1, kk2;    int i, j;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;    int *indx;
    
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   char version[80]="Imach version 0.8a, May 2002, INED-EUROREVES ";    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   char *alph[]={"a","a","b","c","d","e"}, str[4];    void lubksb(double **a, int npar, int *indx, double b[]) ;
     void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
   char z[1]="c", occ;    hess=matrix(1,npar,1,npar);
 #include <sys/time.h>  
 #include <time.h>    printf("\nCalculation of the hessian matrix. Wait...\n");
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
      for (i=1;i<=npar;i++){
   /* long total_usecs;      printf("%d",i);fflush(stdout);
   struct timeval start_time, end_time;      fprintf(ficlog,"%d",i);fflush(ficlog);
       
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   getcwd(pathcd, size);      
       /*  printf(" %f ",p[i]);
   printf("\n%s",version);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   if(argc <=1){    }
     printf("\nEnter the parameter file name: ");    
     scanf("%s",pathtot);    for (i=1;i<=npar;i++) {
   }      for (j=1;j<=npar;j++)  {
   else{        if (j>i) { 
     strcpy(pathtot,argv[1]);          printf(".%d%d",i,j);fflush(stdout);
   }          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/          hess[i][j]=hessij(p,delti,i,j,func,npar);
   /*cygwin_split_path(pathtot,path,optionfile);          
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/          hess[j][i]=hess[i][j];    
   /* cutv(path,optionfile,pathtot,'\\');*/          /*printf(" %lf ",hess[i][j]);*/
         }
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);      }
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    }
   chdir(path);    printf("\n");
   replace(pathc,path);    fprintf(ficlog,"\n");
   
 /*-------- arguments in the command line --------*/    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   strcpy(fileres,"r");    
   strcat(fileres, optionfilefiname);    a=matrix(1,npar,1,npar);
   strcat(fileres,".txt");    /* Other files have txt extension */    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
   /*---------arguments file --------*/    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
   if((ficpar=fopen(optionfile,"r"))==NULL)    {      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     printf("Problem with optionfile %s\n",optionfile);    ludcmp(a,npar,indx,&pd);
     goto end;  
   }    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   strcpy(filereso,"o");      x[j]=1;
   strcat(filereso,fileres);      lubksb(a,npar,indx,x);
   if((ficparo=fopen(filereso,"w"))==NULL) {      for (i=1;i<=npar;i++){ 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        matcov[i][j]=x[i];
   }      }
     }
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){    printf("\n#Hessian matrix#\n");
     ungetc(c,ficpar);    fprintf(ficlog,"\n#Hessian matrix#\n");
     fgets(line, MAXLINE, ficpar);    for (i=1;i<=npar;i++) { 
     puts(line);      for (j=1;j<=npar;j++) { 
     fputs(line,ficparo);        printf("%.3e ",hess[i][j]);
   }        fprintf(ficlog,"%.3e ",hess[i][j]);
   ungetc(c,ficpar);      }
       printf("\n");
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);      fprintf(ficlog,"\n");
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);    }
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);  
 while((c=getc(ficpar))=='#' && c!= EOF){    /* Recompute Inverse */
     ungetc(c,ficpar);    for (i=1;i<=npar;i++)
     fgets(line, MAXLINE, ficpar);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     puts(line);    ludcmp(a,npar,indx,&pd);
     fputs(line,ficparo);  
   }    /*  printf("\n#Hessian matrix recomputed#\n");
   ungetc(c,ficpar);  
      for (j=1;j<=npar;j++) {
          for (i=1;i<=npar;i++) x[i]=0;
   covar=matrix(0,NCOVMAX,1,n);      x[j]=1;
   cptcovn=0;      lubksb(a,npar,indx,x);
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
   ncovmodel=2+cptcovn;        printf("%.3e ",y[i][j]);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */        fprintf(ficlog,"%.3e ",y[i][j]);
        }
   /* Read guess parameters */      printf("\n");
   /* Reads comments: lines beginning with '#' */      fprintf(ficlog,"\n");
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    */
     fgets(line, MAXLINE, ficpar);  
     puts(line);    free_matrix(a,1,npar,1,npar);
     fputs(line,ficparo);    free_matrix(y,1,npar,1,npar);
   }    free_vector(x,1,npar);
   ungetc(c,ficpar);    free_ivector(indx,1,npar);
      free_matrix(hess,1,npar,1,npar);
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)  
     for(j=1; j <=nlstate+ndeath-1; j++){  }
       fscanf(ficpar,"%1d%1d",&i1,&j1);  
       fprintf(ficparo,"%1d%1d",i1,j1);  /*************** hessian matrix ****************/
       printf("%1d%1d",i,j);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
       for(k=1; k<=ncovmodel;k++){  {
         fscanf(ficpar," %lf",&param[i][j][k]);    int i;
         printf(" %lf",param[i][j][k]);    int l=1, lmax=20;
         fprintf(ficparo," %lf",param[i][j][k]);    double k1,k2;
       }    double p2[MAXPARM+1]; /* identical to x */
       fscanf(ficpar,"\n");    double res;
       printf("\n");    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       fprintf(ficparo,"\n");    double fx;
     }    int k=0,kmax=10;
      double l1;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  
     fx=func(x);
   p=param[1][1];    for (i=1;i<=npar;i++) p2[i]=x[i];
      for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
   /* Reads comments: lines beginning with '#' */      l1=pow(10,l);
   while((c=getc(ficpar))=='#' && c!= EOF){      delts=delt;
     ungetc(c,ficpar);      for(k=1 ; k <kmax; k=k+1){
     fgets(line, MAXLINE, ficpar);        delt = delta*(l1*k);
     puts(line);        p2[theta]=x[theta] +delt;
     fputs(line,ficparo);        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
   }        p2[theta]=x[theta]-delt;
   ungetc(c,ficpar);        k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        
   for(i=1; i <=nlstate; i++){  #ifdef DEBUGHESS
     for(j=1; j <=nlstate+ndeath-1; j++){        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       fscanf(ficpar,"%1d%1d",&i1,&j1);        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);
       printf("%1d%1d",i,j);  #endif
       fprintf(ficparo,"%1d%1d",i1,j1);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       for(k=1; k<=ncovmodel;k++){        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
         fscanf(ficpar,"%le",&delti3[i][j][k]);          k=kmax;
         printf(" %le",delti3[i][j][k]);        }
         fprintf(ficparo," %le",delti3[i][j][k]);        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       }          k=kmax; l=lmax*10;
       fscanf(ficpar,"\n");        }
       printf("\n");        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       fprintf(ficparo,"\n");          delts=delt;
     }        }
   }      }
   delti=delti3[1][1];    }
      delti[theta]=delts;
   /* Reads comments: lines beginning with '#' */    return res; 
   while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);  }
     fgets(line, MAXLINE, ficpar);  
     puts(line);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
     fputs(line,ficparo);  {
   }    int i;
   ungetc(c,ficpar);    int l=1, lmax=20;
      double k1,k2,k3,k4,res,fx;
   matcov=matrix(1,npar,1,npar);    double p2[MAXPARM+1];
   for(i=1; i <=npar; i++){    int k;
     fscanf(ficpar,"%s",&str);  
     printf("%s",str);    fx=func(x);
     fprintf(ficparo,"%s",str);    for (k=1; k<=2; k++) {
     for(j=1; j <=i; j++){      for (i=1;i<=npar;i++) p2[i]=x[i];
       fscanf(ficpar," %le",&matcov[i][j]);      p2[thetai]=x[thetai]+delti[thetai]/k;
       printf(" %.5le",matcov[i][j]);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       fprintf(ficparo," %.5le",matcov[i][j]);      k1=func(p2)-fx;
     }    
     fscanf(ficpar,"\n");      p2[thetai]=x[thetai]+delti[thetai]/k;
     printf("\n");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     fprintf(ficparo,"\n");      k2=func(p2)-fx;
   }    
   for(i=1; i <=npar; i++)      p2[thetai]=x[thetai]-delti[thetai]/k;
     for(j=i+1;j<=npar;j++)      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       matcov[i][j]=matcov[j][i];      k3=func(p2)-fx;
        
   printf("\n");      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k4=func(p2)-fx;
     /*-------- Rewriting paramater file ----------*/      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
      strcpy(rfileres,"r");    /* "Rparameterfile */  #ifdef DEBUG
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/      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);
      strcat(rfileres,".");    /* */      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);
      strcat(rfileres,optionfilext);    /* Other files have txt extension */  #endif
     if((ficres =fopen(rfileres,"w"))==NULL) {    }
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    return res;
     }  }
     fprintf(ficres,"#%s\n",version);  
      /************** Inverse of matrix **************/
     /*-------- data file ----------*/  void ludcmp(double **a, int n, int *indx, double *d) 
     if((fic=fopen(datafile,"r"))==NULL)    {  { 
       printf("Problem with datafile: %s\n", datafile);goto end;    int i,imax,j,k; 
     }    double big,dum,sum,temp; 
     double *vv; 
     n= lastobs;   
     severity = vector(1,maxwav);    vv=vector(1,n); 
     outcome=imatrix(1,maxwav+1,1,n);    *d=1.0; 
     num=ivector(1,n);    for (i=1;i<=n;i++) { 
     moisnais=vector(1,n);      big=0.0; 
     annais=vector(1,n);      for (j=1;j<=n;j++) 
     moisdc=vector(1,n);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     andc=vector(1,n);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     agedc=vector(1,n);      vv[i]=1.0/big; 
     cod=ivector(1,n);    } 
     weight=vector(1,n);    for (j=1;j<=n;j++) { 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */      for (i=1;i<j;i++) { 
     mint=matrix(1,maxwav,1,n);        sum=a[i][j]; 
     anint=matrix(1,maxwav,1,n);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     s=imatrix(1,maxwav+1,1,n);        a[i][j]=sum; 
     adl=imatrix(1,maxwav+1,1,n);          } 
     tab=ivector(1,NCOVMAX);      big=0.0; 
     ncodemax=ivector(1,8);      for (i=j;i<=n;i++) { 
         sum=a[i][j]; 
     i=1;        for (k=1;k<j;k++) 
     while (fgets(line, MAXLINE, fic) != NULL)    {          sum -= a[i][k]*a[k][j]; 
       if ((i >= firstobs) && (i <=lastobs)) {        a[i][j]=sum; 
                if ( (dum=vv[i]*fabs(sum)) >= big) { 
         for (j=maxwav;j>=1;j--){          big=dum; 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          imax=i; 
           strcpy(line,stra);        } 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      } 
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      if (j != imax) { 
         }        for (k=1;k<=n;k++) { 
                  dum=a[imax][k]; 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);          a[imax][k]=a[j][k]; 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);          a[j][k]=dum; 
         } 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);        *d = -(*d); 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        vv[imax]=vv[j]; 
       } 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      indx[j]=imax; 
         for (j=ncovcol;j>=1;j--){      if (a[j][j] == 0.0) a[j][j]=TINY; 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      if (j != n) { 
         }        dum=1.0/(a[j][j]); 
         num[i]=atol(stra);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
              } 
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    } 
           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;}*/    free_vector(vv,1,n);  /* Doesn't work */
   ;
         i=i+1;  } 
       }  
     }  void lubksb(double **a, int n, int *indx, double b[]) 
     /* printf("ii=%d", ij);  { 
        scanf("%d",i);*/    int i,ii=0,ip,j; 
   imx=i-1; /* Number of individuals */    double sum; 
    
   /* for (i=1; i<=imx; i++){    for (i=1;i<=n;i++) { 
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      ip=indx[i]; 
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;      sum=b[ip]; 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;      b[ip]=b[i]; 
     }*/      if (ii) 
    /*  for (i=1; i<=imx; i++){        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
      if (s[4][i]==9)  s[4][i]=-1;      else if (sum) ii=i; 
      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]));}*/      b[i]=sum; 
      } 
      for (i=n;i>=1;i--) { 
   /* Calculation of the number of parameter from char model*/      sum=b[i]; 
   Tvar=ivector(1,15);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   Tprod=ivector(1,15);      b[i]=sum/a[i][i]; 
   Tvaraff=ivector(1,15);    } 
   Tvard=imatrix(1,15,1,2);  } 
   Tage=ivector(1,15);        
      void pstamp(FILE *fichier)
   if (strlen(model) >1){  {
     j=0, j1=0, k1=1, k2=1;    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
     j=nbocc(model,'+');  }
     j1=nbocc(model,'*');  
     cptcovn=j+1;  /************ Frequencies ********************/
     cptcovprod=j1;  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 */
     strcpy(modelsav,model);    
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    int i, m, jk, j1, bool, z1,j;
       printf("Error. Non available option model=%s ",model);    int first;
       goto end;    double ***freq; /* Frequencies */
     }    double *pp, **prop;
        double pos,posprop, k2, dateintsum=0,k2cpt=0;
     for(i=(j+1); i>=1;i--){    char fileresp[FILENAMELENGTH];
       cutv(stra,strb,modelsav,'+');    
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    pp=vector(1,nlstate);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/    prop=matrix(1,nlstate,iagemin,iagemax+3);
       /*scanf("%d",i);*/    strcpy(fileresp,"p");
       if (strchr(strb,'*')) {    strcat(fileresp,fileres);
         cutv(strd,strc,strb,'*');    if((ficresp=fopen(fileresp,"w"))==NULL) {
         if (strcmp(strc,"age")==0) {      printf("Problem with prevalence resultfile: %s\n", fileresp);
           cptcovprod--;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
           cutv(strb,stre,strd,'V');      exit(0);
           Tvar[i]=atoi(stre);    }
           cptcovage++;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
             Tage[cptcovage]=i;    j1=0;
             /*printf("stre=%s ", stre);*/    
         }    j=cptcoveff;
         else if (strcmp(strd,"age")==0) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           cptcovprod--;  
           cutv(strb,stre,strc,'V');    first=1;
           Tvar[i]=atoi(stre);  
           cptcovage++;    /* for(k1=1; k1<=j ; k1++){ */  /* Loop on covariates */
           Tage[cptcovage]=i;    /*  for(i1=1; i1<=ncodemax[k1];i1++){ */ /* Now it is 2 */
         }    /*    j1++; */
         else {    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
           cutv(strb,stre,strc,'V');        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           Tvar[i]=ncovcol+k1;          scanf("%d", i);*/
           cutv(strb,strc,strd,'V');        for (i=-5; i<=nlstate+ndeath; i++)  
           Tprod[k1]=i;          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           Tvard[k1][1]=atoi(strc);            for(m=iagemin; m <= iagemax+3; m++)
           Tvard[k1][2]=atoi(stre);              freq[i][jk][m]=0;
           Tvar[cptcovn+k2]=Tvard[k1][1];        
           Tvar[cptcovn+k2+1]=Tvard[k1][2];        for (i=1; i<=nlstate; i++)  
           for (k=1; k<=lastobs;k++)          for(m=iagemin; m <= iagemax+3; m++)
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];            prop[i][m]=0;
           k1++;        
           k2=k2+2;        dateintsum=0;
         }        k2cpt=0;
       }        for (i=1; i<=imx; i++) {
       else {          bool=1;
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
        /*  scanf("%d",i);*/            for (z1=1; z1<=cptcoveff; z1++)       
       cutv(strd,strc,strb,'V');              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
       Tvar[i]=atoi(strc);                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
       }                bool=0;
       strcpy(modelsav,stra);                  /* 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", 
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
         scanf("%d",i);*/                  j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
     }                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
 }              } 
            }
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);   
   printf("cptcovprod=%d ", cptcovprod);          if (bool==1){
   scanf("%d ",i);*/            for(m=firstpass; m<=lastpass; m++){
     fclose(fic);              k2=anint[m][i]+(mint[m][i]/12.);
               /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     /*  if(mle==1){*/                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     if (weightopt != 1) { /* Maximisation without weights*/                if(agev[m][i]==1) agev[m][i]=iagemax+2;
       for(i=1;i<=n;i++) weight[i]=1.0;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     }                if (m<lastpass) {
     /*-calculation of age at interview from date of interview and age at death -*/                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
     agev=matrix(1,maxwav,1,imx);                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                 }
     for (i=1; i<=imx; i++) {                
       for(m=2; (m<= maxwav); m++) {                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){                  dateintsum=dateintsum+k2;
          anint[m][i]=9999;                  k2cpt++;
          s[m][i]=-1;                }
        }                /*}*/
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;            }
       }          }
     }        } /* end i */
          
     for (i=1; i<=imx; i++)  {        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        pstamp(ficresp);
       for(m=1; (m<= maxwav); m++){        if  (cptcovn>0) {
         if(s[m][i] >0){          fprintf(ficresp, "\n#********** Variable "); 
           if (s[m][i] >= nlstate+1) {          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             if(agedc[i]>0)          fprintf(ficresp, "**********\n#");
               if(moisdc[i]!=99 && andc[i]!=9999)          fprintf(ficlog, "\n#********** Variable "); 
                 agev[m][i]=agedc[i];          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/          fprintf(ficlog, "**********\n#");
            else {        }
               if (andc[i]!=9999){        for(i=1; i<=nlstate;i++) 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
               agev[m][i]=-1;        fprintf(ficresp, "\n");
               }        
             }        for(i=iagemin; i <= iagemax+3; i++){
           }          if(i==iagemax+3){
           else if(s[m][i] !=9){ /* Should no more exist */            fprintf(ficlog,"Total");
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          }else{
             if(mint[m][i]==99 || anint[m][i]==9999)            if(first==1){
               agev[m][i]=1;              first=0;
             else if(agev[m][i] <agemin){              printf("See log file for details...\n");
               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);*/            fprintf(ficlog,"Age %d", i);
             }          }
             else if(agev[m][i] >agemax){          for(jk=1; jk <=nlstate ; jk++){
               agemax=agev[m][i];            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/              pp[jk] += freq[jk][m][i]; 
             }          }
             /*agev[m][i]=anint[m][i]-annais[i];*/          for(jk=1; jk <=nlstate ; jk++){
             /*   agev[m][i] = age[i]+2*m;*/            for(m=-1, pos=0; m <=0 ; m++)
           }              pos += freq[jk][m][i];
           else { /* =9 */            if(pp[jk]>=1.e-10){
             agev[m][i]=1;              if(first==1){
             s[m][i]=-1;                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
           }              }
         }              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
         else /*= 0 Unknown */            }else{
           agev[m][i]=1;              if(first==1)
       }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                  fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
     }            }
     for (i=1; i<=imx; i++)  {          }
       for(m=1; (m<= maxwav); m++){  
         if (s[m][i] > (nlstate+ndeath)) {          for(jk=1; jk <=nlstate ; jk++){
           printf("Error: Wrong value in nlstate or ndeath\n");              for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
           goto end;              pp[jk] += freq[jk][m][i];
         }          }       
       }          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     }            pos += pp[jk];
             posprop += prop[jk][i];
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);          }
           for(jk=1; jk <=nlstate ; jk++){
     free_vector(severity,1,maxwav);            if(pos>=1.e-5){
     free_imatrix(outcome,1,maxwav+1,1,n);              if(first==1)
     free_vector(moisnais,1,n);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     free_vector(annais,1,n);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     /* free_matrix(mint,1,maxwav,1,n);            }else{
        free_matrix(anint,1,maxwav,1,n);*/              if(first==1)
     free_vector(moisdc,1,n);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     free_vector(andc,1,n);              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }
                if( i <= iagemax){
     wav=ivector(1,imx);              if(pos>=1.e-5){
     dh=imatrix(1,lastpass-firstpass+1,1,imx);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);                /*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]);*/
     /* Concatenates waves */              }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);              else
                 fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             }
       Tcode=ivector(1,100);          }
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);          
       ncodemax[1]=1;          for(jk=-1; jk <=nlstate+ndeath; jk++)
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);            for(m=-1; m <=nlstate+ndeath; m++)
                    if(freq[jk][m][i] !=0 ) {
    codtab=imatrix(1,100,1,10);              if(first==1)
    h=0;                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
    m=pow(2,cptcoveff);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
                }
    for(k=1;k<=cptcoveff; k++){          if(i <= iagemax)
      for(i=1; i <=(m/pow(2,k));i++){            fprintf(ficresp,"\n");
        for(j=1; j <= ncodemax[k]; j++){          if(first==1)
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){            printf("Others in log...\n");
            h++;          fprintf(ficlog,"\n");
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;        }
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/        /*}*/
          }    }
        }    dateintmean=dateintsum/k2cpt; 
      }   
    }    fclose(ficresp);
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
       codtab[1][2]=1;codtab[2][2]=2; */    free_vector(pp,1,nlstate);
    /* for(i=1; i <=m ;i++){    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
       for(k=1; k <=cptcovn; k++){    /* End of Freq */
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);  }
       }  
       printf("\n");  /************ Prevalence ********************/
       }  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)
       scanf("%d",i);*/  {  
        /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
    /* Calculates basic frequencies. Computes observed prevalence at single age       in each health status at the date of interview (if between dateprev1 and dateprev2).
        and prints on file fileres'p'. */       We still use firstpass and lastpass as another selection.
     */
       
        int i, m, jk, j1, bool, z1,j;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **prop;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double posprop; 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double  y2; /* in fractional years */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    int iagemin, iagemax;
          int first; /** to stop verbosity which is redirected to log file */
     /* 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] */    iagemin= (int) agemin;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    iagemax= (int) agemax;
     /*pp=vector(1,nlstate);*/
     if(mle==1){    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     }    j1=0;
        
     /*--------- results files --------------*/    /*j=cptcoveff;*/
     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);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
      
     first=1;
    jk=1;    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");      /*for(i1=1; i1<=ncodemax[k1];i1++){
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");        j1++;*/
    for(i=1,jk=1; i <=nlstate; i++){        
      for(k=1; k <=(nlstate+ndeath); k++){        for (i=1; i<=nlstate; i++)  
        if (k != i)          for(m=iagemin; m <= iagemax+3; m++)
          {            prop[i][m]=0.0;
            printf("%d%d ",i,k);       
            fprintf(ficres,"%1d%1d ",i,k);        for (i=1; i<=imx; i++) { /* Each individual */
            for(j=1; j <=ncovmodel; j++){          bool=1;
              printf("%f ",p[jk]);          if  (cptcovn>0) {
              fprintf(ficres,"%f ",p[jk]);            for (z1=1; z1<=cptcoveff; z1++) 
              jk++;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
            }                bool=0;
            printf("\n");          } 
            fprintf(ficres,"\n");          if (bool==1) { 
          }            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
      }              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
    }              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
  if(mle==1){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     /* Computing hessian and covariance matrix */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     ftolhess=ftol; /* Usually correct */                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); 
     hesscov(matcov, p, npar, delti, ftolhess, func);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
  }                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     printf("# Scales (for hessian or gradient estimation)\n");                  prop[s[m][i]][iagemax+3] += weight[i]; 
      for(i=1,jk=1; i <=nlstate; i++){                } 
       for(j=1; j <=nlstate+ndeath; j++){              }
         if (j!=i) {            } /* end selection of waves */
           fprintf(ficres,"%1d%1d",i,j);          }
           printf("%1d%1d",i,j);        }
           for(k=1; k<=ncovmodel;k++){        for(i=iagemin; i <= iagemax+3; i++){  
             printf(" %.5e",delti[jk]);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             fprintf(ficres," %.5e",delti[jk]);            posprop += prop[jk][i]; 
             jk++;          } 
           }          
           printf("\n");          for(jk=1; jk <=nlstate ; jk++){     
           fprintf(ficres,"\n");            if( i <=  iagemax){ 
         }              if(posprop>=1.e-5){ 
       }                probs[i][jk][j1]= prop[jk][i]/posprop;
      }              } else{
                    if(first==1){
     k=1;                  first=0;
     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");                  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]);
     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(i=1;i<=npar;i++){              }
       /*  if (k>nlstate) k=1;            } 
       i1=(i-1)/(ncovmodel*nlstate)+1;          }/* end jk */ 
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);        }/* end i */ 
       printf("%s%d%d",alph[k],i1,tab[i]);*/      /*} *//* end i1 */
       fprintf(ficres,"%3d",i);    } /* end j1 */
       printf("%3d",i);    
       for(j=1; j<=i;j++){    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
         fprintf(ficres," %.5e",matcov[i][j]);    /*free_vector(pp,1,nlstate);*/
         printf(" %.5e",matcov[i][j]);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
       }  }  /* End of prevalence */
       fprintf(ficres,"\n");  
       printf("\n");  /************* Waves Concatenation ***************/
       k++;  
     }  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)
      {
     while((c=getc(ficpar))=='#' && c!= EOF){    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       ungetc(c,ficpar);       Death is a valid wave (if date is known).
       fgets(line, MAXLINE, ficpar);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       puts(line);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
       fputs(line,ficparo);       and mw[mi+1][i]. dh depends on stepm.
     }       */
     ungetc(c,ficpar);  
     estepm=0;    int i, mi, m;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     if (estepm==0 || estepm < stepm) estepm=stepm;       double sum=0., jmean=0.;*/
     if (fage <= 2) {    int first;
       bage = ageminpar;    int j, k=0,jk, ju, jl;
       fage = agemaxpar;    double sum=0.;
     }    first=0;
        jmin=100000;
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    jmax=-1;
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    jmean=0.;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    for(i=1; i<=imx; i++){
        mi=0;
     while((c=getc(ficpar))=='#' && c!= EOF){      m=firstpass;
     ungetc(c,ficpar);      while(s[m][i] <= nlstate){
     fgets(line, MAXLINE, ficpar);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     puts(line);          mw[++mi][i]=m;
     fputs(line,ficparo);        if(m >=lastpass)
   }          break;
   ungetc(c,ficpar);        else
            m++;
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);      }/* end while */
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      if (s[m][i] > nlstate){
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        mi++;     /* Death is another wave */
              /* if(mi==0)  never been interviewed correctly before death */
   while((c=getc(ficpar))=='#' && c!= EOF){           /* Only death is a correct wave */
     ungetc(c,ficpar);        mw[mi][i]=m;
     fgets(line, MAXLINE, ficpar);      }
     puts(line);  
     fputs(line,ficparo);      wav[i]=mi;
   }      if(mi==0){
   ungetc(c,ficpar);        nbwarn++;
          if(first==0){
           printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
    dateprev1=anprev1+mprev1/12.+jprev1/365.;          first=1;
    dateprev2=anprev2+mprev2/12.+jprev2/365.;        }
         if(first==1){
   fscanf(ficpar,"pop_based=%d\n",&popbased);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
   fprintf(ficparo,"pop_based=%d\n",popbased);          }
   fprintf(ficres,"pop_based=%d\n",popbased);        } /* end mi==0 */
      } /* End individuals */
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);    for(i=1; i<=imx; i++){
     fgets(line, MAXLINE, ficpar);      for(mi=1; mi<wav[i];mi++){
     puts(line);        if (stepm <=0)
     fputs(line,ficparo);          dh[mi][i]=1;
   }        else{
   ungetc(c,ficpar);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
             if (agedc[i] < 2*AGESUP) {
   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);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
 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);              if(j==0) j=1;  /* Survives at least one month after exam */
 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);              else if(j<0){
                 nberr++;
                 printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
 while((c=getc(ficpar))=='#' && c!= EOF){                j=1; /* Temporary Dangerous patch */
     ungetc(c,ficpar);                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);
     fgets(line, MAXLINE, ficpar);                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]);
     puts(line);                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);
     fputs(line,ficparo);              }
   }              k=k+1;
   ungetc(c,ficpar);              if (j >= jmax){
                 jmax=j;
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);                ijmax=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(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);              if (j <= jmin){
                 jmin=j;
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);                ijmin=i;
               }
 /*------------ gnuplot -------------*/              sum=sum+j;
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);              /*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);*/
 /*------------ free_vector  -------------*/            }
  chdir(path);          }
            else{
  free_ivector(wav,1,imx);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);  /*        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]); */
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);    
  free_ivector(num,1,n);            k=k+1;
  free_vector(agedc,1,n);            if (j >= jmax) {
  /*free_matrix(covar,1,NCOVMAX,1,n);*/              jmax=j;
  fclose(ficparo);              ijmax=i;
  fclose(ficres);            }
             else if (j <= jmin){
 /*--------- index.htm --------*/              jmin=j;
               ijmin=i;
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);            }
             /*        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]);*/
   /*--------------- Prevalence limit --------------*/            if(j<0){
                nberr++;
   strcpy(filerespl,"pl");              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]);
   strcat(filerespl,fileres);              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]);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {            }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;            sum=sum+j;
   }          }
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          jk= j/stepm;
   fprintf(ficrespl,"#Prevalence limit\n");          jl= j -jk*stepm;
   fprintf(ficrespl,"#Age ");          ju= j -(jk+1)*stepm;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
   fprintf(ficrespl,"\n");            if(jl==0){
                dh[mi][i]=jk;
   prlim=matrix(1,nlstate,1,nlstate);              bh[mi][i]=0;
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            }else{ /* We want a negative bias in order to only have interpolation ie
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                    * to avoid the price of an extra matrix product in likelihood */
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              dh[mi][i]=jk+1;
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              bh[mi][i]=ju;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            }
   k=0;          }else{
   agebase=ageminpar;            if(jl <= -ju){
   agelim=agemaxpar;              dh[mi][i]=jk;
   ftolpl=1.e-10;              bh[mi][i]=jl;       /* bias is positive if real duration
   i1=cptcoveff;                                   * is higher than the multiple of stepm and negative otherwise.
   if (cptcovn < 1){i1=1;}                                   */
             }
   for(cptcov=1;cptcov<=i1;cptcov++){            else{
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              dh[mi][i]=jk+1;
         k=k+1;              bh[mi][i]=ju;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/            }
         fprintf(ficrespl,"\n#******");            if(dh[mi][i]==0){
         for(j=1;j<=cptcoveff;j++)              dh[mi][i]=1; /* At least one step */
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              bh[mi][i]=ju; /* At least one step */
         fprintf(ficrespl,"******\n");              /*  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);*/
                    }
         for (age=agebase; age<=agelim; age++){          } /* end if mle */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        }
           fprintf(ficrespl,"%.0f",age );      } /* end wave */
           for(i=1; i<=nlstate;i++)    }
           fprintf(ficrespl," %.5f", prlim[i][i]);    jmean=sum/k;
           fprintf(ficrespl,"\n");    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
         }    fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %d) Max=%d (%d) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
       }   }
     }  
   fclose(ficrespl);  /*********** Tricode ****************************/
   void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
   /*------------- h Pij x at various ages ------------*/  {
      /**< Uses cptcovn+2*cptcovprod as the number of covariates */
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
   if((ficrespij=fopen(filerespij,"w"))==NULL) {     * Boring subroutine which should only output nbcode[Tvar[j]][k]
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
   }     * nbcode[Tvar[j]][1]= 
   printf("Computing pij: result on file '%s' \n", filerespij);    */
    
   stepsize=(int) (stepm+YEARM-1)/YEARM;    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
   /*if (stepm<=24) stepsize=2;*/    int modmaxcovj=0; /* Modality max of covariates j */
     int cptcode=0; /* Modality max of covariates j */
   agelim=AGESUP;    int modmincovj=0; /* Modality min of covariates j */
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
      cptcoveff=0; 
   k=0;   
   for(cptcov=1;cptcov<=i1;cptcov++){    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;    /* Loop on covariates without age and products */
         fprintf(ficrespij,"\n#****** ");    for (j=1; j<=(cptcovs); j++) { /* From model V1 + V2*age+ V3 + V3*V4 keeps V1 + V3 = 2 only */
         for(j=1;j<=cptcoveff;j++)      for (k=-1; k < maxncov; k++) Ndum[k]=0;
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      for (i=1; i<=imx; i++) { /* Loop on individuals: reads the data file to get the maximum value of the 
         fprintf(ficrespij,"******\n");                                 modality of this covariate Vj*/ 
                ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */                                      * If product of Vn*Vm, still boolean *:
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
           oldm=oldms;savm=savms;                                        modality of the nth covariate of individual i. */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          if (ij > modmaxcovj)
           fprintf(ficrespij,"# Age");          modmaxcovj=ij; 
           for(i=1; i<=nlstate;i++)        else if (ij < modmincovj) 
             for(j=1; j<=nlstate+ndeath;j++)          modmincovj=ij; 
               fprintf(ficrespij," %1d-%1d",i,j);        if ((ij < -1) && (ij > NCOVMAX)){
           fprintf(ficrespij,"\n");          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
            for (h=0; h<=nhstepm; h++){          exit(1);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        }else
             for(i=1; i<=nlstate;i++)        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
               for(j=1; j<=nlstate+ndeath;j++)        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
             fprintf(ficrespij,"\n");        /* getting the maximum value of the modality of the covariate
              }           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           female is 1, then modmaxcovj=1.*/
           fprintf(ficrespij,"\n");      } /* end for loop on individuals i */
         }      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
     }      fprintf(ficlog," Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
   }      cptcode=modmaxcovj;
       /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);     /*for (i=0; i<=cptcode; i++) {*/
       for (k=modmincovj;  k<=modmaxcovj; k++) { /* k=-1 ? 0 and 1*//* For each value k of the modality of model-cov j */
   fclose(ficrespij);        printf("Frequencies of covariates %d ie V%d with value %d: %d\n", j, Tvar[j], k, Ndum[k]);
         fprintf(ficlog, "Frequencies of covariates %d ie V%d with value %d: %d\n", j, Tvar[j], k, Ndum[k]);
         if( Ndum[k] != 0 ){ /* Counts if nobody answered modality k ie empty modality, we skip it and reorder */
   /*---------- Forecasting ------------------*/          if( k != -1){
   if((stepm == 1) && (strcmp(model,".")==0)){            ncodemax[j]++;  /* ncodemax[j]= Number of modalities of the j th
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);                               covariate for which somebody answered excluding 
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);                               undefined. Usually 2: 0 and 1. */
   }          }
   else{          ncodemaxwundef[j]++; /* ncodemax[j]= Number of modalities of the j th
     erreur=108;                               covariate for which somebody answered including 
     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);                               undefined. Usually 3: -1, 0 and 1. */
   }        }
          /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
            historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
   /*---------- Health expectancies and variances ------------*/      } /* Ndum[-1] number of undefined modalities */
   
   strcpy(filerest,"t");      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
   strcat(filerest,fileres);      /* For covariate j, modalities could be 1, 2, 3, 4, 5, 6, 7. 
   if((ficrest=fopen(filerest,"w"))==NULL) {         If Ndum[1]=0, Ndum[2]=0, Ndum[3]= 635, Ndum[4]=0, Ndum[5]=0, Ndum[6]=27, Ndum[7]=125;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;         modmincovj=3; modmaxcovj = 7;
   }         There are only 3 modalities non empty 3, 6, 7 (or 2 if 27 is too few) : ncodemax[j]=3;
   printf("Computing Total LEs with variances: file '%s' \n", filerest);         which will be coded 0, 1, 2 which in binary on 2=3-1 digits are 0=00 1=01, 2=10;
          defining two dummy variables: variables V1_1 and V1_2.
          nbcode[Tvar[j]][ij]=k;
   strcpy(filerese,"e");         nbcode[Tvar[j]][1]=0;
   strcat(filerese,fileres);         nbcode[Tvar[j]][2]=1;
   if((ficreseij=fopen(filerese,"w"))==NULL) {         nbcode[Tvar[j]][3]=2;
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);      */
   }      ij=0; /* ij is similar to i but can jumps over null modalities */
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 or from -1 to 1*/
           if (Ndum[i] == 0) { /* If at least one individual responded to this modality k */
  strcpy(fileresv,"v");            break;
   strcat(fileresv,fileres);          }
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          ij++;
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);          nbcode[Tvar[j]][ij]=i;  /* stores the original modality i in an array nbcode, ij modality from 1 to last non-nul modality.*/
   }          cptcode = ij; /* New max modality for covar j */
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);      } /* end of loop on modality i=-1 to 1 or more */
   calagedate=-1;        
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      /*   for (k=0; k<= cptcode; k++) { /\* k=-1 ? k=0 to 1 *\//\* Could be 1 to 4 *\//\* cptcode=modmaxcovj *\/ */
       /*  /\*recode from 0 *\/ */
   k=0;      /*                               k is a modality. If we have model=V1+V1*sex  */
   for(cptcov=1;cptcov<=i1;cptcov++){      /*                               then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      /*                            But if some modality were not used, it is recoded from 0 to a newer modmaxcovj=cptcode *\/ */
       k=k+1;      /*  } */
       fprintf(ficrest,"\n#****** ");      /*  /\* cptcode = ij; *\/ /\* New max modality for covar j *\/ */
       for(j=1;j<=cptcoveff;j++)      /*  if (ij > ncodemax[j]) { */
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      /*    printf( " Error ij=%d > ncodemax[%d]=%d\n", ij, j, ncodemax[j]);  */
       fprintf(ficrest,"******\n");      /*    fprintf(ficlog, " Error ij=%d > ncodemax[%d]=%d\n", ij, j, ncodemax[j]); */
       /*    break; */
       fprintf(ficreseij,"\n#****** ");      /*  } */
       for(j=1;j<=cptcoveff;j++)      /*   }  /\* end of loop on modality k *\/ */
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
       fprintf(ficreseij,"******\n");    
    for (k=-1; k< maxncov; k++) Ndum[k]=0; 
       fprintf(ficresvij,"\n#****** ");    
       for(j=1;j<=cptcoveff;j++)    for (i=1; i<=ncovmodel-2-nagesqr; i++) { /* -2, cste and age and eventually age*age */ 
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
       fprintf(ficresvij,"******\n");     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
      Ndum[ij]++; /* Might be supersed V1 + V1*age */
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);   } 
       oldm=oldms;savm=savms;  
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);     ij=0;
     for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);     /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
       oldm=oldms;savm=savms;     if((Ndum[i]!=0) && (i<=ncovcol)){
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);       ij++;
           /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
        Tvaraff[ij]=i; /*For printing (unclear) */
       }else{
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");         /* Tvaraff[ij]=0; */
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);     }
       fprintf(ficrest,"\n");   }
    /* ij--; */
       epj=vector(1,nlstate+1);   cptcoveff=ij; /*Number of total covariates*/
       for(age=bage; age <=fage ;age++){  
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);  }
         if (popbased==1) {  
           for(i=1; i<=nlstate;i++)  
             prlim[i][i]=probs[(int)age][i][k];  /*********** Health Expectancies ****************/
         }  
          void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
         fprintf(ficrest," %4.0f",age);  
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){  {
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    /* Health expectancies, no variances */
             epj[j] += prlim[i][i]*eij[i][j][(int)age];    int i, j, nhstepm, hstepm, h, nstepm;
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/    int nhstepma, nstepma; /* Decreasing with age */
           }    double age, agelim, hf;
           epj[nlstate+1] +=epj[j];    double ***p3mat;
         }    double eip;
   
         for(i=1, vepp=0.;i <=nlstate;i++)    pstamp(ficreseij);
           for(j=1;j <=nlstate;j++)    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
             vepp += vareij[i][j][(int)age];    fprintf(ficreseij,"# Age");
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));    for(i=1; i<=nlstate;i++){
         for(j=1;j <=nlstate;j++){      for(j=1; j<=nlstate;j++){
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));        fprintf(ficreseij," e%1d%1d ",i,j);
         }      }
         fprintf(ficrest,"\n");      fprintf(ficreseij," e%1d. ",i);
       }    }
     }    fprintf(ficreseij,"\n");
   }  
 free_matrix(mint,1,maxwav,1,n);    
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    if(estepm < stepm){
     free_vector(weight,1,n);      printf ("Problem %d lower than %d\n",estepm, stepm);
   fclose(ficreseij);    }
   fclose(ficresvij);    else  hstepm=estepm;   
   fclose(ficrest);    /* We compute the life expectancy from trapezoids spaced every estepm months
   fclose(ficpar);     * This is mainly to measure the difference between two models: for example
   free_vector(epj,1,nlstate+1);     * 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 
   /*------- Variance limit prevalence------*/       * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
   strcpy(fileresvpl,"vpl");     * estimate the model with stepm=1 month, we can keep estepm to 24 months
   strcat(fileresvpl,fileres);     * to compare the new estimate of Life expectancy with the same linear 
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {     * hypothesis. A more precise result, taking into account a more precise
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);     * curvature will be obtained if estepm is as small as stepm. */
     exit(0);  
   }    /* For example we decided to compute the life expectancy with the smallest unit */
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    /* 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 
   k=0;       nstepm is the number of stepm from age to agelin. 
   for(cptcov=1;cptcov<=i1;cptcov++){       Look at hpijx to understand the reason of that which relies in memory size
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       and note for a fixed period like estepm months */
       k=k+1;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fprintf(ficresvpl,"\n#****** ");       survival function given by stepm (the optimization length). Unfortunately it
       for(j=1;j<=cptcoveff;j++)       means that if the survival funtion is printed only each two years of age and if
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       fprintf(ficresvpl,"******\n");       results. So we changed our mind and took the option of the best precision.
          */
       varpl=matrix(1,nlstate,(int) bage, (int) fage);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       oldm=oldms;savm=savms;  
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    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 */
   fclose(ficresvpl);      
   /* nhstepm age range expressed in number of stepm */
   /*---------- End : free ----------------*/    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      /* if (stepm >= YEARM) hstepm=1;*/
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
    
      for (age=bage; age<=fage; age ++){ 
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);      /* if (stepm >= YEARM) hstepm=1;*/
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
    
   free_matrix(matcov,1,npar,1,npar);      /* If stepm=6 months */
   free_vector(delti,1,npar);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   free_matrix(agev,1,maxwav,1,imx);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);      
       hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   if(erreur >0)      
     printf("End of Imach with error or warning %d\n",erreur);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   else   printf("End of Imach\n");      
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */      printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/      
   /*printf("Total time was %d uSec.\n", total_usecs);*/      /* Computing expectancies */
   /*------ End -----------*/      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
  end:            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
   /* chdir(pathcd);*/            
  /*system("wgnuplot graph.plt");*/            /* 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]);*/
  /*system("../gp37mgw/wgnuplot graph.plt");*/  
  /*system("cd ../gp37mgw");*/          }
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/  
  strcpy(plotcmd,GNUPLOTPROGRAM);      fprintf(ficreseij,"%3.0f",age );
  strcat(plotcmd," ");      for(i=1; i<=nlstate;i++){
  strcat(plotcmd,optionfilegnuplot);        eip=0;
  system(plotcmd);        for(j=1; j<=nlstate;j++){
           eip +=eij[i][j][(int)age];
  /*#ifdef windows*/          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
   while (z[0] != 'q') {        }
     /* chdir(path); */        fprintf(ficreseij,"%9.4f", eip );
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");      }
     scanf("%s",z);      fprintf(ficreseij,"\n");
     if (z[0] == 'c') system("./imach");      
     else if (z[0] == 'e') system(optionfilehtm);    }
     else if (z[0] == 'g') system(plotcmd);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     else if (z[0] == 'q') exit(0);    printf("\n");
   }    fprintf(ficlog,"\n");
   /*#endif */    
 }  }
   
   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[] )
   
   {
     /* Covariances of health expectancies eij and of total life expectancies according
      to initial status i, ei. .
     */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
     int nhstepma, nstepma; /* Decreasing with age */
     double age, agelim, hf;
     double ***p3matp, ***p3matm, ***varhe;
     double **dnewm,**doldm;
     double *xp, *xm;
     double **gp, **gm;
     double ***gradg, ***trgradg;
     int theta;
   
     double eip, vip;
   
     varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     xp=vector(1,npar);
     xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
     doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     
     pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
     fprintf(ficresstdeij,"# Age");
     for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++)
         fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
       fprintf(ficresstdeij," e%1d. ",i);
     }
     fprintf(ficresstdeij,"\n");
   
     pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
     fprintf(ficrescveij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++){
         cptj= (j-1)*nlstate+i;
         for(i2=1; i2<=nlstate;i2++)
           for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
             if(cptj2 <= cptj)
               fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
       }
     fprintf(ficrescveij,"\n");
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
      * if stepm=24 months pijx are given only every 2 years and by summing them
      * we are calculating an estimate of the Life Expectancy assuming a linear 
      * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
      * estimate the model with stepm=1 month, we can keep estepm to 24 months
      * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
      * curvature will be obtained if estepm is as small as stepm. */
   
     /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        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 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   
     /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
     agelim=AGESUP;
     nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     
     p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     gp=matrix(0,nhstepm,1,nlstate*nlstate);
     gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
     for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
       nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
       /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
       /* Computing  Variances of health expectancies */
       /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          decrease memory allocation */
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
         hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     
         for(j=1; j<= nlstate; j++){
           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.;
               gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
             }
           }
         }
        
         for(ij=1; ij<= nlstate*nlstate; ij++)
           for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
           }
       }/* End theta */
       
       
       for(h=0; h<=nhstepm-1; h++)
         for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
       
   
        for(ij=1;ij<=nlstate*nlstate;ij++)
         for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
   
        printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        for(h=0;h<=nhstepm-1;h++){
         for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(ij=1;ij<=nlstate*nlstate;ij++)
             for(ji=1;ji<=nlstate*nlstate;ji++)
               varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
         }
       }
   
       /* Computing expectancies */
       hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
             /* 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(ficresstdeij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
         eip=0.;
         vip=0.;
         for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
           for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
             vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         }
         fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }
       fprintf(ficresstdeij,"\n");
   
       fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
               if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
         }
       fprintf(ficrescveij,"\n");
      
     }
     free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
     fprintf(ficlog,"\n");
   
     free_vector(xm,1,npar);
     free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
   
   /************ Variance ******************/
   void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   {
     /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /* double **newm;*/
     /* int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav)*/
     
     int movingaverage();
     double **dnewm,**doldm;
     double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
     int k;
     double *xp;
     double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
     double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
     double age,agelim, hf;
     double ***mobaverage;
     int theta;
     char digit[4];
     char digitp[25];
   
     char fileresprobmorprev[FILENAMELENGTH];
   
     if(popbased==1){
       if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
     }
     else 
       strcpy(digitp,"-stablbased-");
   
     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);
       }
     }
   
     strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     pstamp(ficresprobmorprev);
     fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }  
     fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
     /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
     fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pstamp(ficresvij);
     fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     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);
     else
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at function hpijx to understand why (it is linked to memory size questions) */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
       gm=matrix(0,nhstepm,1,nlstate);
   
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
     
         for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
             for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
   
         for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
           for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
   
       } /* End theta */
   
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
       for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     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);
     /*  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); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     
     pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     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 */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       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);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ 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[])
   {
     int i, j=0,  k1, l1, tj;
     int k2, l2, j1,  z1;
     int k=0, l;
     int first=1, first1, first2;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age, cov[NCOVMAX+1];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     pstamp(ficresprobcov);
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     pstamp(ficresprobcor);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcor,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
     xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     fprintf(fichtm,"\n");
   
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     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>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   
     cov[1]=1;
     /* tj=cptcoveff; */
     tj = (int) pow(2,cptcoveff);
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(j1=1; j1<=tj;j1++){
       /*for(i1=1; i1<=ncodemax[t];i1++){ */
       /*j1++;*/
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\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]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
         gp=vector(1,(nlstate)*(nlstate+ndeath));
         gm=vector(1,(nlstate)*(nlstate+ndeath));
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           if(nagesqr==1)
             cov[3]= age*age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+nagesqr+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];/* j1 1 2 3 4
                                                            * 1  1 1 1 1
                                                            * 2  2 1 1 1
                                                            * 3  1 2 1 1
                                                            */
             /* nbcode[1][1]=0 nbcode[1][2]=1;*/
           }
           /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=nbcode[Tvar[Tage[k]]][codtab[ij][Tvar[Tage[k]]]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+nagesqr+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 /* 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]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
         free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
         free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
         free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;first2=2;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* 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.;
                     if ((lc2 <0) || (lc1 <0) ){
                       if(first2==1){
                         first1=0;
                       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);
                       }
                       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);
                       /* lc1=fabs(lc1); */ /* If we want to have them positive */
                       /* lc2=fabs(lc2); */
                     }
   
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       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 size 320, 240");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       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(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
         /* } */ /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   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 ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      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 ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=pow(2,cptcoveff);
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      /* for(i1=1; i1<=ncodemax[k1];i1++){ */
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++){ 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
            printf(" V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);fflush(stdout);
          }
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d_1.png\">%s%d_1.png</a><br> \
   <img src=\"%s%d_1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <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 */
          for(cpt=1; cpt<=nlstate;cpt++){
            fprintf(fichtm,"<br>- Convergence to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
   <img src=\"%s%d_%d.png\">", cpt, cpt, nlstate, subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           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> \
   <img src=\"%s%d%d.png\">",cpt,nlstate,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      /* } /\* end i1 *\/ */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br> \
    - 95%% confidence intervals and T statistics are in the log file.<br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Standard deviation of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=pow(2,cptcoveff);
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      /* for(i1=1; i1<=ncodemax[k1];i1++){ */
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d_%d.png <br>\
   <img src=\"%s%d_%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      /* } /\* end i1 *\/ */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     fprintf(ficgp,"\n# 1st: Period (stable) prevalence with CI: 'vpl' files\n");
     for (cpt=1; cpt<= nlstate ; cpt ++) {
       for (k1=1; k1<= m ; k1 ++) { /* plot [100000000000000000000:-100000000000000000000] "mysbiaspar/vplrmysbiaspar.txt to check */
        fprintf(ficgp,"\nset out \"%s%d_%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d_%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small size 320, 240\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," %%lf (%%lf)");
          else        fprintf(ficgp," %%*lf (%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l lt 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," %%lf (%%lf)");
          else fprintf(ficgp," %%*lf (%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95%% CI\" w l lt 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," %%lf (%%lf)");
          else fprintf(ficgp," %%*lf (%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l lt 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     fprintf(ficgp,"\n# 2nd: Total life expectancy with CI: 't' files\n");
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small size 320, 240\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," %%lf (%%lf)");
           else fprintf(ficgp," %%*lf (%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," %%lf (%%lf)");
           else fprintf(ficgp," %%*lf (%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l lt 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," %%lf (%%lf)");
           else fprintf(ficgp," %%*lf (%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l lt 0");
         else fprintf(ficgp,"\" t\"\" w l lt 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small 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);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { /* For each multivariate if any */
       for (cpt=1; cpt<=nlstate ; cpt ++) { /* For each life state */
         k=3;
         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);
         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 */
     fprintf(ficgp,"\n##############\n#MLE estimated parameters\n#############\n");
     for(i=1,jk=1; i <=nlstate; i++){
       fprintf(ficgp,"# initial state %d\n",i);
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           fprintf(ficgp,"#   current state %d\n",k);
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f; ",jk,p[jk]);
             jk++; 
           }
           fprintf(ficgp,"\n");
         }
       }
      }
     fprintf(ficgp,"##############\n#\n");
   
     /*goto avoid;*/
     fprintf(ficgp,"\n##############\n#Graphics of of probabilities or incidences\n#############\n");
     fprintf(ficgp,"# logi(p12/p11)=a12+b12*age+c12age*age+d12*V1+e12*V1*age\n");
     fprintf(ficgp,"# logi(p12/p11)=p1 +p2*age +p3*age*age+ p4*V1+ p5*V1*age\n");
     fprintf(ficgp,"# logi(p13/p11)=a13+b13*age+c13age*age+d13*V1+e13*V1*age\n");
     fprintf(ficgp,"# logi(p13/p11)=p6 +p7*age +p8*age*age+ p9*V1+ p10*V1*age\n");
     fprintf(ficgp,"# p12+p13+p14+p11=1=p11(1+exp(a12+b12*age+c12age*age+d12*V1+e12*V1*age)\n");
     fprintf(ficgp,"#                      +exp(a13+b13*age+c13age*age+d13*V1+e13*V1*age)+...)\n");
     fprintf(ficgp,"# p11=1/(1+exp(a12+b12*age+c12age*age+d12*V1+e12*V1*age)\n");
     fprintf(ficgp,"#                      +exp(a13+b13*age+c13age*age+d13*V1+e13*V1*age)+...)\n");
     fprintf(ficgp,"# p12=exp(a12+b12*age+c12age*age+d12*V1+e12*V1*age)/\n");
     fprintf(ficgp,"#     (1+exp(a12+b12*age+c12age*age+d12*V1+e12*V1*age)\n");
     fprintf(ficgp,"#       +exp(a13+b13*age+c13age*age+d13*V1+e13*V1*age))\n");
     fprintf(ficgp,"#       +exp(a14+b14*age+c14age*age+d14*V1+e14*V1*age)+...)\n");
     fprintf(ficgp,"#\n");
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        fprintf(ficgp,"# ng=%d\n",ng);
        fprintf(ficgp,"#   jk=1 to 2^%d=%d\n",cptcoveff,m);
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"#    jk=%d\n",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)
                  if(nagesqr==0)
                    fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                  else /* nagesqr =1 */
                    fprintf(ficgp," %f*exp(p%d+p%d*x+p%d*x*x",YEARM/stepm,i,i+1,i+1+nagesqr);
                else
                  if(nagesqr==0)
                    fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                  else /* nagesqr =1 */
                    fprintf(ficgp," exp(p%d+p%d*x+p%d*x*x",i,i+1,i+1+nagesqr);
                ij=1;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel-nagesqr; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /* Bug valgrind */
                    fprintf(ficgp,"+p%d*%d*x",i+j+nagesqr-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j+nagesqr-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){ 
                  if(nagesqr==0)
                    fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  else /* nagesqr =1 */
                    fprintf(ficgp,"+exp(p%d+p%d*x+p%d*x*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1,k3+(k1-1)*ncovmodel+1+nagesqr);
     
                  ij=1;
                  for(j=3; j <=ncovmodel-nagesqr; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2+nagesqr,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2+nagesqr,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 ******************/
   void 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, cptcod, i, h, i1;
     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*************/
   void 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];
     int i,j, k, 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 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=0, j=0, n=0;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[MAXLINE], strb[MAXLINE];
     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 */
       strcpy(line, linetmp);
     
   
       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+age*age
      * - nagesqr = 1 if age*age in the model, otherwise 0.
      * - cptcovt total number of covariates of the model nbocc(+)+1 = 8 excepting constant and age and age*age
      * - cptcovn or number of covariates k of the models excluding age*products =6 and age*age
      * - 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  j1, k1, k2;
     char modelsav[80];
     char stra[80], strb[80], strc[80], strd[80],stre[80];
     char *strpt;
   
     /*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;
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=1+age+%s. ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=1+age+%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;
       }
       strcpy(modelsav,model); 
       if ((strpt=strstr(model,"age*age")) !=0){
         printf(" strpt=%s, model=%s\n",strpt, model);
         if(strpt != model){
         printf("Error in model: 'model=%s'; 'age*age' should in first place before other covariates\n \
    'model=1+age+age*age+V1.' or 'model=1+age+age*age+V1+V1*age.', please swap as well as \n \
    corresponding column of parameters.\n",model);
         fprintf(ficlog,"Error in model: 'model=%s'; 'age*age' should in first place before other covariates\n \
    'model=1+age+age*age+V1.' or 'model=1+age+age*age+V1+V1*age.', please swap as well as \n \
    corresponding column of parameters.\n",model); fflush(ficlog);
         return 1;
       }
   
         nagesqr=1;
         if (strstr(model,"+age*age") !=0)
           substrchaine(modelsav, model, "+age*age");
         else if (strstr(model,"age*age+") !=0)
           substrchaine(modelsav, model, "age*age+");
         else 
           substrchaine(modelsav, model, "age*age");
       }else
         nagesqr=0;
       if (strlen(modelsav) >1){
         j=nbocc(modelsav,'+'); /**< j=Number of '+' */
         j1=nbocc(modelsav,'*'); /**< j1=Number of '*' */
         cptcovs=j+1-j1; /**<  Number of simple covariates V1+V1*age+V3 +V3*V4+age*age=> V1 + V3 =2  */
         cptcovt= j+1; /* Number of total covariates in the model, not including
                      * cst, age and age*age 
                      * V1+V1*age+ V3 + V3*V4+age*age=> 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  */
   
       
         /*   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]]=nbcode[Tvar[Tage[k]]][codtab[ij][Tvar[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; V1+V1*age Tvar[2]=1 */
               cptcovage++; /* Sums the number of covariates which include age as a product */
               Tage[cptcovage]=k;  /* Tvar[4]=3, Tage[1] = 4 or V1+V1*age Tvar[2]=1, Tage[1]=2 */
               /*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 + on total covariates */
       } /* end if strlen(modelsave == 0) age*age might exist */
     } /* end if strlen(model == 0) */
     
     /*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);
   }
   
   int 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 = *nberr + 1;
           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 (%d)\n",(int)moisdc[i],(int)andc[i],num[i],i, *nberr);
           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 (%d)\n",(int)moisdc[i],(int)andc[i],num[i],i, *nberr);
           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;
                 }
               }
             } /* agedc > 0 */
           }
           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);
   }
   
   #if defined(_MSC_VER)
   /*printf("Visual C++ compiler: %s \n;", _MSC_FULL_VER);*/
   /*fprintf(ficlog, "Visual C++ compiler: %s \n;", _MSC_FULL_VER);*/
   //#include "stdafx.h"
   //#include <stdio.h>
   //#include <tchar.h>
   //#include <windows.h>
   //#include <iostream>
   typedef BOOL(WINAPI *LPFN_ISWOW64PROCESS) (HANDLE, PBOOL);
   
   LPFN_ISWOW64PROCESS fnIsWow64Process;
   
   BOOL IsWow64()
   {
           BOOL bIsWow64 = FALSE;
   
           //typedef BOOL (APIENTRY *LPFN_ISWOW64PROCESS)
           //  (HANDLE, PBOOL);
   
           //LPFN_ISWOW64PROCESS fnIsWow64Process;
   
           HMODULE module = GetModuleHandle(_T("kernel32"));
           const char funcName[] = "IsWow64Process";
           fnIsWow64Process = (LPFN_ISWOW64PROCESS)
                   GetProcAddress(module, funcName);
   
           if (NULL != fnIsWow64Process)
           {
                   if (!fnIsWow64Process(GetCurrentProcess(),
                           &bIsWow64))
                           //throw std::exception("Unknown error");
                           printf("Unknown error\n");
           }
           return bIsWow64 != FALSE;
   }
   #endif
   
   void syscompilerinfo(int logged)
    {
      /* #include "syscompilerinfo.h"*/
      /* command line Intel compiler 32bit windows, XP compatible:*/
      /* /GS /W3 /Gy
         /Zc:wchar_t /Zi /O2 /Fd"Release\vc120.pdb" /D "WIN32" /D "NDEBUG" /D
         "_CONSOLE" /D "_LIB" /D "_USING_V110_SDK71_" /D "_UNICODE" /D
         "UNICODE" /Qipo /Zc:forScope /Gd /Oi /MT /Fa"Release\" /EHsc /nologo
         /Fo"Release\" /Qprof-dir "Release\" /Fp"Release\IMaCh.pch"
      */ 
      /* 64 bits */
      /*
        /GS /W3 /Gy
        /Zc:wchar_t /Zi /O2 /Fd"x64\Release\vc120.pdb" /D "WIN32" /D "NDEBUG"
        /D "_CONSOLE" /D "_LIB" /D "_UNICODE" /D "UNICODE" /Qipo /Zc:forScope
        /Oi /MD /Fa"x64\Release\" /EHsc /nologo /Fo"x64\Release\" /Qprof-dir
        "x64\Release\" /Fp"x64\Release\IMaCh.pch" */
      /* Optimization are useless and O3 is slower than O2 */
      /*
        /GS /W3 /Gy /Zc:wchar_t /Zi /O3 /Fd"x64\Release\vc120.pdb" /D "WIN32" 
        /D "NDEBUG" /D "_CONSOLE" /D "_LIB" /D "_UNICODE" /D "UNICODE" /Qipo 
        /Zc:forScope /Oi /MD /Fa"x64\Release\" /EHsc /nologo /Qparallel 
        /Fo"x64\Release\" /Qprof-dir "x64\Release\" /Fp"x64\Release\IMaCh.pch" 
      */
      /* Link is */ /* /OUT:"visual studio
         2013\Projects\IMaCh\Release\IMaCh.exe" /MANIFEST /NXCOMPAT
         /PDB:"visual studio
         2013\Projects\IMaCh\Release\IMaCh.pdb" /DYNAMICBASE
         "kernel32.lib" "user32.lib" "gdi32.lib" "winspool.lib"
         "comdlg32.lib" "advapi32.lib" "shell32.lib" "ole32.lib"
         "oleaut32.lib" "uuid.lib" "odbc32.lib" "odbccp32.lib"
         /MACHINE:X86 /OPT:REF /SAFESEH /INCREMENTAL:NO
         /SUBSYSTEM:CONSOLE",5.01" /MANIFESTUAC:"level='asInvoker'
         uiAccess='false'"
         /ManifestFile:"Release\IMaCh.exe.intermediate.manifest" /OPT:ICF
         /NOLOGO /TLBID:1
      */
   #if defined __INTEL_COMPILER
   #if defined(__GNUC__)
           struct utsname sysInfo;  /* For Intel on Linux and OS/X */
   #endif
   #elif defined(__GNUC__) 
   #ifndef  __APPLE__
   #include <gnu/libc-version.h>  /* Only on gnu */
   #endif
      struct utsname sysInfo;
      int cross = CROSS;
      if (cross){
              printf("Cross-");
              if(logged) fprintf(ficlog, "Cross-");
      }
   #endif
   
   #include <stdint.h>
   
      printf("Compiled with:");if(logged)fprintf(ficlog,"Compiled with:");
   #if defined(__clang__)
      printf(" Clang/LLVM");if(logged)fprintf(ficlog," Clang/LLVM");       /* Clang/LLVM. ---------------------------------------------- */
   #endif
   #if defined(__ICC) || defined(__INTEL_COMPILER)
      printf(" Intel ICC/ICPC");if(logged)fprintf(ficlog," Intel ICC/ICPC");/* Intel ICC/ICPC. ------------------------------------------ */
   #endif
   #if defined(__GNUC__) || defined(__GNUG__)
      printf(" GNU GCC/G++");if(logged)fprintf(ficlog," GNU GCC/G++");/* GNU GCC/G++. --------------------------------------------- */
   #endif
   #if defined(__HP_cc) || defined(__HP_aCC)
      printf(" Hewlett-Packard C/aC++");if(logged)fprintf(fcilog," Hewlett-Packard C/aC++"); /* Hewlett-Packard C/aC++. ---------------------------------- */
   #endif
   #if defined(__IBMC__) || defined(__IBMCPP__)
      printf(" IBM XL C/C++"); if(logged) fprintf(ficlog," IBM XL C/C++");/* IBM XL C/C++. -------------------------------------------- */
   #endif
   #if defined(_MSC_VER)
      printf(" Microsoft Visual Studio");if(logged)fprintf(ficlog," Microsoft Visual Studio");/* Microsoft Visual Studio. --------------------------------- */
   #endif
   #if defined(__PGI)
      printf(" Portland Group PGCC/PGCPP");if(logged) fprintf(ficlog," Portland Group PGCC/PGCPP");/* Portland Group PGCC/PGCPP. ------------------------------- */
   #endif
   #if defined(__SUNPRO_C) || defined(__SUNPRO_CC)
      printf(" Oracle Solaris Studio");if(logged)fprintf(ficlog," Oracle Solaris Studio\n");/* Oracle Solaris Studio. ----------------------------------- */
   #endif
      printf(" for "); if (logged) fprintf(ficlog, " for ");
      
   // http://stackoverflow.com/questions/4605842/how-to-identify-platform-compiler-from-preprocessor-macros
   #ifdef _WIN32 // note the underscore: without it, it's not msdn official!
       // Windows (x64 and x86)
      printf("Windows (x64 and x86) ");if(logged) fprintf(ficlog,"Windows (x64 and x86) ");
   #elif __unix__ // all unices, not all compilers
       // Unix
      printf("Unix ");if(logged) fprintf(ficlog,"Unix ");
   #elif __linux__
       // linux
      printf("linux ");if(logged) fprintf(ficlog,"linux ");
   #elif __APPLE__
       // Mac OS, not sure if this is covered by __posix__ and/or __unix__ though..
      printf("Mac OS ");if(logged) fprintf(ficlog,"Mac OS ");
   #endif
   
   /*  __MINGW32__   */
   /*  __CYGWIN__   */
   /* __MINGW64__  */
   // http://msdn.microsoft.com/en-us/library/b0084kay.aspx
   /* _MSC_VER  //the Visual C++ compiler is 17.00.51106.1, the _MSC_VER macro evaluates to 1700. Type cl /?  */
   /* _MSC_FULL_VER //the Visual C++ compiler is 15.00.20706.01, the _MSC_FULL_VER macro evaluates to 150020706 */
   /* _WIN64  // Defined for applications for Win64. */
   /* _M_X64 // Defined for compilations that target x64 processors. */
   /* _DEBUG // Defined when you compile with /LDd, /MDd, and /MTd. */
   
   #if UINTPTR_MAX == 0xffffffff
      printf(" 32-bit"); if(logged) fprintf(ficlog," 32-bit");/* 32-bit */
   #elif UINTPTR_MAX == 0xffffffffffffffff
      printf(" 64-bit"); if(logged) fprintf(ficlog," 64-bit");/* 64-bit */
   #else
      printf(" wtf-bit"); if(logged) fprintf(ficlog," wtf-bit");/* wtf */
   #endif
   
   #if defined(__GNUC__)
   # if defined(__GNUC_PATCHLEVEL__)
   #  define __GNUC_VERSION__ (__GNUC__ * 10000 \
                               + __GNUC_MINOR__ * 100 \
                               + __GNUC_PATCHLEVEL__)
   # else
   #  define __GNUC_VERSION__ (__GNUC__ * 10000 \
                               + __GNUC_MINOR__ * 100)
   # endif
      printf(" using GNU C version %d.\n", __GNUC_VERSION__);
      if(logged) fprintf(ficlog, " using GNU C version %d.\n", __GNUC_VERSION__);
   
      if (uname(&sysInfo) != -1) {
        printf("Running on: %s %s %s %s %s\n",sysInfo.sysname, sysInfo.nodename, sysInfo.release, sysInfo.version, sysInfo.machine);
            if(logged) fprintf(ficlog,"Running on: %s %s %s %s %s\n ",sysInfo.sysname, sysInfo.nodename, sysInfo.release, sysInfo.version, sysInfo.machine);
      }
      else
         perror("uname() error");
      //#ifndef __INTEL_COMPILER 
   #if !defined (__INTEL_COMPILER) && !defined(__APPLE__)
      printf("GNU libc version: %s\n", gnu_get_libc_version()); 
      if(logged) fprintf(ficlog,"GNU libc version: %s\n", gnu_get_libc_version());
   #endif
   #endif
   
      //   void main()
      //   {
   #if defined(_MSC_VER)
      if (IsWow64()){
              printf("\nThe program (probably compiled for 32bit) is running under WOW64 (64bit) emulation.\n");
              if (logged) fprintf(ficlog, "\nThe program (probably compiled for 32bit) is running under WOW64 (64bit) emulation.\n");
      }
      else{
              printf("\nThe program is not running under WOW64 (i.e probably on a 64bit Windows).\n");
              if (logged) fprintf(ficlog, "\nThe programm is not running under WOW64 (i.e probably on a 64bit Windows).\n");
      }
      //      printf("\nPress Enter to continue...");
      //      getchar();
      //   }
   
   #endif
      
   
    }
   
   int prevalence_limit(double *p, double **prlim, double ageminpar, double agemaxpar){
     /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     int i, j, k, i1 ;
     double ftolpl = 1.e-10;
     double age, agebase, agelim;
   
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);return 1;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);return 1;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       /* prlim=matrix(1,nlstate,1,nlstate);*/ /* back in main */
   
       agebase=ageminpar;
       agelim=agemaxpar;
   
       i1=pow(2,cptcoveff);
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
       /* for(cptcov=1,k=0;cptcov<=1;cptcov++){ */
         //for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           //printf("cptcov=%d cptcod=%d codtab=%d\n",cptcov, cptcod,codtab[cptcod][cptcov]);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
   
           fprintf(ficrespl,"#Age ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl,"V%d %d",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
           fprintf(ficrespl,"\n");
           
           for (age=agebase; age<=agelim; age++){
           /* for (age=agebase; age<=agebase; age++){ */
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           } /* Age */
           /* was end of cptcod */
       } /* cptcov */
           return 0;
   }
   
   int hPijx(double *p, int bage, int fage){
       /*------------- h Pij x at various ages ------------*/
   
     int stepsize;
     int agelim;
     int hstepm;
     int nhstepm;
     int h, i, i1, j, k;
   
     double agedeb;
     double ***p3mat;
   
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij); return 1;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij); return 1;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       i1= pow(2,cptcoveff);
      /* for(cptcov=1,k=0;cptcov<=i1;cptcov++){ */
      /*    /\*for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*\/ */
      /*   k=k+1;  */
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
         fprintf(ficrespij,"\n#****** ");
         for(j=1;j<=cptcoveff;j++) 
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         fprintf(ficrespij,"******\n");
         
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
           
           /*        nhstepm=nhstepm*YEARM; aff par mois*/
           
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           oldm=oldms;savm=savms;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
           for(i=1; i<=nlstate;i++)
             for(j=1; j<=nlstate+ndeath;j++)
               fprintf(ficrespij," %1d-%1d",i,j);
           fprintf(ficrespij,"\n");
           for (h=0; h<=nhstepm; h++){
             /*agedebphstep = agedeb + h*hstepm/YEARM*stepm;*/
             fprintf(ficrespij,"%d %3.f %3.f",k, agedeb, agedeb + h*hstepm/YEARM*stepm );
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);
             fprintf(ficrespij,"\n");
           }
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"\n");
         }
         /*}*/
       }
           return 0;
   }
   
   
   /***********************************************/
   /**************** 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=0,m,size=100, cptcod;
   
     int jj, ll, li, lj, lk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb=0.;
   
     double ageminpar=AGEOVERFLOW,agemin=AGEOVERFLOW, agemaxpar=-AGEOVERFLOW, agemax=-AGEOVERFLOW;
   
     double fret;
     double dum=0.; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
   
     char line[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int c,  h , cpt;
     int jl=0;
     int i1, j1, jk, stepsize=0;
     int count=0;
   
     int *tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm=0, nhstepm=0;
     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=0, fage=110., age, agelim=0., agebase=0.;
     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 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";
   
     /*char  *strt;*/
     char strtend[80];
   
   
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     rstart_time = time(NULL);  
     /*  (void) gettimeofday(&start_time,&tzp);*/
     start_time = *localtime(&rstart_time);
     curr_time=start_time;
     /*tml = *localtime(&start_time.tm_sec);*/
     /* strcpy(strstart,asctime(&tml)); */
     strcpy(strstart,asctime(&start_time));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tm_sec = tp.tm_sec +86400; */
   /*  tm = *localtime(&start_time.tm_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.tm_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;
   #ifdef WIN32
     _getcwd(pathcd, size);
   #else
     getcwd(pathcd, size);
   #endif
     syscompilerinfo(0);
     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';
       i=strlen(pathr);
       if(pathr[i-1]==' ') /* This may happen when dragging on oS/X! */
         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);
   #ifdef WIN32
     _chdir(path); /* Can be a relative path */
     if(_getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
   #else
     chdir(path); /* Can be a relative path */
     if (getcwd(pathcd, MAXLINE) > 0) /* So pathcd is the full path */
   #endif
     printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Directory already exists (or can't create it) %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 --------*/
   
     /* Main 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);
   
     syscompilerinfo(0);
   
     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.tm_sec-start_time.tm_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /* Main ---------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=1+age+%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar=numlinepar+3; /* In general */
     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=1+age+%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     if(model[strlen(model)-1]=='.') /* Suppressing leading dot in the model */
       model[strlen(model)-1]='\0';
     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=1+age+%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=1+age+%s.\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     /* if(model[0]=='#'|| model[0]== '\0'){ */
     if(model[0]=='#'){
       printf("Error in 'model' line: model should start with 'model=1+age+' and end with '.' \n \
    'model=1+age+.' or 'model=1+age+V1.' or 'model=1+age+age*age+V1+V1*age.' or \n \
    'model=1+age+V1+V2.' or 'model=1+age+V1+V2+V1*V2.' etc. \n");          \
       if(mle != -1){
         printf("Fix the model line and run imach with mle=-1 to get a correct template of the parameter file.\n");
         exit(1);
       }
     }
     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,age*age makes 3*/
     else
       ncovmodel=2; /* Constant and age */
     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 chose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You chose 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) { /* Main Wizard */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You chose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You chose 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 != jj)){
             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,jj);
           fprintf(ficlog,"%1d%1d",i,jj);
           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.;
         
       /* Scans npar lines */
       for(i=1; i <=npar; i++){
         count=fscanf(ficpar,"%1d%1d%1d",&i1,&j1,&jk);
         if(count != 3){
           printf("Error! Error in parameter file %s at line %d after line starting with %1d%1d%1d\n\
   This is probably because your covariance matrix doesn't \n  contain exactly %d lines corresponding to your model line '1+age+%s'.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",optionfile,numlinepar, i1,j1,jk, npar, model);
           fprintf(ficlog,"Error! Error in parameter file %s at line %d after line starting with %1d%1d%1d\n\
   This is probably because your covariance matrix doesn't \n  contain exactly %d lines corresponding to your model line '1+age+%s'.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",optionfile,numlinepar, i1,j1,jk, npar, model);
           exit(1);
         }else
         if(mle==1)
           printf("%1d%1d%1d",i1,j1,jk);
         fprintf(ficlog,"%1d%1d%1d",i1,j1,jk);
         fprintf(ficparo,"%1d%1d%1d",i1,j1,jk);
         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");
       }
       /* End of read covariance matrix npar lines */
       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 */
   
     /*  Main data
      */
     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 */
     ncodemaxwundef=ivector(1,NCOVMAX); /* Number of code per covariate; if - 1 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
                         */  
   
   /* Main decodemodel */
   
   
     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-nagesqr > 2 ) /* That is if covariate other than cst, age and age*age */
       tricode(Tvar,nbcode,imx, Ndum); /**< Fills nbcode[Tvar[j]][l]; */
     /* Nbcode gives the value of the lth modality of jth covariate, in
        V2+V1*age, there are 3 covariates Tvar[2]=1 (V1).*/
     /* 1 to ncodemax[j] is the maximum value of this jth covariate */
   
     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]);*/
     /* codtab gives the value 1 or 2 of the hth combination of k covariates (1 or 2).*/
     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
              * For k=4 covariates, h goes from 1 to 2**k
              * codtabm(h,k)=  1 & (h-1) >> (k-1) ;
              *     h\k   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[12][3]=1; */
             /*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);
   
   
       
     /* Initialisation of ----------- 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);*/
   
   
     /* Initialisation of --------- 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);
   #ifdef WIN32
     _chdir(optionfilefiname); /* Move to directory named optionfile */
   #else
     chdir(optionfilefiname); /* Move to directory named optionfile */
   #endif
             
     
     /* 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*/
     /* For mortality only */
     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");
   #else
       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");
   #else
       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]));
         fprintf(ficlog,"%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 / */
       if(ageminpar == AGEOVERFLOW ||agemaxpar == AGEOVERFLOW){
           printf("Warning! Error in gnuplot file with ageminpar %f or agemaxpar %f overflow\n\
   This is probably because your parameter file doesn't \n  contain the exact number of lines (or columns) corresponding to your model line.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpar);
           fprintf(ficlog,"Warning! Error in gnuplot file with ageminpar %f or agemaxpar %f overflow\n\
   This is probably because your parameter file doesn't \n  contain the exact number of lines (or columns) corresponding to your model line.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpar);
       }else
         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 mortality only */
     /* Standard maximisation */
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       /* Computes likelihood for initial parameters */
       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; /* again, 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, Real Maximisation */
         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=1+age+%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("%12.7f ",p[jk]);
               fprintf(ficlog,"%12.7f ",p[jk]);
               fprintf(ficres,"%12.7f ",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);
       }
       printf("Parameters and 95%% confidence intervals\n");
       fprintf(ficlog, "Parameters, T and confidence intervals\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);
             for(j=1; j <=ncovmodel; j++){
               printf("%12.7f T=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-2*sqrt(matcov[jk][jk]),p[jk]+2*sqrt(matcov[jk][jk]));
               fprintf(ficlog,"%12.7f T=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-2*sqrt(matcov[jk][jk]),p[jk]+2*sqrt(matcov[jk][jk]));
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
           }
         }
       }
   
       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);
   
       /* Other stuffs, more or less useful */    
       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(ficlog,"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 / */
       if(ageminpar == AGEOVERFLOW ||agemaxpar == -AGEOVERFLOW){
           printf("Warning! Error in gnuplot file with ageminpar %f or agemaxpar %f overflow\n\
   This is probably because your parameter file doesn't \n  contain the exact number of lines (or columns) corresponding to your model line.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpar);
           fprintf(ficlog,"Warning! Error in gnuplot file with ageminpar %f or agemaxpar %f overflow\n\
   This is probably because your parameter file doesn't \n  contain the exact number of lines (or columns) corresponding to your model line.\n\
   Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpar);
       }else
         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);
   
   
       /* Other results (useful)*/
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
       /*#include "prevlim.h"*/  /* Use ficrespl, ficlog */
       prlim=matrix(1,nlstate,1,nlstate);
       prevalence_limit(p, prlim,  ageminpar, agemaxpar);
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
       /*#include "hpijx.h"*/
       hPijx(p, bage, fage);
       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); */
         /*      } */
       }
    
       /* ------ Other prevalence ratios------------ */
   
       /* 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 */
             cptcod= 0; /* To be deleted */
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart); /* cptcod not initialized Intel */
             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(ncodemaxwundef,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);*/
     rend_time = time(NULL);  
     end_time = *localtime(&rend_time);
     /* tml = *localtime(&end_time.tm_sec); */
     strcpy(strtend,asctime(&end_time));
     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(rend_time -rstart_time,tmpout));
   
     printf("Total time was %.0lf Sec.\n", difftime(rend_time,rstart_time));
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(rend_time -rstart_time,tmpout));
     fprintf(ficlog,"Total time was %.0lf Sec.\n", difftime(rend_time,rstart_time));
     /*  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);
   #ifdef WIN32
      if (_chdir(pathcd) != 0)
              printf("Can't move to directory %s!\n",path);
      if(_getcwd(pathcd,MAXLINE) > 0)
   #else
      if(chdir(pathcd) != 0)
              printf("Can't move to directory %s!\n", path);
      if (getcwd(pathcd, MAXLINE) > 0)
   #endif 
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifdef _WIN32
     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(" Successful, 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 __APPLE__
         sprintf(pplotcmd, "open %s", optionfilehtm);
   #elif __linux
         sprintf(pplotcmd, "xdg-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.1.41.2.1  
changed lines
  Added in v.1.194


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