Diff for /imach/src/imach.c between versions 1.42 and 1.170

version 1.42, 2002/05/21 18:44:41 version 1.170, 2014/12/23 11:17:12
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.170  2014/12/23 11:17:12  brouard
      Summary: Cleaning some \%% back to %%
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    The escape was mandatory for a specific compiler (which one?), but too many warnings.
   first survey ("cross") where individuals from different ages are  
   interviewed on their health status or degree of disability (in the    Revision 1.169  2014/12/22 23:08:31  brouard
   case of a health survey which is our main interest) -2- at least a    Summary: 0.98p
   second wave of interviews ("longitudinal") which measure each change  
   (if any) in individual health status.  Health expectancies are    Outputs some informations on compiler used, OS etc. Testing on different platforms.
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.168  2014/12/22 15:17:42  brouard
   Maximum Likelihood of the parameters involved in the model.  The    Summary: update
   simplest model is the multinomial logistic model where pij is the  
   probability to be observed in state j at the second wave    Revision 1.167  2014/12/22 13:50:56  brouard
   conditional to be observed in state i at the first wave. Therefore    Summary: Testing uname and compiler version and if compiled 32 or 64
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where  
   'age' is age and 'sex' is a covariate. If you want to have a more    Testing on Linux 64
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.166  2014/12/22 11:40:47  brouard
   you to do it.  More covariates you add, slower the    *** empty log message ***
   convergence.  
     Revision 1.165  2014/12/16 11:20:36  brouard
   The advantage of this computer programme, compared to a simple    Summary: After compiling on Visual C
   multinomial logistic model, is clear when the delay between waves is not  
   identical for each individual. Also, if a individual missed an    * imach.c (Module): Merging 1.61 to 1.162
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.164  2014/12/16 10:52:11  brouard
     Summary: Merging with Visual C after suppressing some warnings for unused variables. Also fixing Saito's bug 0.98Xn
   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    * imach.c (Module): Merging 1.61 to 1.162
   split into an exact number (nh*stepm) of unobserved intermediate  
   states. This elementary transition (by month or quarter trimester,    Revision 1.163  2014/12/16 10:30:11  brouard
   semester or year) is model as a multinomial logistic.  The hPx    * imach.c (Module): Merging 1.61 to 1.162
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.162  2014/09/25 11:43:39  brouard
   hPijx.    Summary: temporary backup 0.99!
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.1  2014/09/16 11:06:58  brouard
   of the life expectancies. It also computes the prevalence limits.    Summary: With some code (wrong) for nlopt
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Author:
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.161  2014/09/15 20:41:41  brouard
   from the European Union.    Summary: Problem with macro SQR on Intel compiler
   It is copyrighted identically to a GNU software product, ie programme and  
   software can be distributed freely for non commercial use. Latest version    Revision 1.160  2014/09/02 09:24:05  brouard
   can be accessed at http://euroreves.ined.fr/imach .    *** empty log message ***
   **********************************************************************/  
      Revision 1.159  2014/09/01 10:34:10  brouard
 #include <math.h>    Summary: WIN32
 #include <stdio.h>    Author: Brouard
 #include <stdlib.h>  
 #include <unistd.h>    Revision 1.158  2014/08/27 17:11:51  brouard
     *** empty log message ***
 #define MAXLINE 256  
 #define GNUPLOTPROGRAM "gnuplot"    Revision 1.157  2014/08/27 16:26:55  brouard
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    Summary: Preparing windows Visual studio version
 #define FILENAMELENGTH 80    Author: Brouard
 /*#define DEBUG*/  
 #define windows    In order to compile on Visual studio, time.h is now correct and time_t
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    and tm struct should be used. difftime should be used but sometimes I
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    just make the differences in raw time format (time(&now).
     Trying to suppress #ifdef LINUX
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Add xdg-open for __linux in order to open default browser.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.156  2014/08/25 20:10:10  brouard
 #define NINTERVMAX 8    *** empty log message ***
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.155  2014/08/25 18:32:34  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    Summary: New compile, minor changes
 #define MAXN 20000    Author: Brouard
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.154  2014/06/20 17:32:08  brouard
 #define AGEBASE 40    Summary: Outputs now all graphs of convergence to period prevalence
   
     Revision 1.153  2014/06/20 16:45:46  brouard
 int erreur; /* Error number */    Summary: If 3 live state, convergence to period prevalence on same graph
 int nvar;    Author: Brouard
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.152  2014/06/18 17:54:09  brouard
 int nlstate=2; /* Number of live states */    Summary: open browser, use gnuplot on same dir than imach if not found in the path
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.151  2014/06/18 16:43:30  brouard
 int popbased=0;    *** empty log message ***
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.150  2014/06/18 16:42:35  brouard
 int maxwav; /* Maxim number of waves */    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
 int jmin, jmax; /* min, max spacing between 2 waves */    Author: brouard
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.149  2014/06/18 15:51:14  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Summary: Some fixes in parameter files errors
 double jmean; /* Mean space between 2 waves */    Author: Nicolas Brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Revision 1.148  2014/06/17 17:38:48  brouard
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    Summary: Nothing new
 FILE *ficgp,*ficresprob,*ficpop;    Author: Brouard
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Just a new packaging for OS/X version 0.98nS
  FILE  *ficresvij;  
   char fileresv[FILENAMELENGTH];    Revision 1.147  2014/06/16 10:33:11  brouard
  FILE  *ficresvpl;    *** empty log message ***
   char fileresvpl[FILENAMELENGTH];  
     Revision 1.146  2014/06/16 10:20:28  brouard
 #define NR_END 1    Summary: Merge
 #define FREE_ARG char*    Author: Brouard
 #define FTOL 1.0e-10  
     Merge, before building revised version.
 #define NRANSI  
 #define ITMAX 200    Revision 1.145  2014/06/10 21:23:15  brouard
     Summary: Debugging with valgrind
 #define TOL 2.0e-4    Author: Nicolas Brouard
   
 #define CGOLD 0.3819660    Lot of changes in order to output the results with some covariates
 #define ZEPS 1.0e-10    After the Edimburgh REVES conference 2014, it seems mandatory to
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    improve the code.
     No more memory valgrind error but a lot has to be done in order to
 #define GOLD 1.618034    continue the work of splitting the code into subroutines.
 #define GLIMIT 100.0    Also, decodemodel has been improved. Tricode is still not
 #define TINY 1.0e-20    optimal. nbcode should be improved. Documentation has been added in
     the source code.
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.143  2014/01/26 09:45:38  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define rint(a) floor(a+0.5)    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
   
 static double sqrarg;    Revision 1.142  2014/01/26 03:57:36  brouard
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int imx;  
 int stepm;    Revision 1.141  2014/01/26 02:42:01  brouard
 /* Stepm, step in month: minimum step interpolation*/    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   
 int estepm;    Revision 1.140  2011/09/02 10:37:54  brouard
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    Summary: times.h is ok with mingw32 now.
   
 int m,nb;    Revision 1.139  2010/06/14 07:50:17  brouard
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.138  2010/04/30 18:19:40  brouard
     *** empty log message ***
 double *weight;  
 int **s; /* Status */    Revision 1.137  2010/04/29 18:11:38  brouard
 double *agedc, **covar, idx;    (Module): Checking covariates for more complex models
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    than V1+V2. A lot of change to be done. Unstable.
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Revision 1.136  2010/04/26 20:30:53  brouard
 double ftolhess; /* Tolerance for computing hessian */    (Module): merging some libgsl code. Fixing computation
     of likelione (using inter/intrapolation if mle = 0) in order to
 /**************** split *************************/    get same likelihood as if mle=1.
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    Some cleaning of code and comments added.
 {  
    char *s;                             /* pointer */    Revision 1.135  2009/10/29 15:33:14  brouard
    int  l1, l2;                         /* length counters */    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   
    l1 = strlen( path );                 /* length of path */    Revision 1.134  2009/10/29 13:18:53  brouard
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 #ifdef windows  
    s = strrchr( path, '\\' );           /* find last / */    Revision 1.133  2009/07/06 10:21:25  brouard
 #else    just nforces
    s = strrchr( path, '/' );            /* find last / */  
 #endif    Revision 1.132  2009/07/06 08:22:05  brouard
    if ( s == NULL ) {                   /* no directory, so use current */    Many tings
 #if     defined(__bsd__)                /* get current working directory */  
       extern char       *getwd( );    Revision 1.131  2009/06/20 16:22:47  brouard
     Some dimensions resccaled
       if ( getwd( dirc ) == NULL ) {  
 #else    Revision 1.130  2009/05/26 06:44:34  brouard
       extern char       *getcwd( );    (Module): Max Covariate is now set to 20 instead of 8. A
     lot of cleaning with variables initialized to 0. Trying to make
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 #endif  
          return( GLOCK_ERROR_GETCWD );    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
       strcpy( name, path );             /* we've got it */  
    } else {                             /* strip direcotry from path */    Revision 1.128  2006/06/30 13:02:05  brouard
       s++;                              /* after this, the filename */    (Module): Clarifications on computing e.j
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.127  2006/04/28 18:11:50  brouard
       strcpy( name, s );                /* save file name */    (Module): Yes the sum of survivors was wrong since
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    imach-114 because nhstepm was no more computed in the age
       dirc[l1-l2] = 0;                  /* add zero */    loop. Now we define nhstepma in the age loop.
    }    (Module): In order to speed up (in case of numerous covariates) we
    l1 = strlen( dirc );                 /* length of directory */    compute health expectancies (without variances) in a first step
 #ifdef windows    and then all the health expectancies with variances or standard
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    deviation (needs data from the Hessian matrices) which slows the
 #else    computation.
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    In the future we should be able to stop the program is only health
 #endif    expectancies and graph are needed without standard deviations.
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Revision 1.126  2006/04/28 17:23:28  brouard
    strcpy(ext,s);                       /* save extension */    (Module): Yes the sum of survivors was wrong since
    l1= strlen( name);    imach-114 because nhstepm was no more computed in the age
    l2= strlen( s)+1;    loop. Now we define nhstepma in the age loop.
    strncpy( finame, name, l1-l2);    Version 0.98h
    finame[l1-l2]= 0;  
    return( 0 );                         /* we're done */    Revision 1.125  2006/04/04 15:20:31  lievre
 }    Errors in calculation of health expectancies. Age was not initialized.
     Forecasting file added.
   
 /******************************************/    Revision 1.124  2006/03/22 17:13:53  lievre
     Parameters are printed with %lf instead of %f (more numbers after the comma).
 void replace(char *s, char*t)    The log-likelihood is printed in the log file
 {  
   int i;    Revision 1.123  2006/03/20 10:52:43  brouard
   int lg=20;    * imach.c (Module): <title> changed, corresponds to .htm file
   i=0;    name. <head> headers where missing.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    * imach.c (Module): Weights can have a decimal point as for
     (s[i] = t[i]);    English (a comma might work with a correct LC_NUMERIC environment,
     if (t[i]== '\\') s[i]='/';    otherwise the weight is truncated).
   }    Modification of warning when the covariates values are not 0 or
 }    1.
     Version 0.98g
 int nbocc(char *s, char occ)  
 {    Revision 1.122  2006/03/20 09:45:41  brouard
   int i,j=0;    (Module): Weights can have a decimal point as for
   int lg=20;    English (a comma might work with a correct LC_NUMERIC environment,
   i=0;    otherwise the weight is truncated).
   lg=strlen(s);    Modification of warning when the covariates values are not 0 or
   for(i=0; i<= lg; i++) {    1.
   if  (s[i] == occ ) j++;    Version 0.98g
   }  
   return j;    Revision 1.121  2006/03/16 17:45:01  lievre
 }    * imach.c (Module): Comments concerning covariates added
   
 void cutv(char *u,char *v, char*t, char occ)    * imach.c (Module): refinements in the computation of lli if
 {    status=-2 in order to have more reliable computation if stepm is
   int i,lg,j,p=0;    not 1 month. Version 0.98f
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {    Revision 1.120  2006/03/16 15:10:38  lievre
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    (Module): refinements in the computation of lli if
   }    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
   lg=strlen(t);  
   for(j=0; j<p; j++) {    Revision 1.119  2006/03/15 17:42:26  brouard
     (u[j] = t[j]);    (Module): Bug if status = -2, the loglikelihood was
   }    computed as likelihood omitting the logarithm. Version O.98e
      u[p]='\0';  
     Revision 1.118  2006/03/14 18:20:07  brouard
    for(j=0; j<= lg; j++) {    (Module): varevsij Comments added explaining the second
     if (j>=(p+1))(v[j-p-1] = t[j]);    table of variances if popbased=1 .
   }    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 }    (Module): Function pstamp added
     (Module): Version 0.98d
 /********************** nrerror ********************/  
     Revision 1.117  2006/03/14 17:16:22  brouard
 void nrerror(char error_text[])    (Module): varevsij Comments added explaining the second
 {    table of variances if popbased=1 .
   fprintf(stderr,"ERREUR ...\n");    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   fprintf(stderr,"%s\n",error_text);    (Module): Function pstamp added
   exit(1);    (Module): Version 0.98d
 }  
 /*********************** vector *******************/    Revision 1.116  2006/03/06 10:29:27  brouard
 double *vector(int nl, int nh)    (Module): Variance-covariance wrong links and
 {    varian-covariance of ej. is needed (Saito).
   double *v;  
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    Revision 1.115  2006/02/27 12:17:45  brouard
   if (!v) nrerror("allocation failure in vector");    (Module): One freematrix added in mlikeli! 0.98c
   return v-nl+NR_END;  
 }    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 /************************ free vector ******************/    filename with strsep.
 void free_vector(double*v, int nl, int nh)  
 {    Revision 1.113  2006/02/24 14:20:24  brouard
   free((FREE_ARG)(v+nl-NR_END));    (Module): Memory leaks checks with valgrind and:
 }    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Revision 1.112  2006/01/30 09:55:26  brouard
 {    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Revision 1.111  2006/01/25 20:38:18  brouard
   if (!v) nrerror("allocation failure in ivector");    (Module): Lots of cleaning and bugs added (Gompertz)
   return v-nl+NR_END;    (Module): Comments can be added in data file. Missing date values
 }    can be a simple dot '.'.
   
 /******************free ivector **************************/    Revision 1.110  2006/01/25 00:51:50  brouard
 void free_ivector(int *v, long nl, long nh)    (Module): Lots of cleaning and bugs added (Gompertz)
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.109  2006/01/24 19:37:15  brouard
 }    (Module): Comments (lines starting with a #) are allowed in data.
   
 /******************* imatrix *******************************/    Revision 1.108  2006/01/19 18:05:42  lievre
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Gnuplot problem appeared...
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    To be fixed
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Revision 1.107  2006/01/19 16:20:37  brouard
   int **m;    Test existence of gnuplot in imach path
    
   /* allocate pointers to rows */    Revision 1.106  2006/01/19 13:24:36  brouard
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    Some cleaning and links added in html output
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.105  2006/01/05 20:23:19  lievre
   m -= nrl;    *** empty log message ***
    
      Revision 1.104  2005/09/30 16:11:43  lievre
   /* allocate rows and set pointers to them */    (Module): sump fixed, loop imx fixed, and simplifications.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    (Module): If the status is missing at the last wave but we know
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    that the person is alive, then we can code his/her status as -2
   m[nrl] += NR_END;    (instead of missing=-1 in earlier versions) and his/her
   m[nrl] -= ncl;    contributions to the likelihood is 1 - Prob of dying from last
      health status (= 1-p13= p11+p12 in the easiest case of somebody in
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    the healthy state at last known wave). Version is 0.98
    
   /* return pointer to array of pointers to rows */    Revision 1.103  2005/09/30 15:54:49  lievre
   return m;    (Module): sump fixed, loop imx fixed, and simplifications.
 }  
     Revision 1.102  2004/09/15 17:31:30  brouard
 /****************** free_imatrix *************************/    Add the possibility to read data file including tab characters.
 void free_imatrix(m,nrl,nrh,ncl,nch)  
       int **m;    Revision 1.101  2004/09/15 10:38:38  brouard
       long nch,ncl,nrh,nrl;    Fix on curr_time
      /* free an int matrix allocated by imatrix() */  
 {    Revision 1.100  2004/07/12 18:29:06  brouard
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    Add version for Mac OS X. Just define UNIX in Makefile
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Revision 1.99  2004/06/05 08:57:40  brouard
     *** empty log message ***
 /******************* matrix *******************************/  
 double **matrix(long nrl, long nrh, long ncl, long nch)    Revision 1.98  2004/05/16 15:05:56  brouard
 {    New version 0.97 . First attempt to estimate force of mortality
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    directly from the data i.e. without the need of knowing the health
   double **m;    state at each age, but using a Gompertz model: log u =a + b*age .
     This is the basic analysis of mortality and should be done before any
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    other analysis, in order to test if the mortality estimated from the
   if (!m) nrerror("allocation failure 1 in matrix()");    cross-longitudinal survey is different from the mortality estimated
   m += NR_END;    from other sources like vital statistic data.
   m -= nrl;  
     The same imach parameter file can be used but the option for mle should be -3.
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Agnès, who wrote this part of the code, tried to keep most of the
   m[nrl] += NR_END;    former routines in order to include the new code within the former code.
   m[nrl] -= ncl;  
     The output is very simple: only an estimate of the intercept and of
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    the slope with 95% confident intervals.
   return m;  
 }    Current limitations:
     A) Even if you enter covariates, i.e. with the
 /*************************free matrix ************************/    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    B) There is no computation of Life Expectancy nor Life Table.
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.97  2004/02/20 13:25:42  lievre
   free((FREE_ARG)(m+nrl-NR_END));    Version 0.96d. Population forecasting command line is (temporarily)
 }    suppressed.
   
 /******************* ma3x *******************************/    Revision 1.96  2003/07/15 15:38:55  brouard
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 {    rewritten within the same printf. Workaround: many printfs.
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  
   double ***m;    Revision 1.95  2003/07/08 07:54:34  brouard
     * imach.c (Repository):
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    (Repository): Using imachwizard code to output a more meaningful covariance
   if (!m) nrerror("allocation failure 1 in matrix()");    matrix (cov(a12,c31) instead of numbers.
   m += NR_END;  
   m -= nrl;    Revision 1.94  2003/06/27 13:00:02  brouard
     Just cleaning
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Revision 1.93  2003/06/25 16:33:55  brouard
   m[nrl] += NR_END;    (Module): On windows (cygwin) function asctime_r doesn't
   m[nrl] -= ncl;    exist so I changed back to asctime which exists.
     (Module): Version 0.96b
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
     Revision 1.92  2003/06/25 16:30:45  brouard
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    (Module): On windows (cygwin) function asctime_r doesn't
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    exist so I changed back to asctime which exists.
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;    Revision 1.91  2003/06/25 15:30:29  brouard
   for (j=ncl+1; j<=nch; j++)    * imach.c (Repository): Duplicated warning errors corrected.
     m[nrl][j]=m[nrl][j-1]+nlay;    (Repository): Elapsed time after each iteration is now output. It
      helps to forecast when convergence will be reached. Elapsed time
   for (i=nrl+1; i<=nrh; i++) {    is stamped in powell.  We created a new html file for the graphs
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    concerning matrix of covariance. It has extension -cov.htm.
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;    Revision 1.90  2003/06/24 12:34:15  brouard
   }    (Module): Some bugs corrected for windows. Also, when
   return m;    mle=-1 a template is output in file "or"mypar.txt with the design
 }    of the covariance matrix to be input.
   
 /*************************free ma3x ************************/    Revision 1.89  2003/06/24 12:30:52  brouard
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    of the covariance matrix to be input.
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));    Revision 1.88  2003/06/23 17:54:56  brouard
 }    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
   
 /***************** f1dim *************************/    Revision 1.87  2003/06/18 12:26:01  brouard
 extern int ncom;    Version 0.96
 extern double *pcom,*xicom;  
 extern double (*nrfunc)(double []);    Revision 1.86  2003/06/17 20:04:08  brouard
      (Module): Change position of html and gnuplot routines and added
 double f1dim(double x)    routine fileappend.
 {  
   int j;    Revision 1.85  2003/06/17 13:12:43  brouard
   double f;    * imach.c (Repository): Check when date of death was earlier that
   double *xt;    current date of interview. It may happen when the death was just
      prior to the death. In this case, dh was negative and likelihood
   xt=vector(1,ncom);    was wrong (infinity). We still send an "Error" but patch by
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    assuming that the date of death was just one stepm after the
   f=(*nrfunc)(xt);    interview.
   free_vector(xt,1,ncom);    (Repository): Because some people have very long ID (first column)
   return f;    we changed int to long in num[] and we added a new lvector for
 }    memory allocation. But we also truncated to 8 characters (left
     truncation)
 /*****************brent *************************/    (Repository): No more line truncation errors.
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {    Revision 1.84  2003/06/13 21:44:43  brouard
   int iter;    * imach.c (Repository): Replace "freqsummary" at a correct
   double a,b,d,etemp;    place. It differs from routine "prevalence" which may be called
   double fu,fv,fw,fx;    many times. Probs is memory consuming and must be used with
   double ftemp;    parcimony.
   double p,q,r,tol1,tol2,u,v,w,x,xm;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   double e=0.0;  
      Revision 1.83  2003/06/10 13:39:11  lievre
   a=(ax < cx ? ax : cx);    *** empty log message ***
   b=(ax > cx ? ax : cx);  
   x=w=v=bx;    Revision 1.82  2003/06/05 15:57:20  brouard
   fw=fv=fx=(*f)(x);    Add log in  imach.c and  fullversion number is now printed.
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);  */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  /*
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/     Interpolated Markov Chain
     printf(".");fflush(stdout);  
 #ifdef DEBUG    Short summary of the programme:
     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);    
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    This program computes Healthy Life Expectancies from
 #endif    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    first survey ("cross") where individuals from different ages are
       *xmin=x;    interviewed on their health status or degree of disability (in the
       return fx;    case of a health survey which is our main interest) -2- at least a
     }    second wave of interviews ("longitudinal") which measure each change
     ftemp=fu;    (if any) in individual health status.  Health expectancies are
     if (fabs(e) > tol1) {    computed from the time spent in each health state according to a
       r=(x-w)*(fx-fv);    model. More health states you consider, more time is necessary to reach the
       q=(x-v)*(fx-fw);    Maximum Likelihood of the parameters involved in the model.  The
       p=(x-v)*q-(x-w)*r;    simplest model is the multinomial logistic model where pij is the
       q=2.0*(q-r);    probability to be observed in state j at the second wave
       if (q > 0.0) p = -p;    conditional to be observed in state i at the first wave. Therefore
       q=fabs(q);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
       etemp=e;    'age' is age and 'sex' is a covariate. If you want to have a more
       e=d;    complex model than "constant and age", you should modify the program
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    where the markup *Covariates have to be included here again* invites
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    you to do it.  More covariates you add, slower the
       else {    convergence.
         d=p/q;  
         u=x+d;    The advantage of this computer programme, compared to a simple
         if (u-a < tol2 || b-u < tol2)    multinomial logistic model, is clear when the delay between waves is not
           d=SIGN(tol1,xm-x);    identical for each individual. Also, if a individual missed an
       }    intermediate interview, the information is lost, but taken into
     } else {    account using an interpolation or extrapolation.  
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  
     }    hPijx is the probability to be observed in state i at age x+h
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    conditional to the observed state i at age x. The delay 'h' can be
     fu=(*f)(u);    split into an exact number (nh*stepm) of unobserved intermediate
     if (fu <= fx) {    states. This elementary transition (by month, quarter,
       if (u >= x) a=x; else b=x;    semester or year) is modelled as a multinomial logistic.  The hPx
       SHFT(v,w,x,u)    matrix is simply the matrix product of nh*stepm elementary matrices
         SHFT(fv,fw,fx,fu)    and the contribution of each individual to the likelihood is simply
         } else {    hPijx.
           if (u < x) a=u; else b=u;  
           if (fu <= fw || w == x) {    Also this programme outputs the covariance matrix of the parameters but also
             v=w;    of the life expectancies. It also computes the period (stable) prevalence. 
             w=u;    
             fv=fw;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
             fw=fu;             Institut national d'études démographiques, Paris.
           } else if (fu <= fv || v == x || v == w) {    This software have been partly granted by Euro-REVES, a concerted action
             v=u;    from the European Union.
             fv=fu;    It is copyrighted identically to a GNU software product, ie programme and
           }    software can be distributed freely for non commercial use. Latest version
         }    can be accessed at http://euroreves.ined.fr/imach .
   }  
   nrerror("Too many iterations in brent");    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   *xmin=x;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   return fx;    
 }    **********************************************************************/
   /*
 /****************** mnbrak ***********************/    main
     read parameterfile
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,    read datafile
             double (*func)(double))    concatwav
 {    freqsummary
   double ulim,u,r,q, dum;    if (mle >= 1)
   double fu;      mlikeli
      print results files
   *fa=(*func)(*ax);    if mle==1 
   *fb=(*func)(*bx);       computes hessian
   if (*fb > *fa) {    read end of parameter file: agemin, agemax, bage, fage, estepm
     SHFT(dum,*ax,*bx,dum)        begin-prev-date,...
       SHFT(dum,*fb,*fa,dum)    open gnuplot file
       }    open html file
   *cx=(*bx)+GOLD*(*bx-*ax);    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
   *fc=(*func)(*cx);     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
   while (*fb > *fc) {                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
     r=(*bx-*ax)*(*fb-*fc);      freexexit2 possible for memory heap.
     q=(*bx-*cx)*(*fb-*fa);  
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    h Pij x                         | pij_nom  ficrestpij
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
     ulim=(*bx)+GLIMIT*(*cx-*bx);         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
     if ((*bx-u)*(u-*cx) > 0.0) {         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
       fu=(*func)(u);         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
       if (fu < *fc) {    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
           SHFT(*fb,*fc,fu,(*func)(u))     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {    forecasting if prevfcast==1 prevforecast call prevalence()
       u=ulim;    health expectancies
       fu=(*func)(u);    Variance-covariance of DFLE
     } else {    prevalence()
       u=(*cx)+GOLD*(*cx-*bx);     movingaverage()
       fu=(*func)(u);    varevsij() 
     }    if popbased==1 varevsij(,popbased)
     SHFT(*ax,*bx,*cx,u)    total life expectancies
       SHFT(*fa,*fb,*fc,fu)    Variance of period (stable) prevalence
       }   end
 }  */
   
 /*************** linmin ************************/  #define POWELL /* Instead of NLOPT */
   
 int ncom;  #include <math.h>
 double *pcom,*xicom;  #include <stdio.h>
 double (*nrfunc)(double []);  #include <stdlib.h>
    #include <string.h>
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  #ifdef _WIN32
   double brent(double ax, double bx, double cx,  #include <io.h>
                double (*f)(double), double tol, double *xmin);  #else
   double f1dim(double x);  #include <unistd.h>
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #endif
               double *fc, double (*func)(double));  
   int j;  #include <limits.h>
   double xx,xmin,bx,ax;  #include <sys/types.h>
   double fx,fb,fa;  #include <sys/utsname.h>
    #include <sys/stat.h>
   ncom=n;  #include <errno.h>
   pcom=vector(1,n);  /* extern int errno; */
   xicom=vector(1,n);  
   nrfunc=func;  /* #ifdef LINUX */
   for (j=1;j<=n;j++) {  /* #include <time.h> */
     pcom[j]=p[j];  /* #include "timeval.h" */
     xicom[j]=xi[j];  /* #else */
   }  /* #include <sys/time.h> */
   ax=0.0;  /* #endif */
   xx=1.0;  
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  #include <time.h>
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  #ifdef GSL
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  #include <gsl/gsl_errno.h>
 #endif  #include <gsl/gsl_multimin.h>
   for (j=1;j<=n;j++) {  #endif
     xi[j] *= xmin;  
     p[j] += xi[j];  
   }  #ifdef NLOPT
   free_vector(xicom,1,n);  #include <nlopt.h>
   free_vector(pcom,1,n);  typedef struct {
 }    double (* function)(double [] );
   } myfunc_data ;
 /*************** powell ************************/  #endif
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  
             double (*func)(double []))  /* #include <libintl.h> */
 {  /* #define _(String) gettext (String) */
   void linmin(double p[], double xi[], int n, double *fret,  
               double (*func)(double []));  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   int i,ibig,j;  
   double del,t,*pt,*ptt,*xit;  #define GNUPLOTPROGRAM "gnuplot"
   double fp,fptt;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   double *xits;  #define FILENAMELENGTH 132
   pt=vector(1,n);  
   ptt=vector(1,n);  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   xit=vector(1,n);  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   xits=vector(1,n);  
   *fret=(*func)(p);  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
   for (j=1;j<=n;j++) pt[j]=p[j];  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
   for (*iter=1;;++(*iter)) {  
     fp=(*fret);  #define NINTERVMAX 8
     ibig=0;  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
     del=0.0;  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
     for (i=1;i<=n;i++)  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
       printf(" %d %.12f",i, p[i]);  #define MAXN 20000
     printf("\n");  #define YEARM 12. /**< Number of months per year */
     for (i=1;i<=n;i++) {  #define AGESUP 130
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  #define AGEBASE 40
       fptt=(*fret);  #define AGEGOMP 10 /**< Minimal age for Gompertz adjustment */
 #ifdef DEBUG  #ifdef _WIN32
       printf("fret=%lf \n",*fret);  #define DIRSEPARATOR '\\'
 #endif  #define CHARSEPARATOR "\\"
       printf("%d",i);fflush(stdout);  #define ODIRSEPARATOR '/'
       linmin(p,xit,n,fret,func);  #else
       if (fabs(fptt-(*fret)) > del) {  #define DIRSEPARATOR '/'
         del=fabs(fptt-(*fret));  #define CHARSEPARATOR "/"
         ibig=i;  #define ODIRSEPARATOR '\\'
       }  #endif
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  /* $Id$ */
       for (j=1;j<=n;j++) {  /* $State$ */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  
         printf(" x(%d)=%.12e",j,xit[j]);  char version[]="Imach version 0.98p, December 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015";
       }  char fullversion[]="$Revision$ $Date$"; 
       for(j=1;j<=n;j++)  char strstart[80];
         printf(" p=%.12e",p[j]);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       printf("\n");  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 #endif  int nvar=0, nforce=0; /* Number of variables, number of forces */
     }  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
 #ifdef DEBUG  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
       int k[2],l;  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
       k[0]=1;  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
       k[1]=-1;  int cptcovprodnoage=0; /**< Number of covariate products without age */   
       printf("Max: %.12e",(*func)(p));  int cptcoveff=0; /* Total number of covariates to vary for printing results */
       for (j=1;j<=n;j++)  int cptcov=0; /* Working variable */
         printf(" %.12e",p[j]);  int npar=NPARMAX;
       printf("\n");  int nlstate=2; /* Number of live states */
       for(l=0;l<=1;l++) {  int ndeath=1; /* Number of dead states */
         for (j=1;j<=n;j++) {  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  int popbased=0;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  
         }  int *wav; /* Number of waves for this individuual 0 is possible */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  int maxwav=0; /* Maxim number of waves */
       }  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
 #endif  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
   int gipmx=0, gsw=0; /* Global variables on the number of contributions 
                      to the likelihood and the sum of weights (done by funcone)*/
       free_vector(xit,1,n);  int mle=1, weightopt=0;
       free_vector(xits,1,n);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       free_vector(ptt,1,n);  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       free_vector(pt,1,n);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       return;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
     }  int countcallfunc=0;  /* Count the number of calls to func */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  double jmean=1; /* Mean space between 2 waves */
     for (j=1;j<=n;j++) {  double **matprod2(); /* test */
       ptt[j]=2.0*p[j]-pt[j];  double **oldm, **newm, **savm; /* Working pointers to matrices */
       xit[j]=p[j]-pt[j];  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       pt[j]=p[j];  /*FILE *fic ; */ /* Used in readdata only */
     }  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     fptt=(*func)(ptt);  FILE *ficlog, *ficrespow;
     if (fptt < fp) {  int globpr=0; /* Global variable for printing or not */
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  double fretone; /* Only one call to likelihood */
       if (t < 0.0) {  long ipmx=0; /* Number of contributions */
         linmin(p,xit,n,fret,func);  double sw; /* Sum of weights */
         for (j=1;j<=n;j++) {  char filerespow[FILENAMELENGTH];
           xi[j][ibig]=xi[j][n];  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
           xi[j][n]=xit[j];  FILE *ficresilk;
         }  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 #ifdef DEBUG  FILE *ficresprobmorprev;
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  FILE *fichtm, *fichtmcov; /* Html File */
         for(j=1;j<=n;j++)  FILE *ficreseij;
           printf(" %.12e",xit[j]);  char filerese[FILENAMELENGTH];
         printf("\n");  FILE *ficresstdeij;
 #endif  char fileresstde[FILENAMELENGTH];
       }  FILE *ficrescveij;
     }  char filerescve[FILENAMELENGTH];
   }  FILE  *ficresvij;
 }  char fileresv[FILENAMELENGTH];
   FILE  *ficresvpl;
 /**** Prevalence limit ****************/  char fileresvpl[FILENAMELENGTH];
   char title[MAXLINE];
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
 {  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
      matrix by transitions matrix until convergence is reached */  char command[FILENAMELENGTH];
   int  outcmd=0;
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
   double **matprod2();  
   double **out, cov[NCOVMAX], **pmij();  char filelog[FILENAMELENGTH]; /* Log file */
   double **newm;  char filerest[FILENAMELENGTH];
   double agefin, delaymax=50 ; /* Max number of years to converge */  char fileregp[FILENAMELENGTH];
   char popfile[FILENAMELENGTH];
   for (ii=1;ii<=nlstate+ndeath;ii++)  
     for (j=1;j<=nlstate+ndeath;j++){  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  /* struct timeval start_time, end_time, curr_time, last_time, forecast_time; */
   /* struct timezone tzp; */
    cov[1]=1.;  /* extern int gettimeofday(); */
    struct tm tml, *gmtime(), *localtime();
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  extern time_t time();
     newm=savm;  
     /* Covariates have to be included here again */  struct tm start_time, end_time, curr_time, last_time, forecast_time;
      cov[2]=agefin;  time_t  rstart_time, rend_time, rcurr_time, rlast_time, rforecast_time; /* raw time */
    struct tm tm;
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  char strcurr[80], strfor[80];
         /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/  
       }  char *endptr;
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  long lval;
       for (k=1; k<=cptcovprod;k++)  double dval;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  
   #define NR_END 1
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  #define FREE_ARG char*
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  #define FTOL 1.0e-10
       /*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);  #define NRANSI 
   #define ITMAX 200 
     savm=oldm;  
     oldm=newm;  #define TOL 2.0e-4 
     maxmax=0.;  
     for(j=1;j<=nlstate;j++){  #define CGOLD 0.3819660 
       min=1.;  #define ZEPS 1.0e-10 
       max=0.;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       for(i=1; i<=nlstate; i++) {  
         sumnew=0;  #define GOLD 1.618034 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  #define GLIMIT 100.0 
         prlim[i][j]= newm[i][j]/(1-sumnew);  #define TINY 1.0e-20 
         max=FMAX(max,prlim[i][j]);  
         min=FMIN(min,prlim[i][j]);  static double maxarg1,maxarg2;
       }  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       maxmin=max-min;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
       maxmax=FMAX(maxmax,maxmin);    
     }  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
     if(maxmax < ftolpl){  #define rint(a) floor(a+0.5)
       return prlim;  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/myutils_8h-source.html */
     }  /* #define mytinydouble 1.0e-16 */
   }  /* #define DEQUAL(a,b) (fabs((a)-(b))<mytinydouble) */
 }  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/mynrutils_8h-source.html */
   /* static double dsqrarg; */
 /*************** transition probabilities ***************/  /* #define DSQR(a) (DEQUAL((dsqrarg=(a)),0.0) ? 0.0 : dsqrarg*dsqrarg) */
   static double sqrarg;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   double s1, s2;  int agegomp= AGEGOMP;
   /*double t34;*/  
   int i,j,j1, nc, ii, jj;  int imx; 
   int stepm=1;
     for(i=1; i<= nlstate; i++){  /* Stepm, step in month: minimum step interpolation*/
     for(j=1; j<i;j++){  
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  int estepm;
         /*s2 += param[i][j][nc]*cov[nc];*/  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  int m,nb;
       }  long *num;
       ps[i][j]=s2;  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     }  double **pmmij, ***probs;
     for(j=i+1; j<=nlstate+ndeath;j++){  double *ageexmed,*agecens;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  double dateintmean=0;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  double *weight;
       }  int **s; /* Status */
       ps[i][j]=s2;  double *agedc;
     }  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
   }                    * covar=matrix(0,NCOVMAX,1,n); 
     /*ps[3][2]=1;*/                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
   double  idx; 
   for(i=1; i<= nlstate; i++){  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
      s1=0;  int *Ndum; /** Freq of modality (tricode */
     for(j=1; j<i; j++)  int **codtab; /**< codtab=imatrix(1,100,1,10); */
       s1+=exp(ps[i][j]);  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
     for(j=i+1; j<=nlstate+ndeath; j++)  double *lsurv, *lpop, *tpop;
       s1+=exp(ps[i][j]);  
     ps[i][i]=1./(s1+1.);  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
     for(j=1; j<i; j++)  double ftolhess; /**< Tolerance for computing hessian */
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     for(j=i+1; j<=nlstate+ndeath; j++)  /**************** split *************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  {
   } /* end i */    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
        the name of the file (name), its extension only (ext) and its first part of the name (finame)
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    */ 
     for(jj=1; jj<= nlstate+ndeath; jj++){    char  *ss;                            /* pointer */
       ps[ii][jj]=0;    int   l1, l2;                         /* length counters */
       ps[ii][ii]=1;  
     }    l1 = strlen(path );                   /* length of path */
   }    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     if ( ss == NULL ) {                   /* no directory, so determine current directory */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      strcpy( name, path );               /* we got the fullname name because no directory */
     for(jj=1; jj<= nlstate+ndeath; jj++){      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
      printf("%lf ",ps[ii][jj]);        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
    }      /* get current working directory */
     printf("\n ");      /*    extern  char* getcwd ( char *buf , int len);*/
     }      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     printf("\n ");printf("%lf ",cov[2]);*/        return( GLOCK_ERROR_GETCWD );
 /*      }
   for(i=1; i<= npar; i++) printf("%f ",x[i]);      /* got dirc from getcwd*/
   goto end;*/      printf(" DIRC = %s \n",dirc);
     return ps;    } else {                              /* strip direcotry from path */
 }      ss++;                               /* after this, the filename */
       l2 = strlen( ss );                  /* length of filename */
 /**************** Product of 2 matrices ******************/      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       strcpy( name, ss );         /* save file name */
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 {      dirc[l1-l2] = 0;                    /* add zero */
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times      printf(" DIRC2 = %s \n",dirc);
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    }
   /* in, b, out are matrice of pointers which should have been initialized    /* We add a separator at the end of dirc if not exists */
      before: only the contents of out is modified. The function returns    l1 = strlen( dirc );                  /* length of directory */
      a pointer to pointers identical to out */    if( dirc[l1-1] != DIRSEPARATOR ){
   long i, j, k;      dirc[l1] =  DIRSEPARATOR;
   for(i=nrl; i<= nrh; i++)      dirc[l1+1] = 0; 
     for(k=ncolol; k<=ncoloh; k++)      printf(" DIRC3 = %s \n",dirc);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    }
         out[i][k] +=in[i][j]*b[j][k];    ss = strrchr( name, '.' );            /* find last / */
     if (ss >0){
   return out;      ss++;
 }      strcpy(ext,ss);                     /* save extension */
       l1= strlen( name);
       l2= strlen(ss)+1;
 /************* Higher Matrix Product ***************/      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    }
 {  
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    return( 0 );                          /* we're done */
      duration (i.e. until  }
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  
      (typically every 2 years instead of every month which is too big).  /******************************************/
      Model is determined by parameters x and covariates have to be  
      included manually here.  void replace_back_to_slash(char *s, char*t)
   {
      */    int i;
     int lg=0;
   int i, j, d, h, k;    i=0;
   double **out, cov[NCOVMAX];    lg=strlen(t);
   double **newm;    for(i=0; i<= lg; i++) {
       (s[i] = t[i]);
   /* Hstepm could be zero and should return the unit matrix */      if (t[i]== '\\') s[i]='/';
   for (i=1;i<=nlstate+ndeath;i++)    }
     for (j=1;j<=nlstate+ndeath;j++){  }
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);  char *trimbb(char *out, char *in)
     }  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    char *s;
   for(h=1; h <=nhstepm; h++){    s=out;
     for(d=1; d <=hstepm; d++){    while (*in != '\0'){
       newm=savm;      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
       /* Covariates have to be included here again */        in++;
       cov[1]=1.;      }
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      *out++ = *in++;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    }
       for (k=1; k<=cptcovage;k++)    *out='\0';
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    return s;
       for (k=1; k<=cptcovprod;k++)  }
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  
   char *cutl(char *blocc, char *alocc, char *in, char occ)
   {
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,       gives blocc="abcdef2ghi" and alocc="j".
                    pmij(pmmij,cov,ncovmodel,x,nlstate));       If occ is not found blocc is null and alocc is equal to in. Returns blocc
       savm=oldm;    */
       oldm=newm;    char *s, *t;
     }    t=in;s=in;
     for(i=1; i<=nlstate+ndeath; i++)    while ((*in != occ) && (*in != '\0')){
       for(j=1;j<=nlstate+ndeath;j++) {      *alocc++ = *in++;
         po[i][j][h]=newm[i][j];    }
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    if( *in == occ){
          */      *(alocc)='\0';
       }      s=++in;
   } /* end h */    }
   return po;   
 }    if (s == t) {/* occ not found */
       *(alocc-(in-s))='\0';
       in=s;
 /*************** log-likelihood *************/    }
 double func( double *x)    while ( *in != '\0'){
 {      *blocc++ = *in++;
   int i, ii, j, k, mi, d, kk;    }
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;    *blocc='\0';
   double sw; /* Sum of weights */    return t;
   double lli; /* Individual log likelihood */  }
   long ipmx;  char *cutv(char *blocc, char *alocc, char *in, char occ)
   /*extern weight */  {
   /* We are differentiating ll according to initial status */    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
   /*for(i=1;i<imx;i++)       gives blocc="abcdef2ghi" and alocc="j".
     printf(" %d\n",s[4][i]);       If occ is not found blocc is null and alocc is equal to in. Returns alocc
   */    */
   cov[1]=1.;    char *s, *t;
     t=in;s=in;
   for(k=1; k<=nlstate; k++) ll[k]=0.;    while (*in != '\0'){
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      while( *in == occ){
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];        *blocc++ = *in++;
     for(mi=1; mi<= wav[i]-1; mi++){        s=in;
       for (ii=1;ii<=nlstate+ndeath;ii++)      }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      *blocc++ = *in++;
       for(d=0; d<dh[mi][i]; d++){    }
         newm=savm;    if (s == t) /* occ not found */
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      *(blocc-(in-s))='\0';
         for (kk=1; kk<=cptcovage;kk++) {    else
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      *(blocc-(in-s)-1)='\0';
         }    in=s;
            while ( *in != '\0'){
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      *alocc++ = *in++;
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    }
         savm=oldm;  
         oldm=newm;    *alocc='\0';
            return s;
          }
       } /* end mult */  
        int nbocc(char *s, char occ)
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  {
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    int i,j=0;
       ipmx +=1;    int lg=20;
       sw += weight[i];    i=0;
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    lg=strlen(s);
     } /* end of wave */    for(i=0; i<= lg; i++) {
   } /* end of individual */    if  (s[i] == occ ) j++;
     }
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    return j;
   /* 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 */  
   return -l;  /* 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'  */
   /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
 /*********** Maximum Likelihood Estimation ***************/  /*      gives u="abcdef2ghi" and v="j" *\/ */
   /*   int i,lg,j,p=0; */
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  /*   i=0; */
 {  /*   lg=strlen(t); */
   int i,j, iter;  /*   for(j=0; j<=lg-1; j++) { */
   double **xi,*delti;  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   double fret;  /*   } */
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)  /*   for(j=0; j<p; j++) { */
     for (j=1;j<=npar;j++)  /*     (u[j] = t[j]); */
       xi[i][j]=(i==j ? 1.0 : 0.0);  /*   } */
   printf("Powell\n");  /*      u[p]='\0'; */
   powell(p,xi,npar,ftol,&iter,&fret,func);  
   /*    for(j=0; j<= lg; j++) { */
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));  /*   } */
   /* } */
 }  
   #ifdef _WIN32
 /**** Computes Hessian and covariance matrix ***/  char * strsep(char **pp, const char *delim)
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  {
 {    char *p, *q;
   double  **a,**y,*x,pd;           
   double **hess;    if ((p = *pp) == NULL)
   int i, j,jk;      return 0;
   int *indx;    if ((q = strpbrk (p, delim)) != NULL)
     {
   double hessii(double p[], double delta, int theta, double delti[]);      *pp = q + 1;
   double hessij(double p[], double delti[], int i, int j);      *q = '\0';
   void lubksb(double **a, int npar, int *indx, double b[]) ;    }
   void ludcmp(double **a, int npar, int *indx, double *d) ;    else
       *pp = 0;
   hess=matrix(1,npar,1,npar);    return p;
   }
   printf("\nCalculation of the hessian matrix. Wait...\n");  #endif
   for (i=1;i<=npar;i++){  
     printf("%d",i);fflush(stdout);  /********************** nrerror ********************/
     hess[i][i]=hessii(p,ftolhess,i,delti);  
     /*printf(" %f ",p[i]);*/  void nrerror(char error_text[])
     /*printf(" %lf ",hess[i][i]);*/  {
   }    fprintf(stderr,"ERREUR ...\n");
      fprintf(stderr,"%s\n",error_text);
   for (i=1;i<=npar;i++) {    exit(EXIT_FAILURE);
     for (j=1;j<=npar;j++)  {  }
       if (j>i) {  /*********************** vector *******************/
         printf(".%d%d",i,j);fflush(stdout);  double *vector(int nl, int nh)
         hess[i][j]=hessij(p,delti,i,j);  {
         hess[j][i]=hess[i][j];        double *v;
         /*printf(" %lf ",hess[i][j]);*/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       }    if (!v) nrerror("allocation failure in vector");
     }    return v-nl+NR_END;
   }  }
   printf("\n");  
   /************************ free vector ******************/
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  void free_vector(double*v, int nl, int nh)
    {
   a=matrix(1,npar,1,npar);    free((FREE_ARG)(v+nl-NR_END));
   y=matrix(1,npar,1,npar);  }
   x=vector(1,npar);  
   indx=ivector(1,npar);  /************************ivector *******************************/
   for (i=1;i<=npar;i++)  int *ivector(long nl,long nh)
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  {
   ludcmp(a,npar,indx,&pd);    int *v;
     v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   for (j=1;j<=npar;j++) {    if (!v) nrerror("allocation failure in ivector");
     for (i=1;i<=npar;i++) x[i]=0;    return v-nl+NR_END;
     x[j]=1;  }
     lubksb(a,npar,indx,x);  
     for (i=1;i<=npar;i++){  /******************free ivector **************************/
       matcov[i][j]=x[i];  void free_ivector(int *v, long nl, long nh)
     }  {
   }    free((FREE_ARG)(v+nl-NR_END));
   }
   printf("\n#Hessian matrix#\n");  
   for (i=1;i<=npar;i++) {  /************************lvector *******************************/
     for (j=1;j<=npar;j++) {  long *lvector(long nl,long nh)
       printf("%.3e ",hess[i][j]);  {
     }    long *v;
     printf("\n");    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   }    if (!v) nrerror("allocation failure in ivector");
     return v-nl+NR_END;
   /* Recompute Inverse */  }
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  /******************free lvector **************************/
   ludcmp(a,npar,indx,&pd);  void free_lvector(long *v, long nl, long nh)
   {
   /*  printf("\n#Hessian matrix recomputed#\n");    free((FREE_ARG)(v+nl-NR_END));
   }
   for (j=1;j<=npar;j++) {  
     for (i=1;i<=npar;i++) x[i]=0;  /******************* imatrix *******************************/
     x[j]=1;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     lubksb(a,npar,indx,x);       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     for (i=1;i<=npar;i++){  { 
       y[i][j]=x[i];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
       printf("%.3e ",y[i][j]);    int **m; 
     }    
     printf("\n");    /* allocate pointers to rows */ 
   }    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   */    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
   free_matrix(a,1,npar,1,npar);    m -= nrl; 
   free_matrix(y,1,npar,1,npar);    
   free_vector(x,1,npar);    
   free_ivector(indx,1,npar);    /* allocate rows and set pointers to them */ 
   free_matrix(hess,1,npar,1,npar);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     m[nrl] += NR_END; 
 }    m[nrl] -= ncl; 
     
 /*************** hessian matrix ****************/    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
 double hessii( double x[], double delta, int theta, double delti[])    
 {    /* return pointer to array of pointers to rows */ 
   int i;    return m; 
   int l=1, lmax=20;  } 
   double k1,k2;  
   double p2[NPARMAX+1];  /****************** free_imatrix *************************/
   double res;  void free_imatrix(m,nrl,nrh,ncl,nch)
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        int **m;
   double fx;        long nch,ncl,nrh,nrl; 
   int k=0,kmax=10;       /* free an int matrix allocated by imatrix() */ 
   double l1;  { 
     free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   fx=func(x);    free((FREE_ARG) (m+nrl-NR_END)); 
   for (i=1;i<=npar;i++) p2[i]=x[i];  } 
   for(l=0 ; l <=lmax; l++){  
     l1=pow(10,l);  /******************* matrix *******************************/
     delts=delt;  double **matrix(long nrl, long nrh, long ncl, long nch)
     for(k=1 ; k <kmax; k=k+1){  {
       delt = delta*(l1*k);    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       p2[theta]=x[theta] +delt;    double **m;
       k1=func(p2)-fx;  
       p2[theta]=x[theta]-delt;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       k2=func(p2)-fx;    if (!m) nrerror("allocation failure 1 in matrix()");
       /*res= (k1-2.0*fx+k2)/delt/delt; */    m += NR_END;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    m -= nrl;
        
 #ifdef DEBUG    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 #endif    m[nrl] += NR_END;
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    m[nrl] -= ncl;
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  
         k=kmax;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       }    return m;
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
         k=kmax; l=lmax*10.;  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
       }  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){     */
         delts=delt;  }
       }  
     }  /*************************free matrix ************************/
   }  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   delti[theta]=delts;  {
   return res;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
      free((FREE_ARG)(m+nrl-NR_END));
 }  }
   
 double hessij( double x[], double delti[], int thetai,int thetaj)  /******************* ma3x *******************************/
 {  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   int i;  {
   int l=1, l1, lmax=20;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   double k1,k2,k3,k4,res,fx;    double ***m;
   double p2[NPARMAX+1];  
   int k;    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
   fx=func(x);    m += NR_END;
   for (k=1; k<=2; k++) {    m -= nrl;
     for (i=1;i<=npar;i++) p2[i]=x[i];  
     p2[thetai]=x[thetai]+delti[thetai]/k;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     k1=func(p2)-fx;    m[nrl] += NR_END;
      m[nrl] -= ncl;
     p2[thetai]=x[thetai]+delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     k2=func(p2)-fx;  
      m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     p2[thetai]=x[thetai]-delti[thetai]/k;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    m[nrl][ncl] += NR_END;
     k3=func(p2)-fx;    m[nrl][ncl] -= nll;
      for (j=ncl+1; j<=nch; j++) 
     p2[thetai]=x[thetai]-delti[thetai]/k;      m[nrl][j]=m[nrl][j-1]+nlay;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    
     k4=func(p2)-fx;    for (i=nrl+1; i<=nrh; i++) {
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
 #ifdef DEBUG      for (j=ncl+1; j<=nch; j++) 
     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);        m[i][j]=m[i][j-1]+nlay;
 #endif    }
   }    return m; 
   return res;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 }             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     */
 /************** Inverse of matrix **************/  }
 void ludcmp(double **a, int n, int *indx, double *d)  
 {  /*************************free ma3x ************************/
   int i,imax,j,k;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   double big,dum,sum,temp;  {
   double *vv;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
      free((FREE_ARG)(m[nrl]+ncl-NR_END));
   vv=vector(1,n);    free((FREE_ARG)(m+nrl-NR_END));
   *d=1.0;  }
   for (i=1;i<=n;i++) {  
     big=0.0;  /*************** function subdirf ***********/
     for (j=1;j<=n;j++)  char *subdirf(char fileres[])
       if ((temp=fabs(a[i][j])) > big) big=temp;  {
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    /* Caution optionfilefiname is hidden */
     vv[i]=1.0/big;    strcpy(tmpout,optionfilefiname);
   }    strcat(tmpout,"/"); /* Add to the right */
   for (j=1;j<=n;j++) {    strcat(tmpout,fileres);
     for (i=1;i<j;i++) {    return tmpout;
       sum=a[i][j];  }
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  
       a[i][j]=sum;  /*************** function subdirf2 ***********/
     }  char *subdirf2(char fileres[], char *preop)
     big=0.0;  {
     for (i=j;i<=n;i++) {    
       sum=a[i][j];    /* Caution optionfilefiname is hidden */
       for (k=1;k<j;k++)    strcpy(tmpout,optionfilefiname);
         sum -= a[i][k]*a[k][j];    strcat(tmpout,"/");
       a[i][j]=sum;    strcat(tmpout,preop);
       if ( (dum=vv[i]*fabs(sum)) >= big) {    strcat(tmpout,fileres);
         big=dum;    return tmpout;
         imax=i;  }
       }  
     }  /*************** function subdirf3 ***********/
     if (j != imax) {  char *subdirf3(char fileres[], char *preop, char *preop2)
       for (k=1;k<=n;k++) {  {
         dum=a[imax][k];    
         a[imax][k]=a[j][k];    /* Caution optionfilefiname is hidden */
         a[j][k]=dum;    strcpy(tmpout,optionfilefiname);
       }    strcat(tmpout,"/");
       *d = -(*d);    strcat(tmpout,preop);
       vv[imax]=vv[j];    strcat(tmpout,preop2);
     }    strcat(tmpout,fileres);
     indx[j]=imax;    return tmpout;
     if (a[j][j] == 0.0) a[j][j]=TINY;  }
     if (j != n) {  
       dum=1.0/(a[j][j]);  char *asc_diff_time(long time_sec, char ascdiff[])
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  {
     }    long sec_left, days, hours, minutes;
   }    days = (time_sec) / (60*60*24);
   free_vector(vv,1,n);  /* Doesn't work */    sec_left = (time_sec) % (60*60*24);
 ;    hours = (sec_left) / (60*60) ;
 }    sec_left = (sec_left) %(60*60);
     minutes = (sec_left) /60;
 void lubksb(double **a, int n, int *indx, double b[])    sec_left = (sec_left) % (60);
 {    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
   int i,ii=0,ip,j;    return ascdiff;
   double sum;  }
    
   for (i=1;i<=n;i++) {  /***************** f1dim *************************/
     ip=indx[i];  extern int ncom; 
     sum=b[ip];  extern double *pcom,*xicom;
     b[ip]=b[i];  extern double (*nrfunc)(double []); 
     if (ii)   
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  double f1dim(double x) 
     else if (sum) ii=i;  { 
     b[i]=sum;    int j; 
   }    double f;
   for (i=n;i>=1;i--) {    double *xt; 
     sum=b[i];   
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    xt=vector(1,ncom); 
     b[i]=sum/a[i][i];    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   }    f=(*nrfunc)(xt); 
 }    free_vector(xt,1,ncom); 
     return f; 
 /************ Frequencies ********************/  } 
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)  
 {  /* Some frequencies */  /*****************brent *************************/
    double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  { 
   double ***freq; /* Frequencies */    int iter; 
   double *pp;    double a,b,d,etemp;
   double pos, k2, dateintsum=0,k2cpt=0;    double fu=0,fv,fw,fx;
   FILE *ficresp;    double ftemp=0.;
   char fileresp[FILENAMELENGTH];    double p,q,r,tol1,tol2,u,v,w,x,xm; 
      double e=0.0; 
   pp=vector(1,nlstate);   
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    a=(ax < cx ? ax : cx); 
   strcpy(fileresp,"p");    b=(ax > cx ? ax : cx); 
   strcat(fileresp,fileres);    x=w=v=bx; 
   if((ficresp=fopen(fileresp,"w"))==NULL) {    fw=fv=fx=(*f)(x); 
     printf("Problem with prevalence resultfile: %s\n", fileresp);    for (iter=1;iter<=ITMAX;iter++) { 
     exit(0);      xm=0.5*(a+b); 
   }      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   j1=0;      printf(".");fflush(stdout);
        fprintf(ficlog,".");fflush(ficlog);
   j=cptcoveff;  #ifdef DEBUGBRENT
   if (cptcovn<1) {j=1;ncodemax[1]=1;}      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(k1=1; k1<=j;k1++){      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     for(i1=1; i1<=ncodemax[k1];i1++){  #endif
       j1++;      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        *xmin=x; 
         scanf("%d", i);*/        return fx; 
       for (i=-1; i<=nlstate+ndeath; i++)        } 
         for (jk=-1; jk<=nlstate+ndeath; jk++)        ftemp=fu;
           for(m=agemin; m <= agemax+3; m++)      if (fabs(e) > tol1) { 
             freq[i][jk][m]=0;        r=(x-w)*(fx-fv); 
              q=(x-v)*(fx-fw); 
       dateintsum=0;        p=(x-v)*q-(x-w)*r; 
       k2cpt=0;        q=2.0*(q-r); 
       for (i=1; i<=imx; i++) {        if (q > 0.0) p = -p; 
         bool=1;        q=fabs(q); 
         if  (cptcovn>0) {        etemp=e; 
           for (z1=1; z1<=cptcoveff; z1++)        e=d; 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
               bool=0;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         }        else { 
         if (bool==1) {          d=p/q; 
           for(m=firstpass; m<=lastpass; m++){          u=x+d; 
             k2=anint[m][i]+(mint[m][i]/12.);          if (u-a < tol2 || b-u < tol2) 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {            d=SIGN(tol1,xm-x); 
               if(agev[m][i]==0) agev[m][i]=agemax+1;        } 
               if(agev[m][i]==1) agev[m][i]=agemax+2;      } else { 
               if (m<lastpass) {        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];      } 
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
               }      fu=(*f)(u); 
                    if (fu <= fx) { 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        if (u >= x) a=x; else b=x; 
                 dateintsum=dateintsum+k2;        SHFT(v,w,x,u) 
                 k2cpt++;          SHFT(fv,fw,fx,fu) 
               }          } else { 
             }            if (u < x) a=u; else b=u; 
           }            if (fu <= fw || w == x) { 
         }              v=w; 
       }              w=u; 
                      fv=fw; 
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
       if  (cptcovn>0) {              v=u; 
         fprintf(ficresp, "\n#********** Variable ");              fv=fu; 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);            } 
         fprintf(ficresp, "**********\n#");          } 
       }    } 
       for(i=1; i<=nlstate;i++)    nrerror("Too many iterations in brent"); 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    *xmin=x; 
       fprintf(ficresp, "\n");    return fx; 
        } 
       for(i=(int)agemin; i <= (int)agemax+3; i++){  
         if(i==(int)agemax+3)  /****************** mnbrak ***********************/
           printf("Total");  
         else  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
           printf("Age %d", i);              double (*func)(double)) 
         for(jk=1; jk <=nlstate ; jk++){  { 
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    double ulim,u,r,q, dum;
             pp[jk] += freq[jk][m][i];    double fu; 
         }   
         for(jk=1; jk <=nlstate ; jk++){    *fa=(*func)(*ax); 
           for(m=-1, pos=0; m <=0 ; m++)    *fb=(*func)(*bx); 
             pos += freq[jk][m][i];    if (*fb > *fa) { 
           if(pp[jk]>=1.e-10)      SHFT(dum,*ax,*bx,dum) 
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        SHFT(dum,*fb,*fa,dum) 
           else        } 
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);    *cx=(*bx)+GOLD*(*bx-*ax); 
         }    *fc=(*func)(*cx); 
     while (*fb > *fc) { /* Declining fa, fb, fc */
         for(jk=1; jk <=nlstate ; jk++){      r=(*bx-*ax)*(*fb-*fc); 
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      q=(*bx-*cx)*(*fb-*fa); 
             pp[jk] += freq[jk][m][i];      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
         }        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); /* Minimum abscisse of a parabolic estimated from (a,fa), (b,fb) and (c,fc). */
       ulim=(*bx)+GLIMIT*(*cx-*bx); /* Maximum abscisse where function can be evaluated */
         for(jk=1,pos=0; jk <=nlstate ; jk++)      if ((*bx-u)*(u-*cx) > 0.0) { /* if u between b and c */
           pos += pp[jk];        fu=(*func)(u); 
         for(jk=1; jk <=nlstate ; jk++){  #ifdef DEBUG
           if(pos>=1.e-5)        /* f(x)=A(x-u)**2+f(u) */
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        double A, fparabu; 
           else        A= (*fb - *fa)/(*bx-*ax)/(*bx+*ax-2*u);
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        fparabu= *fa - A*(*ax-u)*(*ax-u);
           if( i <= (int) agemax){        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);
             if(pos>=1.e-5){        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);
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  #endif 
               probs[i][jk][j1]= pp[jk]/pos;      } else if ((*cx-u)*(u-ulim) > 0.0) { /* u is after c but before ulim */
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/        fu=(*func)(u); 
             }        if (fu < *fc) { 
             else          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);            SHFT(*fb,*fc,fu,(*func)(u)) 
           }            } 
         }      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { /* u outside ulim (verifying that ulim is beyond c) */
                u=ulim; 
         for(jk=-1; jk <=nlstate+ndeath; jk++)        fu=(*func)(u); 
           for(m=-1; m <=nlstate+ndeath; m++)      } else { 
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);        u=(*cx)+GOLD*(*cx-*bx); 
         if(i <= (int) agemax)        fu=(*func)(u); 
           fprintf(ficresp,"\n");      } 
         printf("\n");      SHFT(*ax,*bx,*cx,u) 
       }        SHFT(*fa,*fb,*fc,fu) 
     }        } 
   }  } 
   dateintmean=dateintsum/k2cpt;  
    /*************** linmin ************************/
   fclose(ficresp);  /* Given an n -dimensional point p[1..n] and an n -dimensional direction xi[1..n] , moves and
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);  resets p to where the function func(p) takes on a minimum along the direction xi from p ,
   free_vector(pp,1,nlstate);  and replaces xi by the actual vector displacement that p was moved. Also returns as fret
    the value of func at the returned location p . This is actually all accomplished by calling the
   /* End of Freq */  routines mnbrak and brent .*/
 }  int ncom; 
   double *pcom,*xicom;
 /************ Prevalence ********************/  double (*nrfunc)(double []); 
 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 */  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
    { 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    double brent(double ax, double bx, double cx, 
   double ***freq; /* Frequencies */                 double (*f)(double), double tol, double *xmin); 
   double *pp;    double f1dim(double x); 
   double pos, k2;    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
                 double *fc, double (*func)(double)); 
   pp=vector(1,nlstate);    int j; 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    double xx,xmin,bx,ax; 
      double fx,fb,fa;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);   
   j1=0;    ncom=n; 
      pcom=vector(1,n); 
   j=cptcoveff;    xicom=vector(1,n); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    nrfunc=func; 
      for (j=1;j<=n;j++) { 
   for(k1=1; k1<=j;k1++){      pcom[j]=p[j]; 
     for(i1=1; i1<=ncodemax[k1];i1++){      xicom[j]=xi[j]; 
       j1++;    } 
          ax=0.0; 
       for (i=-1; i<=nlstate+ndeath; i++)      xx=1.0; 
         for (jk=-1; jk<=nlstate+ndeath; jk++)      mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); /* Find a bracket a,x,b in direction n=xi ie xicom */
           for(m=agemin; m <= agemax+3; m++)    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); /* Find a minimum P+lambda n in that direction (lambdamin), with TOL between abscisses */
             freq[i][jk][m]=0;  #ifdef DEBUG
          printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       for (i=1; i<=imx; i++) {    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         bool=1;  #endif
         if  (cptcovn>0) {    for (j=1;j<=n;j++) { 
           for (z1=1; z1<=cptcoveff; z1++)      xi[j] *= xmin; 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      p[j] += xi[j]; 
               bool=0;    } 
         }    free_vector(xicom,1,n); 
         if (bool==1) {    free_vector(pcom,1,n); 
           for(m=firstpass; m<=lastpass; m++){  } 
             k2=anint[m][i]+(mint[m][i]/12.);  
             if ((k2>=dateprev1) && (k2<=dateprev2)) {  
               if(agev[m][i]==0) agev[m][i]=agemax+1;  /*************** powell ************************/
               if(agev[m][i]==1) agev[m][i]=agemax+2;  /*
               if (m<lastpass) {  Minimization of a function func of n variables. Input consists of an initial starting point
                 if (calagedate>0)  p[1..n] ; an initial matrix xi[1..n][1..n] , whose columns contain the initial set of di-
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];  rections (usually the n unit vectors); and ftol , the fractional tolerance in the function value
                 else  such that failure to decrease by more than this amount on one iteration signals doneness. On
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  output, p is set to the best point found, xi is the then-current direction set, fret is the returned
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];  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 [])) 
         }  { 
       }    void linmin(double p[], double xi[], int n, double *fret, 
       for(i=(int)agemin; i <= (int)agemax+3; i++){                double (*func)(double [])); 
         for(jk=1; jk <=nlstate ; jk++){    int i,ibig,j; 
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    double del,t,*pt,*ptt,*xit;
             pp[jk] += freq[jk][m][i];    double fp,fptt;
         }    double *xits;
         for(jk=1; jk <=nlstate ; jk++){    int niterf, itmp;
           for(m=-1, pos=0; m <=0 ; m++)  
             pos += freq[jk][m][i];    pt=vector(1,n); 
         }    ptt=vector(1,n); 
            xit=vector(1,n); 
         for(jk=1; jk <=nlstate ; jk++){    xits=vector(1,n); 
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    *fret=(*func)(p); 
             pp[jk] += freq[jk][m][i];    for (j=1;j<=n;j++) pt[j]=p[j]; 
         }      rcurr_time = time(NULL);  
            for (*iter=1;;++(*iter)) { 
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];      fp=(*fret); 
              ibig=0; 
         for(jk=1; jk <=nlstate ; jk++){          del=0.0; 
           if( i <= (int) agemax){      rlast_time=rcurr_time;
             if(pos>=1.e-5){      /* (void) gettimeofday(&curr_time,&tzp); */
               probs[i][jk][j1]= pp[jk]/pos;      rcurr_time = time(NULL);  
             }      curr_time = *localtime(&rcurr_time);
           }      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, rcurr_time-rlast_time, rcurr_time-rstart_time);fflush(stdout);
         }      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret,rcurr_time-rlast_time, rcurr_time-rstart_time); fflush(ficlog);
          /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tm_sec-start_time.tm_sec); */
       }     for (i=1;i<=n;i++) {
     }        printf(" %d %.12f",i, p[i]);
   }        fprintf(ficlog," %d %.12lf",i, p[i]);
         fprintf(ficrespow," %.12lf", p[i]);
        }
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      printf("\n");
   free_vector(pp,1,nlstate);      fprintf(ficlog,"\n");
        fprintf(ficrespow,"\n");fflush(ficrespow);
 }  /* End of Freq */      if(*iter <=3){
         tml = *localtime(&rcurr_time);
 /************* Waves Concatenation ***************/        strcpy(strcurr,asctime(&tml));
         rforecast_time=rcurr_time; 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)        itmp = strlen(strcurr);
 {        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          strcurr[itmp-1]='\0';
      Death is a valid wave (if date is known).        printf("\nConsidering the time needed for the last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        for(niterf=10;niterf<=30;niterf+=10){
      and mw[mi+1][i]. dh depends on stepm.          rforecast_time=rcurr_time+(niterf-*iter)*(rcurr_time-rlast_time);
      */          forecast_time = *localtime(&rforecast_time);
           strcpy(strfor,asctime(&forecast_time));
   int i, mi, m;          itmp = strlen(strfor);
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          if(strfor[itmp-1]=='\n')
      double sum=0., jmean=0.;*/          strfor[itmp-1]='\0';
           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);
   int j, k=0,jk, ju, jl;          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);
   double sum=0.;        }
   jmin=1e+5;      }
   jmax=-1;      for (i=1;i<=n;i++) { 
   jmean=0.;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   for(i=1; i<=imx; i++){        fptt=(*fret); 
     mi=0;  #ifdef DEBUG
     m=firstpass;            printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
     while(s[m][i] <= nlstate){            fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
       if(s[m][i]>=1)  #endif
         mw[++mi][i]=m;        printf("%d",i);fflush(stdout);
       if(m >=lastpass)        fprintf(ficlog,"%d",i);fflush(ficlog);
         break;        linmin(p,xit,n,fret,func); 
       else        if (fabs(fptt-(*fret)) > del) { 
         m++;          del=fabs(fptt-(*fret)); 
     }/* end while */          ibig=i; 
     if (s[m][i] > nlstate){        } 
       mi++;     /* Death is another wave */  #ifdef DEBUG
       /* if(mi==0)  never been interviewed correctly before death */        printf("%d %.12e",i,(*fret));
          /* Only death is a correct wave */        fprintf(ficlog,"%d %.12e",i,(*fret));
       mw[mi][i]=m;        for (j=1;j<=n;j++) {
     }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           printf(" x(%d)=%.12e",j,xit[j]);
     wav[i]=mi;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     if(mi==0)        }
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        for(j=1;j<=n;j++) {
   }          printf(" p(%d)=%.12e",j,p[j]);
           fprintf(ficlog," p(%d)=%.12e",j,p[j]);
   for(i=1; i<=imx; i++){        }
     for(mi=1; mi<wav[i];mi++){        printf("\n");
       if (stepm <=0)        fprintf(ficlog,"\n");
         dh[mi][i]=1;  #endif
       else{      } /* end i */
         if (s[mw[mi+1][i]][i] > nlstate) {      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
           if (agedc[i] < 2*AGESUP) {  #ifdef DEBUG
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);        int k[2],l;
           if(j==0) j=1;  /* Survives at least one month after exam */        k[0]=1;
           k=k+1;        k[1]=-1;
           if (j >= jmax) jmax=j;        printf("Max: %.12e",(*func)(p));
           if (j <= jmin) jmin=j;        fprintf(ficlog,"Max: %.12e",(*func)(p));
           sum=sum+j;        for (j=1;j<=n;j++) {
           /*if (j<0) printf("j=%d num=%d \n",j,i); */          printf(" %.12e",p[j]);
           }          fprintf(ficlog," %.12e",p[j]);
         }        }
         else{        printf("\n");
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        fprintf(ficlog,"\n");
           k=k+1;        for(l=0;l<=1;l++) {
           if (j >= jmax) jmax=j;          for (j=1;j<=n;j++) {
           else if (j <= jmin)jmin=j;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           sum=sum+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]);
         }          }
         jk= j/stepm;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         jl= j -jk*stepm;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
         ju= j -(jk+1)*stepm;        }
         if(jl <= -ju)  #endif
           dh[mi][i]=jk;  
         else  
           dh[mi][i]=jk+1;        free_vector(xit,1,n); 
         if(dh[mi][i]==0)        free_vector(xits,1,n); 
           dh[mi][i]=1; /* At least one step */        free_vector(ptt,1,n); 
       }        free_vector(pt,1,n); 
     }        return; 
   }      } 
   jmean=sum/k;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);      for (j=1;j<=n;j++) { /* Computes an extrapolated point */
  }        ptt[j]=2.0*p[j]-pt[j]; 
 /*********** Tricode ****************************/        xit[j]=p[j]-pt[j]; 
 void tricode(int *Tvar, int **nbcode, int imx)        pt[j]=p[j]; 
 {      } 
   int Ndum[20],ij=1, k, j, i;      fptt=(*func)(ptt); 
   int cptcode=0;      if (fptt < fp) { /* If extrapolated point is better, decide if we keep that new direction or not */
   cptcoveff=0;        /* (x1 f1=fp), (x2 f2=*fret), (x3 f3=fptt), (xm fm) */
          /* From x1 (P0) distance of x2 is at h and x3 is 2h */
   for (k=0; k<19; k++) Ndum[k]=0;        /* Let f"(x2) be the 2nd derivative equal everywhere.  */
   for (k=1; k<=7; k++) ncodemax[k]=0;        /* 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<=(cptcovn+2*cptcovprod); j++) {        /* f1-f3 = delta(2h) = 2 h**2 f'' = 2(f1- 2f2 +f3) */
     for (i=1; i<=imx; i++) {        /* Thus we compare delta(2h) with observed f1-f3 */
       ij=(int)(covar[Tvar[j]][i]);        /* or best gain on one ancient line 'del' with total  */
       Ndum[ij]++;        /* gain f1-f2 = f1 - f2 - 'del' with del  */
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/        /* t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); */
       if (ij > cptcode) cptcode=ij;  
     }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del);
         t= t- del*SQR(fp-fptt);
     for (i=0; i<=cptcode; i++) {        printf("t1= %.12lf, t2= %.12lf, t=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t);
       if(Ndum[i]!=0) ncodemax[j]++;        fprintf(ficlog,"t1= %.12lf, t2= %.12lf, t=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t);
     }  #ifdef DEBUG
     ij=1;        printf("t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
                (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
         fprintf(ficlog,"t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
     for (i=1; i<=ncodemax[j]; i++) {               (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
       for (k=0; k<=19; k++) {        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);
         if (Ndum[k] != 0) {        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);
           nbcode[Tvar[j]][ij]=k;  #endif
                  if (t < 0.0) { /* Then we use it for last direction */
           ij++;          linmin(p,xit,n,fret,func); /* computes mean on the extrapolated direction.*/
         }          for (j=1;j<=n;j++) { 
         if (ij > ncodemax[j]) break;            xi[j][ibig]=xi[j][n]; /* Replace the direction with biggest decrease by n */
       }              xi[j][n]=xit[j];      /* and nth direction by the extrapolated */
     }          }
   }            printf("Gaining to use average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig);
           fprintf(ficlog,"Gaining to use average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig);
  for (k=0; k<19; k++) Ndum[k]=0;  
   #ifdef DEBUG
  for (i=1; i<=ncovmodel-2; i++) {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       ij=Tvar[i];          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       Ndum[ij]++;          for(j=1;j<=n;j++){
     }            printf(" %.12e",xit[j]);
             fprintf(ficlog," %.12e",xit[j]);
  ij=1;          }
  for (i=1; i<=10; i++) {          printf("\n");
    if((Ndum[i]!=0) && (i<=ncovcol)){          fprintf(ficlog,"\n");
      Tvaraff[ij]=i;  #endif
      ij++;        } /* end of t negative */
    }      } /* end if (fptt < fp)  */
  }    } 
    } 
     cptcoveff=ij-1;  
 }  /**** Prevalence limit (stable or period prevalence)  ****************/
   
 /*********** Health Expectancies ****************/  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   {
 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 )    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
        matrix by transitions matrix until convergence is reached */
 {    
   /* Health expectancies */    int i, ii,j,k;
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;    double min, max, maxmin, maxmax,sumnew=0.;
   double age, agelim, hf;    /* double **matprod2(); */ /* test */
   double ***p3mat,***varhe;    double **out, cov[NCOVMAX+1], **pmij();
   double **dnewm,**doldm;    double **newm;
   double *xp;    double agefin, delaymax=50 ; /* Max number of years to converge */
   double **gp, **gm;    
   double ***gradg, ***trgradg;    for (ii=1;ii<=nlstate+ndeath;ii++)
   int theta;      for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);      }
   xp=vector(1,npar);    
   dnewm=matrix(1,nlstate*2,1,npar);    cov[1]=1.;
   doldm=matrix(1,nlstate*2,1,nlstate*2);    
      /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   fprintf(ficreseij,"# Health expectancies\n");    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   fprintf(ficreseij,"# Age");      newm=savm;
   for(i=1; i<=nlstate;i++)      /* Covariates have to be included here again */
     for(j=1; j<=nlstate;j++)      cov[2]=agefin;
       fprintf(ficreseij," %1d-%1d (SE)",i,j);      
   fprintf(ficreseij,"\n");      for (k=1; k<=cptcovn;k++) {
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   if(estepm < stepm){        /*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]]);*/
     printf ("Problem %d lower than %d\n",estepm, stepm);      }
   }      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
   else  hstepm=estepm;        /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
   /* We compute the life expectancy from trapezoids spaced every estepm months      /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
    * 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      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
    * we are calculating an estimate of the Life Expectancy assuming a linear      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
    * progression inbetween and thus overestimating or underestimating according      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
    * to the curvature of the survival function. If, for the same date, we      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
    * estimate the model with stepm=1 month, we can keep estepm to 24 months      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
    * to compare the new estimate of Life expectancy with the same linear      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
    * hypothesis. A more precise result, taking into account a more precise      
    * curvature will be obtained if estepm is as small as stepm. */      savm=oldm;
       oldm=newm;
   /* For example we decided to compute the life expectancy with the smallest unit */      maxmax=0.;
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.      for(j=1;j<=nlstate;j++){
      nhstepm is the number of hstepm from age to agelim        min=1.;
      nstepm is the number of stepm from age to agelin.        max=0.;
      Look at hpijx to understand the reason of that which relies in memory size        for(i=1; i<=nlstate; i++) {
      and note for a fixed period like estepm months */          sumnew=0;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
      survival function given by stepm (the optimization length). Unfortunately it          prlim[i][j]= newm[i][j]/(1-sumnew);
      means that if the survival funtion is printed only each two years of age and if          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          max=FMAX(max,prlim[i][j]);
      results. So we changed our mind and took the option of the best precision.          min=FMIN(min,prlim[i][j]);
   */        }
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
   agelim=AGESUP;      } /* j loop */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      if(maxmax < ftolpl){
     /* nhstepm age range expressed in number of stepm */        return prlim;
     nstepm=(int) rint((agelim-age)*YEARM/stepm);      }
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */    } /* age loop */
     /* if (stepm >= YEARM) hstepm=1;*/    return prlim; /* should not reach here */
     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*2);  /*************** transition probabilities ***************/ 
     gp=matrix(0,nhstepm,1,nlstate*2);  
     gm=matrix(0,nhstepm,1,nlstate*2);  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   {
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    /* According to parameters values stored in x and the covariate's values stored in cov,
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */       computes the probability to be observed in state j being in state i by appying the
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);         model to the ncovmodel covariates (including constant and age).
         lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
        and, according on how parameters are entered, the position of the coefficient xij(nc) of the
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */       ncth covariate in the global vector x is given by the formula:
        j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
     /* Computing Variances of health expectancies */       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
        Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
      for(theta=1; theta <=npar; theta++){       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
       for(i=1; i<=npar; i++){       Outputs ps[i][j] the probability to be observed in j being in j according to
         xp[i] = x[i] + (i==theta ?delti[theta]:0);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
       }    */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      double s1, lnpijopii;
      /*double t34;*/
       cptj=0;    int i,j, nc, ii, jj;
       for(j=1; j<= nlstate; j++){  
         for(i=1; i<=nlstate; i++){      for(i=1; i<= nlstate; i++){
           cptj=cptj+1;        for(j=1; j<i;j++){
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            /*lnpijopii += param[i][j][nc]*cov[nc];*/
           }            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
         }  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
       }          }
                ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
        /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
       for(i=1; i<=npar; i++)        }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        for(j=i+1; j<=nlstate+ndeath;j++){
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
                  /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
       cptj=0;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
       for(j=1; j<= nlstate; j++){  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
         for(i=1;i<=nlstate;i++){          }
           cptj=cptj+1;          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){        }
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;      }
           }      
         }      for(i=1; i<= nlstate; i++){
       }        s1=0;
              for(j=1; j<i; j++){
              s1+=exp(ps[i][j]); /* In fact sums pij/pii */
           /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
       for(j=1; j<= nlstate*2; j++)        }
         for(h=0; h<=nhstepm-1; h++){        for(j=i+1; j<=nlstate+ndeath; j++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         }          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }
      }        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
            ps[i][i]=1./(s1+1.);
 /* End theta */        /* Computing other pijs */
         for(j=1; j<i; j++)
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          ps[i][j]= exp(ps[i][j])*ps[i][i];
         for(j=i+1; j<=nlstate+ndeath; j++)
      for(h=0; h<=nhstepm-1; h++)          ps[i][j]= exp(ps[i][j])*ps[i][i];
       for(j=1; j<=nlstate*2;j++)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         for(theta=1; theta <=npar; theta++)      } /* end i */
         trgradg[h][j][theta]=gradg[h][theta][j];      
       for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         for(jj=1; jj<= nlstate+ndeath; jj++){
      for(i=1;i<=nlstate*2;i++)          ps[ii][jj]=0;
       for(j=1;j<=nlstate*2;j++)          ps[ii][ii]=1;
         varhe[i][j][(int)age] =0.;        }
       }
      printf("%d||",(int)age);fflush(stdout);      
     for(h=0;h<=nhstepm-1;h++){      
       for(k=0;k<=nhstepm-1;k++){      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
         for(i=1;i<=nlstate*2;i++)      /*   } */
           for(j=1;j<=nlstate*2;j++)      /*   printf("\n "); */
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;      /* } */
       }      /* printf("\n ");printf("%lf ",cov[2]);*/
     }      /*
         for(i=1; i<= npar; i++) printf("%f ",x[i]);
              goto end;*/
     /* Computing expectancies */      return ps;
     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++){  /**************** Product of 2 matrices ******************/
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;  
            double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
 /* 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]);*/  {
     /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
         }       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     /* in, b, out are matrice of pointers which should have been initialized 
     fprintf(ficreseij,"%3.0f",age );       before: only the contents of out is modified. The function returns
     cptj=0;       a pointer to pointers identical to out */
     for(i=1; i<=nlstate;i++)    int i, j, k;
       for(j=1; j<=nlstate;j++){    for(i=nrl; i<= nrh; i++)
         cptj++;      for(k=ncolol; k<=ncoloh; k++){
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );        out[i][k]=0.;
       }        for(j=ncl; j<=nch; j++)
     fprintf(ficreseij,"\n");          out[i][k] +=in[i][j]*b[j][k];
          }
     free_matrix(gm,0,nhstepm,1,nlstate*2);    return out;
     free_matrix(gp,0,nhstepm,1,nlstate*2);  }
     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);  /************* Higher Matrix Product ***************/
   }  
   free_vector(xp,1,npar);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   free_matrix(dnewm,1,nlstate*2,1,npar);  {
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);    /* Computes the transition matrix starting at age 'age' over 
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);       'nhstepm*hstepm*stepm' months (i.e. until
 }       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
 /************ Variance ******************/       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
 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)       (typically every 2 years instead of every month which is too big 
 {       for the memory).
   /* Variance of health expectancies */       Model is determined by parameters x and covariates have to be 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/       included manually here. 
   double **newm;  
   double **dnewm,**doldm;       */
   int i, j, nhstepm, hstepm, h, nstepm ;  
   int k, cptcode;    int i, j, d, h, k;
   double *xp;    double **out, cov[NCOVMAX+1];
   double **gp, **gm;    double **newm;
   double ***gradg, ***trgradg;  
   double ***p3mat;    /* Hstepm could be zero and should return the unit matrix */
   double age,agelim, hf;    for (i=1;i<=nlstate+ndeath;i++)
   int theta;      for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
    fprintf(ficresvij,"# Covariances of life expectancies\n");        po[i][j][0]=(i==j ? 1.0 : 0.0);
   fprintf(ficresvij,"# Age");      }
   for(i=1; i<=nlstate;i++)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     for(j=1; j<=nlstate;j++)    for(h=1; h <=nhstepm; h++){
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);      for(d=1; d <=hstepm; d++){
   fprintf(ficresvij,"\n");        newm=savm;
         /* Covariates have to be included here again */
   xp=vector(1,npar);        cov[1]=1.;
   dnewm=matrix(1,nlstate,1,npar);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   doldm=matrix(1,nlstate,1,nlstate);        for (k=1; k<=cptcovn;k++) 
            cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   if(estepm < stepm){        for (k=1; k<=cptcovage;k++)
     printf ("Problem %d lower than %d\n",estepm, stepm);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   }        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
   else  hstepm=estepm;            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   /* 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        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
      nstepm is the number of stepm from age to agelin.        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
      Look at hpijx to understand the reason of that which relies in memory size        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
      and note for a fixed period like k years */                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the        savm=oldm;
      survival function given by stepm (the optimization length). Unfortunately it        oldm=newm;
      means that if the survival funtion is printed only each two years of age and if      }
      you sum them up and add 1 year (area under the trapezoids) you won't get the same      for(i=1; i<=nlstate+ndeath; i++)
      results. So we changed our mind and took the option of the best precision.        for(j=1;j<=nlstate+ndeath;j++) {
   */          po[i][j][h]=newm[i][j];
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
   agelim = AGESUP;        }
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      /*printf("h=%d ",h);*/
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    } /* end h */
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  /*     printf("\n H=%d \n",h); */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    return po;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  }
     gp=matrix(0,nhstepm,1,nlstate);  
     gm=matrix(0,nhstepm,1,nlstate);  #ifdef NLOPT
     double  myfunc(unsigned n, const double *p1, double *grad, void *pd){
     for(theta=1; theta <=npar; theta++){    double fret;
       for(i=1; i<=npar; i++){ /* Computes gradient */    double *xt;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    int j;
       }    myfunc_data *d2 = (myfunc_data *) pd;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    /* xt = (p1-1); */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    xt=vector(1,n); 
     for (j=1;j<=n;j++)   xt[j]=p1[j-1]; /* xt[1]=p1[0] */
       if (popbased==1) {  
         for(i=1; i<=nlstate;i++)    fret=(d2->function)(xt); /*  p xt[1]@8 is fine */
           prlim[i][i]=probs[(int)age][i][ij];    /* fret=(*func)(xt); /\*  p xt[1]@8 is fine *\/ */
       }    printf("Function = %.12lf ",fret);
      for (j=1;j<=n;j++) printf(" %d %.8lf", j, xt[j]); 
       for(j=1; j<= nlstate; j++){    printf("\n");
         for(h=0; h<=nhstepm; h++){   free_vector(xt,1,n);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    return fret;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];  }
         }  #endif
       }  
      /*************** log-likelihood *************/
       for(i=1; i<=npar; i++) /* Computes gradient */  double func( double *x)
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      int i, ii, j, k, mi, d, kk;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
      double **out;
       if (popbased==1) {    double sw; /* Sum of weights */
         for(i=1; i<=nlstate;i++)    double lli; /* Individual log likelihood */
           prlim[i][i]=probs[(int)age][i][ij];    int s1, s2;
       }    double bbh, survp;
     long ipmx;
       for(j=1; j<= nlstate; j++){    /*extern weight */
         for(h=0; h<=nhstepm; h++){    /* We are differentiating ll according to initial status */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    /*for(i=1;i<imx;i++) 
         }      printf(" %d\n",s[4][i]);
       }    */
   
       for(j=1; j<= nlstate; j++)    ++countcallfunc;
         for(h=0; h<=nhstepm; h++){  
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    cov[1]=1.;
         }  
     } /* End theta */    for(k=1; k<=nlstate; k++) ll[k]=0.;
   
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(h=0; h<=nhstepm; h++)        /* Computes the values of the ncovmodel covariates of the model
       for(j=1; j<=nlstate;j++)           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
         for(theta=1; theta <=npar; theta++)           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
           trgradg[h][j][theta]=gradg[h][theta][j];           to be observed in j being in i according to the model.
          */
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
     for(i=1;i<=nlstate;i++)          cov[2+k]=covar[Tvar[k]][i];
       for(j=1;j<=nlstate;j++)        }
         vareij[i][j][(int)age] =0.;        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
            is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
     for(h=0;h<=nhstepm;h++){           has been calculated etc */
       for(k=0;k<=nhstepm;k++){        for(mi=1; mi<= wav[i]-1; mi++){
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);          for (ii=1;ii<=nlstate+ndeath;ii++)
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);            for (j=1;j<=nlstate+ndeath;j++){
         for(i=1;i<=nlstate;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(j=1;j<=nlstate;j++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;            }
       }          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     fprintf(ficresvij,"%.0f ",age );            for (kk=1; kk<=cptcovage;kk++) {
     for(i=1; i<=nlstate;i++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
       for(j=1; j<=nlstate;j++){            }
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     fprintf(ficresvij,"\n");            savm=oldm;
     free_matrix(gp,0,nhstepm,1,nlstate);            oldm=newm;
     free_matrix(gm,0,nhstepm,1,nlstate);          } /* end mult */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          /* But now since version 0.9 we anticipate for bias at large stepm.
   } /* End age */           * If stepm is larger than one month (smallest stepm) and if the exact delay 
             * (in months) between two waves is not a multiple of stepm, we rounded to 
   free_vector(xp,1,npar);           * the nearest (and in case of equal distance, to the lowest) interval but now
   free_matrix(doldm,1,nlstate,1,npar);           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   free_matrix(dnewm,1,nlstate,1,nlstate);           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
            * probability in order to take into account the bias as a fraction of the way
 }           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
            * -stepm/2 to stepm/2 .
 /************ Variance of prevlim ******************/           * For stepm=1 the results are the same as for previous versions of Imach.
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)           * For stepm > 1 the results are less biased than in previous versions. 
 {           */
   /* Variance of prevalence limit */          s1=s[mw[mi][i]][i];
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          s2=s[mw[mi+1][i]][i];
   double **newm;          bbh=(double)bh[mi][i]/(double)stepm; 
   double **dnewm,**doldm;          /* bias bh is positive if real duration
   int i, j, nhstepm, hstepm;           * is higher than the multiple of stepm and negative otherwise.
   int k, cptcode;           */
   double *xp;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   double *gp, *gm;          if( s2 > nlstate){ 
   double **gradg, **trgradg;            /* i.e. if s2 is a death state and if the date of death is known 
   double age,agelim;               then the contribution to the likelihood is the probability to 
   int theta;               die between last step unit time and current  step unit time, 
                   which is also equal to probability to die before dh 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");               minus probability to die before dh-stepm . 
   fprintf(ficresvpl,"# Age");               In version up to 0.92 likelihood was computed
   for(i=1; i<=nlstate;i++)          as if date of death was unknown. Death was treated as any other
       fprintf(ficresvpl," %1d-%1d",i,i);          health state: the date of the interview describes the actual state
   fprintf(ficresvpl,"\n");          and not the date of a change in health state. The former idea was
           to consider that at each interview the state was recorded
   xp=vector(1,npar);          (healthy, disable or death) and IMaCh was corrected; but when we
   dnewm=matrix(1,nlstate,1,npar);          introduced the exact date of death then we should have modified
   doldm=matrix(1,nlstate,1,nlstate);          the contribution of an exact death to the likelihood. This new
            contribution is smaller and very dependent of the step unit
   hstepm=1*YEARM; /* Every year of age */          stepm. It is no more the probability to die between last interview
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          and month of death but the probability to survive from last
   agelim = AGESUP;          interview up to one month before death multiplied by the
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          probability to die within a month. Thanks to Chris
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          Jackson for correcting this bug.  Former versions increased
     if (stepm >= YEARM) hstepm=1;          mortality artificially. The bad side is that we add another loop
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          which slows down the processing. The difference can be up to 10%
     gradg=matrix(1,npar,1,nlstate);          lower mortality.
     gp=vector(1,nlstate);            */
     gm=vector(1,nlstate);            lli=log(out[s1][s2] - savm[s1][s2]);
   
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++){ /* Computes gradient */          } else if  (s2==-2) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            for (j=1,survp=0. ; j<=nlstate; j++) 
       }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            /*survp += out[s1][j]; */
       for(i=1;i<=nlstate;i++)            lli= log(survp);
         gp[i] = prlim[i][i];          }
              
       for(i=1; i<=npar; i++) /* Computes gradient */          else if  (s2==-4) { 
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            for (j=3,survp=0. ; j<=nlstate; j++)  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       for(i=1;i<=nlstate;i++)            lli= log(survp); 
         gm[i] = prlim[i][i];          } 
   
       for(i=1;i<=nlstate;i++)          else if  (s2==-5) { 
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];            for (j=1,survp=0. ; j<=2; j++)  
     } /* End theta */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             lli= log(survp); 
     trgradg =matrix(1,nlstate,1,npar);          } 
           
     for(j=1; j<=nlstate;j++)          else{
       for(theta=1; theta <=npar; theta++)            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         trgradg[j][theta]=gradg[theta][j];            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
           } 
     for(i=1;i<=nlstate;i++)          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       varpl[i][(int)age] =0.;          /*if(lli ==000.0)*/
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);          /*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); */
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);          ipmx +=1;
     for(i=1;i<=nlstate;i++)          sw += weight[i];
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
     fprintf(ficresvpl,"%.0f ",age );      } /* end of individual */
     for(i=1; i<=nlstate;i++)    }  else if(mle==2){
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     fprintf(ficresvpl,"\n");        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_vector(gp,1,nlstate);        for(mi=1; mi<= wav[i]-1; mi++){
     free_vector(gm,1,nlstate);          for (ii=1;ii<=nlstate+ndeath;ii++)
     free_matrix(gradg,1,npar,1,nlstate);            for (j=1;j<=nlstate+ndeath;j++){
     free_matrix(trgradg,1,nlstate,1,npar);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   } /* End age */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
   free_vector(xp,1,npar);          for(d=0; d<=dh[mi][i]; d++){
   free_matrix(doldm,1,nlstate,1,npar);            newm=savm;
   free_matrix(dnewm,1,nlstate,1,nlstate);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
 }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
 /************ Variance of one-step probabilities  ******************/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 {            savm=oldm;
   int i, j, i1, k1, j1, z1;            oldm=newm;
   int k=0, cptcode;          } /* end mult */
   double **dnewm,**doldm;        
   double *xp;          s1=s[mw[mi][i]][i];
   double *gp, *gm;          s2=s[mw[mi+1][i]][i];
   double **gradg, **trgradg;          bbh=(double)bh[mi][i]/(double)stepm; 
   double age,agelim, cov[NCOVMAX];          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 */
   int theta;          ipmx +=1;
   char fileresprob[FILENAMELENGTH];          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   strcpy(fileresprob,"prob");        } /* end of wave */
   strcat(fileresprob,fileres);      } /* end of individual */
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    }  else if(mle==3){  /* exponential inter-extrapolation */
     printf("Problem with resultfile: %s\n", fileresprob);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);        for(mi=1; mi<= wav[i]-1; mi++){
            for (ii=1;ii<=nlstate+ndeath;ii++)
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");            for (j=1;j<=nlstate+ndeath;j++){
   fprintf(ficresprob,"# Age");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(i=1; i<=nlstate;i++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(j=1; j<=(nlstate+ndeath);j++)            }
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficresprob,"\n");            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
   xp=vector(1,npar);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));            savm=oldm;
              oldm=newm;
   cov[1]=1;          } /* end mult */
   j=cptcoveff;        
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          s1=s[mw[mi][i]][i];
   j1=0;          s2=s[mw[mi+1][i]][i];
   for(k1=1; k1<=1;k1++){          bbh=(double)bh[mi][i]/(double)stepm; 
     for(i1=1; i1<=ncodemax[k1];i1++){          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 */
     j1++;          ipmx +=1;
           sw += weight[i];
     if  (cptcovn>0) {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficresprob, "\n#********** Variable ");        } /* end of wave */
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      } /* end of individual */
       fprintf(ficresprob, "**********\n#");    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
            for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for (age=bage; age<=fage; age ++){        for(mi=1; mi<= wav[i]-1; mi++){
         cov[2]=age;          for (ii=1;ii<=nlstate+ndeath;ii++)
         for (k=1; k<=cptcovn;k++) {            for (j=1;j<=nlstate+ndeath;j++){
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                        savm[ii][j]=(ii==j ? 1.0 : 0.0);
         }            }
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          for(d=0; d<dh[mi][i]; d++){
         for (k=1; k<=cptcovprod;k++)            newm=savm;
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                    for (kk=1; kk<=cptcovage;kk++) {
         gradg=matrix(1,npar,1,9);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         trgradg=matrix(1,9,1,npar);            }
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                             1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(theta=1; theta <=npar; theta++){            savm=oldm;
           for(i=1; i<=npar; i++)            oldm=newm;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);          } /* end mult */
                  
           pmij(pmmij,cov,ncovmodel,xp,nlstate);          s1=s[mw[mi][i]][i];
                    s2=s[mw[mi+1][i]][i];
           k=0;          if( s2 > nlstate){ 
           for(i=1; i<= (nlstate+ndeath); i++){            lli=log(out[s1][s2] - savm[s1][s2]);
             for(j=1; j<=(nlstate+ndeath);j++){          }else{
               k=k+1;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
               gp[k]=pmmij[i][j];          }
             }          ipmx +=1;
           }          sw += weight[i];
                    ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           for(i=1; i<=npar; i++)  /*      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]); */
             xp[i] = x[i] - (i==theta ?delti[theta]:0);        } /* end of wave */
          } /* end of individual */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
           k=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           for(i=1; i<=(nlstate+ndeath); i++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
             for(j=1; j<=(nlstate+ndeath);j++){        for(mi=1; mi<= wav[i]-1; mi++){
               k=k+1;          for (ii=1;ii<=nlstate+ndeath;ii++)
               gm[k]=pmmij[i][j];            for (j=1;j<=nlstate+ndeath;j++){
             }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
                  }
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)          for(d=0; d<dh[mi][i]; d++){
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];              newm=savm;
         }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           for(theta=1; theta <=npar; theta++)            }
             trgradg[j][theta]=gradg[theta][j];          
                    out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);            savm=oldm;
                    oldm=newm;
         pmij(pmmij,cov,ncovmodel,x,nlstate);          } /* end mult */
                
         k=0;          s1=s[mw[mi][i]][i];
         for(i=1; i<=(nlstate+ndeath); i++){          s2=s[mw[mi+1][i]][i];
           for(j=1; j<=(nlstate+ndeath);j++){          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
             k=k+1;          ipmx +=1;
             gm[k]=pmmij[i][j];          sw += weight[i];
           }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
              } /* end of wave */
      /*printf("\n%d ",(int)age);      } /* end of individual */
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    } /* End of if */
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    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 */
         fprintf(ficresprob,"\n%d ",(int)age);    return -l;
   }
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)  
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));  /*************** log-likelihood *************/
    double funcone( double *x)
       }  {
     }    /* Same as likeli but slower because of a lot of printf and if */
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    int i, ii, j, k, mi, d, kk;
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    double **out;
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    double lli; /* Individual log likelihood */
   }    double llt;
   free_vector(xp,1,npar);    int s1, s2;
   fclose(ficresprob);    double bbh, survp;
      /*extern weight */
 }    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
 /******************* Printing html file ***********/    /*for(i=1;i<imx;i++) 
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \      printf(" %d\n",s[4][i]);
  int lastpass, int stepm, int weightopt, char model[],\    */
  int imx,int jmin, int jmax, double jmeanint,char optionfile[], \    cov[1]=1.;
  char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\  
  char version[], int popforecast, int estepm ){    for(k=1; k<=nlstate; k++) ll[k]=0.;
   int jj1, k1, i1, cpt;  
   FILE *fichtm;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   /*char optionfilehtm[FILENAMELENGTH];*/      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(mi=1; mi<= wav[i]-1; mi++){
   strcpy(optionfilehtm,optionfile);        for (ii=1;ii<=nlstate+ndeath;ii++)
   strcat(optionfilehtm,".htm");          for (j=1;j<=nlstate+ndeath;j++){
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     printf("Problem with %s \n",optionfilehtm), exit(0);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   }          }
         for(d=0; d<dh[mi][i]; d++){
  fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n          newm=savm;
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 \n          for (kk=1; kk<=cptcovage;kk++) {
 Total number of observations=%d <br>\n            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n          }
 <hr  size=\"2\" color=\"#EC5E5E\">          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
  <ul><li>Outputs files<br>\n          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
  - Gnuplot file name: <a href=\"%s\">%s</a><br>\n          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
  - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
  - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>\n          savm=oldm;
  - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>\n          oldm=newm;
  - 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);        } /* end mult */
         
  fprintf(fichtm,"\n        s1=s[mw[mi][i]][i];
  - Parameter file with estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>\n        s2=s[mw[mi+1][i]][i];
   - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n        bbh=(double)bh[mi][i]/(double)stepm; 
  - Variances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n        /* bias is positive if real duration
  - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>\n         * is higher than the multiple of stepm and negative otherwise.
  - 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( s2 > nlstate && (mle <5) ){  /* Jackson */
  if(popforecast==1) fprintf(fichtm,"\n          lli=log(out[s1][s2] - savm[s1][s2]);
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n        } else if  (s2==-2) {
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n          for (j=1,survp=0. ; j<=nlstate; j++) 
         <br>",fileres,fileres,fileres,fileres);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
  else          lli= log(survp);
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);        }else if (mle==1){
 fprintf(fichtm," <li>Graphs</li><p>");          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         } else if(mle==2){
  m=cptcoveff;          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 */
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}        } 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 */
  jj1=0;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
  for(k1=1; k1<=m;k1++){          lli=log(out[s1][s2]); /* Original formula */
    for(i1=1; i1<=ncodemax[k1];i1++){        } else{  /* mle=0 back to 1 */
        jj1++;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
        if (cptcovn > 0) {          /*lli=log(out[s1][s2]); */ /* Original formula */
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");        } /* End of if */
          for (cpt=1; cpt<=cptcoveff;cpt++)        ipmx +=1;
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);        sw += weight[i];
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");        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(fichtm,"<br>- Probabilities: pe%s%d.png<br>        if(globpr){
 <img src=\"pe%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
        for(cpt=1; cpt<nlstate;cpt++){   %11.6f %11.6f %11.6f ", \
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.png<br>                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
        }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     for(cpt=1; cpt<=nlstate;cpt++) {            llt +=ll[k]*gipmx/gsw;
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
 interval) in state (%d): v%s%d%d.png <br>          }
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            fprintf(ficresilk," %10.6f\n", -llt);
      }        }
      for(cpt=1; cpt<=nlstate;cpt++) {      } /* end of wave */
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>    } /* end of individual */
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
 health expectancies in states (1) and (2): e%s%d.png<br>    if(globpr==0){ /* First time we count the contributions and weights */
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      gipmx=ipmx;
 fprintf(fichtm,"\n</body>");      gsw=sw;
    }    }
    }    return -l;
 fclose(fichtm);  }
 }  
   
 /******************* Gnuplot file **************/  /*************** function likelione ***********/
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;    /* This routine should help understanding what is done with 
        the selection of individuals/waves and
   strcpy(optionfilegnuplot,optionfilefiname);       to check the exact contribution to the likelihood.
   strcat(optionfilegnuplot,".gp.txt");       Plotting could be done.
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {     */
     printf("Problem with file %s",optionfilegnuplot);    int k;
   }  
     if(*globpri !=0){ /* Just counts and sums, no printings */
 #ifdef windows      strcpy(fileresilk,"ilk"); 
     fprintf(ficgp,"cd \"%s\" \n",pathc);      strcat(fileresilk,fileres);
 #endif      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
 m=pow(2,cptcoveff);        printf("Problem with resultfile: %s\n", fileresilk);
          fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
  /* 1eme*/      }
   for (cpt=1; cpt<= nlstate ; cpt ++) {      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
    for (k1=1; k1<= m ; k1 ++) {      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]); */
 #ifdef windows      for(k=1; k<=nlstate; k++) 
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n\n",strtok(optionfile, "."),cpt,k1);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
 #endif    }
 #ifdef unix  
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n\n",strtok(optionfile, "."),cpt,k1);    *fretone=(*funcone)(p);
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);    if(*globpri !=0){
 #endif      fclose(ficresilk);
       fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
 for (i=1; i<= nlstate ; i ++) {      fflush(fichtm); 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");    return;
 }  }
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);  
     for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  /*********** Maximum Likelihood Estimation ***************/
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  {
      for (i=1; i<= nlstate ; i ++) {    int i,j, iter=0;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    double **xi;
   else fprintf(ficgp," \%%*lf (\%%*lf)");    double fret;
 }      double fretone; /* Only one call to likelihood */
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    /*  char filerespow[FILENAMELENGTH];*/
 #ifdef unix  
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");  #ifdef NLOPT
 #endif    int creturn;
    }    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 *\/ */
   /*2 eme*/    double *lb;
     double minf; /* the minimum objective value, upon return */
   for (k1=1; k1<= m ; k1 ++) {    double * p1; /* Shifted parameters from 0 instead of 1 */
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n\n",strtok(optionfile, "."),k1);    myfunc_data dinst, *d = &dinst;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);  #endif
      
     for (i=1; i<= nlstate+1 ; i ++) {  
       k=2*i;    xi=matrix(1,npar,1,npar);
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    for (i=1;i<=npar;i++)
       for (j=1; j<= nlstate+1 ; j ++) {      for (j=1;j<=npar;j++)
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        xi[i][j]=(i==j ? 1.0 : 0.0);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    printf("Powell\n");  fprintf(ficlog,"Powell\n");
 }      strcpy(filerespow,"pow"); 
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    strcat(filerespow,fileres);
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);      printf("Problem with resultfile: %s\n", filerespow);
       for (j=1; j<= nlstate+1 ; j ++) {      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    }
         else fprintf(ficgp," \%%*lf (\%%*lf)");    fprintf(ficrespow,"# Powell\n# iter -2*LL");
 }      for (i=1;i<=nlstate;i++)
       fprintf(ficgp,"\" t\"\" w l 0,");      for(j=1;j<=nlstate+ndeath;j++)
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       for (j=1; j<= nlstate+1 ; j ++) {    fprintf(ficrespow,"\n");
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  #ifdef POWELL
   else fprintf(ficgp," \%%*lf (\%%*lf)");    powell(p,xi,npar,ftol,&iter,&fret,func);
 }    #endif
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");  
       else fprintf(ficgp,"\" t\"\" w l 0,");  #ifdef NLOPT
     }  #ifdef NEWUOA
   }    opt = nlopt_create(NLOPT_LN_NEWUOA,npar);
    #else
   /*3eme*/    opt = nlopt_create(NLOPT_LN_BOBYQA,npar);
   #endif
   for (k1=1; k1<= m ; k1 ++) {    lb=vector(0,npar-1);
     for (cpt=1; cpt<= nlstate ; cpt ++) {    for (i=0;i<npar;i++) lb[i]= -HUGE_VAL;
       k=2+nlstate*(2*cpt-2);    nlopt_set_lower_bounds(opt, lb);
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n\n",strtok(optionfile, "."),cpt,k1);    nlopt_set_initial_step1(opt, 0.1);
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);    
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    p1= (p+1); /*  p *(p+1)@8 and p *(p1)@8 are equal p1[0]=p[1] */
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    d->function = func;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);    printf(" Func %.12lf \n",myfunc(npar,p1,NULL,d));
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    nlopt_set_min_objective(opt, myfunc, d);
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    nlopt_set_xtol_rel(opt, ftol);
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);    if ((creturn=nlopt_optimize(opt, p1, &minf)) < 0) {
       printf("nlopt failed! %d\n",creturn); 
 */    }
       for (i=1; i< nlstate ; i ++) {    else {
         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);      printf("found minimum after %d evaluations (NLOPT=%d)\n", countcallfunc ,NLOPT);
       printf("found minimum at f(%g,%g) = %0.10g\n", p[0], p[1], minf);
       }      iter=1; /* not equal */
     }    }
   }    nlopt_destroy(opt);
    #endif
   /* CV preval stat */    free_matrix(xi,1,npar,1,npar);
     for (k1=1; k1<= m ; k1 ++) {    fclose(ficrespow);
     for (cpt=1; cpt<nlstate ; cpt ++) {    printf("\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
       k=3;    fprintf(ficlog,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
       fprintf(ficgp,"set out \"p%s%d%d.png\" \n\n",strtok(optionfile, "."),cpt,k1);    fprintf(ficres,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);  
   }
       for (i=1; i< nlstate ; i ++)  
         fprintf(ficgp,"+$%d",k+i+1);  /**** Computes Hessian and covariance matrix ***/
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
        {
       l=3+(nlstate+ndeath)*cpt;    double  **a,**y,*x,pd;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    double **hess;
       for (i=1; i< nlstate ; i ++) {    int i, j;
         l=3+(nlstate+ndeath)*cpt;    int *indx;
         fprintf(ficgp,"+$%d",l+i+1);  
       }    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     }    void lubksb(double **a, int npar, int *indx, double b[]) ;
   }      void ludcmp(double **a, int npar, int *indx, double *d) ;
      double gompertz(double p[]);
   /* proba elementaires */    hess=matrix(1,npar,1,npar);
    for(i=1,jk=1; i <=nlstate; i++){  
     for(k=1; k <=(nlstate+ndeath); k++){    printf("\nCalculation of the hessian matrix. Wait...\n");
       if (k != i) {    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
         for(j=1; j <=ncovmodel; j++){    for (i=1;i<=npar;i++){
              printf("%d",i);fflush(stdout);
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);      fprintf(ficlog,"%d",i);fflush(ficlog);
           jk++;     
           fprintf(ficgp,"\n");       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
         }      
       }      /*  printf(" %f ",p[i]);
     }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
    }    }
     
    for(jk=1; jk <=m; jk++) {    for (i=1;i<=npar;i++) {
      fprintf(ficgp,"\nset out \"pe%s%d.png\" \n\n",strtok(optionfile, "."),jk);      for (j=1;j<=npar;j++)  {
      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);        if (j>i) { 
      i=1;          printf(".%d%d",i,j);fflush(stdout);
      for(k2=1; k2<=nlstate; k2++) {          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
        k3=i;          hess[i][j]=hessij(p,delti,i,j,func,npar);
        for(k=1; k<=(nlstate+ndeath); k++) {          
          if (k != k2){          hess[j][i]=hess[i][j];    
            fprintf(ficgp," exp(p%d+p%d*x",i,i+1);          /*printf(" %lf ",hess[i][j]);*/
            ij=1;        }
            for(j=3; j <=ncovmodel; j++) {      }
              if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    }
                fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    printf("\n");
                ij++;    fprintf(ficlog,"\n");
              }  
              else    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
                fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
            }    
            fprintf(ficgp,")/(1");    a=matrix(1,npar,1,npar);
                y=matrix(1,npar,1,npar);
            for(k1=1; k1 <=nlstate; k1++){      x=vector(1,npar);
              fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    indx=ivector(1,npar);
              ij=1;    for (i=1;i<=npar;i++)
              for(j=3; j <=ncovmodel; j++){      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    ludcmp(a,npar,indx,&pd);
                  fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);  
                  ij++;    for (j=1;j<=npar;j++) {
                }      for (i=1;i<=npar;i++) x[i]=0;
                else      x[j]=1;
                  fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      lubksb(a,npar,indx,x);
              }      for (i=1;i<=npar;i++){ 
              fprintf(ficgp,")");        matcov[i][j]=x[i];
            }      }
            fprintf(ficgp,") t \"p%d%d\" ", k2,k);    }
            if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");  
            i=i+ncovmodel;    printf("\n#Hessian matrix#\n");
          }    fprintf(ficlog,"\n#Hessian matrix#\n");
        }    for (i=1;i<=npar;i++) { 
      }      for (j=1;j<=npar;j++) { 
    }        printf("%.3e ",hess[i][j]);
            fprintf(ficlog,"%.3e ",hess[i][j]);
    fclose(ficgp);      }
 }  /* end gnuplot */      printf("\n");
       fprintf(ficlog,"\n");
     }
 /*************** Moving average **************/  
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){    /* Recompute Inverse */
     for (i=1;i<=npar;i++)
   int i, cpt, cptcod;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)    ludcmp(a,npar,indx,&pd);
       for (i=1; i<=nlstate;i++)  
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    /*  printf("\n#Hessian matrix recomputed#\n");
           mobaverage[(int)agedeb][i][cptcod]=0.;  
        for (j=1;j<=npar;j++) {
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){      for (i=1;i<=npar;i++) x[i]=0;
       for (i=1; i<=nlstate;i++){      x[j]=1;
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      lubksb(a,npar,indx,x);
           for (cpt=0;cpt<=4;cpt++){      for (i=1;i<=npar;i++){ 
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];        y[i][j]=x[i];
           }        printf("%.3e ",y[i][j]);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;        fprintf(ficlog,"%.3e ",y[i][j]);
         }      }
       }      printf("\n");
     }      fprintf(ficlog,"\n");
        }
 }    */
   
     free_matrix(a,1,npar,1,npar);
 /************** Forecasting ******************/    free_matrix(y,1,npar,1,npar);
 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){    free_vector(x,1,npar);
      free_ivector(indx,1,npar);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    free_matrix(hess,1,npar,1,npar);
   int *popage;  
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  
   double *popeffectif,*popcount;  }
   double ***p3mat;  
   char fileresf[FILENAMELENGTH];  /*************** hessian matrix ****************/
   double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
  agelim=AGESUP;  {
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    int i;
     int l=1, lmax=20;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    double k1,k2;
      double p2[MAXPARM+1]; /* identical to x */
      double res;
   strcpy(fileresf,"f");    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   strcat(fileresf,fileres);    double fx;
   if((ficresf=fopen(fileresf,"w"))==NULL) {    int k=0,kmax=10;
     printf("Problem with forecast resultfile: %s\n", fileresf);    double l1;
   }  
   printf("Computing forecasting: result on file '%s' \n", fileresf);    fx=func(x);
     for (i=1;i<=npar;i++) p2[i]=x[i];
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
       l1=pow(10,l);
   if (mobilav==1) {      delts=delt;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(k=1 ; k <kmax; k=k+1){
     movingaverage(agedeb, fage, ageminpar, mobaverage);        delt = delta*(l1*k);
   }        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
   stepsize=(int) (stepm+YEARM-1)/YEARM;        p2[theta]=x[theta]-delt;
   if (stepm<=12) stepsize=1;        k2=func(p2)-fx;
          /*res= (k1-2.0*fx+k2)/delt/delt; */
   agelim=AGESUP;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
          
   hstepm=1;  #ifdef DEBUGHESS
   hstepm=hstepm/stepm;        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);
   yp1=modf(dateintmean,&yp);        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);
   anprojmean=yp;  #endif
   yp2=modf((yp1*12),&yp);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   mprojmean=yp;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   yp1=modf((yp2*30.5),&yp);          k=kmax;
   jprojmean=yp;        }
   if(jprojmean==0) jprojmean=1;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   if(mprojmean==0) jprojmean=1;          k=kmax; l=lmax*10;
          }
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            delts=delt;
   for(cptcov=1;cptcov<=i2;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      }
       k=k+1;    }
       fprintf(ficresf,"\n#******");    delti[theta]=delts;
       for(j=1;j<=cptcoveff;j++) {    return res; 
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    
       }  }
       fprintf(ficresf,"******\n");  
       fprintf(ficresf,"# StartingAge FinalAge");  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  {
          int i;
          int l=1, lmax=20;
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {    double k1,k2,k3,k4,res,fx;
         fprintf(ficresf,"\n");    double p2[MAXPARM+1];
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      int k;
   
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    fx=func(x);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    for (k=1; k<=2; k++) {
           nhstepm = nhstepm/hstepm;      for (i=1;i<=npar;i++) p2[i]=x[i];
                p2[thetai]=x[thetai]+delti[thetai]/k;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           oldm=oldms;savm=savms;      k1=func(p2)-fx;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      
              p2[thetai]=x[thetai]+delti[thetai]/k;
           for (h=0; h<=nhstepm; h++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
             if (h==(int) (calagedate+YEARM*cpt)) {      k2=func(p2)-fx;
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    
             }      p2[thetai]=x[thetai]-delti[thetai]/k;
             for(j=1; j<=nlstate+ndeath;j++) {      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
               kk1=0.;kk2=0;      k3=func(p2)-fx;
               for(i=1; i<=nlstate;i++) {                  
                 if (mobilav==1)      p2[thetai]=x[thetai]-delti[thetai]/k;
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                 else {      k4=func(p2)-fx;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
                 }  #ifdef DEBUG
                      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
               }      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);
               if (h==(int)(calagedate+12*cpt)){  #endif
                 fprintf(ficresf," %.3f", kk1);    }
                            return res;
               }  }
             }  
           }  /************** Inverse of matrix **************/
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  void ludcmp(double **a, int n, int *indx, double *d) 
         }  { 
       }    int i,imax,j,k; 
     }    double big,dum,sum,temp; 
   }    double *vv; 
           
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    vv=vector(1,n); 
     *d=1.0; 
   fclose(ficresf);    for (i=1;i<=n;i++) { 
 }      big=0.0; 
 /************** Forecasting ******************/      for (j=1;j<=n;j++) 
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){        if ((temp=fabs(a[i][j])) > big) big=temp; 
        if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      vv[i]=1.0/big; 
   int *popage;    } 
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    for (j=1;j<=n;j++) { 
   double *popeffectif,*popcount;      for (i=1;i<j;i++) { 
   double ***p3mat,***tabpop,***tabpopprev;        sum=a[i][j]; 
   char filerespop[FILENAMELENGTH];        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      } 
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      big=0.0; 
   agelim=AGESUP;      for (i=j;i<=n;i++) { 
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;        sum=a[i][j]; 
          for (k=1;k<j;k++) 
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);          sum -= a[i][k]*a[k][j]; 
          a[i][j]=sum; 
          if ( (dum=vv[i]*fabs(sum)) >= big) { 
   strcpy(filerespop,"pop");          big=dum; 
   strcat(filerespop,fileres);          imax=i; 
   if((ficrespop=fopen(filerespop,"w"))==NULL) {        } 
     printf("Problem with forecast resultfile: %s\n", filerespop);      } 
   }      if (j != imax) { 
   printf("Computing forecasting: result on file '%s' \n", filerespop);        for (k=1;k<=n;k++) { 
           dum=a[imax][k]; 
   if (cptcoveff==0) ncodemax[cptcoveff]=1;          a[imax][k]=a[j][k]; 
           a[j][k]=dum; 
   if (mobilav==1) {        } 
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        *d = -(*d); 
     movingaverage(agedeb, fage, ageminpar, mobaverage);        vv[imax]=vv[j]; 
   }      } 
       indx[j]=imax; 
   stepsize=(int) (stepm+YEARM-1)/YEARM;      if (a[j][j] == 0.0) a[j][j]=TINY; 
   if (stepm<=12) stepsize=1;      if (j != n) { 
          dum=1.0/(a[j][j]); 
   agelim=AGESUP;        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
        } 
   hstepm=1;    } 
   hstepm=hstepm/stepm;    free_vector(vv,1,n);  /* Doesn't work */
    ;
   if (popforecast==1) {  } 
     if((ficpop=fopen(popfile,"r"))==NULL) {  
       printf("Problem with population file : %s\n",popfile);exit(0);  void lubksb(double **a, int n, int *indx, double b[]) 
     }  { 
     popage=ivector(0,AGESUP);    int i,ii=0,ip,j; 
     popeffectif=vector(0,AGESUP);    double sum; 
     popcount=vector(0,AGESUP);   
        for (i=1;i<=n;i++) { 
     i=1;        ip=indx[i]; 
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;      sum=b[ip]; 
          b[ip]=b[i]; 
     imx=i;      if (ii) 
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   }      else if (sum) ii=i; 
       b[i]=sum; 
   for(cptcov=1;cptcov<=i2;cptcov++){    } 
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    for (i=n;i>=1;i--) { 
       k=k+1;      sum=b[i]; 
       fprintf(ficrespop,"\n#******");      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       for(j=1;j<=cptcoveff;j++) {      b[i]=sum/a[i][i]; 
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    } 
       }  } 
       fprintf(ficrespop,"******\n");  
       fprintf(ficrespop,"# Age");  void pstamp(FILE *fichier)
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);  {
       if (popforecast==1)  fprintf(ficrespop," [Population]");    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
        }
       for (cpt=0; cpt<=0;cpt++) {  
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);    /************ Frequencies ********************/
          void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){  {  /* Some frequencies */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    
           nhstepm = nhstepm/hstepm;    int i, m, jk, j1, bool, z1,j;
              int first;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double ***freq; /* Frequencies */
           oldm=oldms;savm=savms;    double *pp, **prop;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double pos,posprop, k2, dateintsum=0,k2cpt=0;
            char fileresp[FILENAMELENGTH];
           for (h=0; h<=nhstepm; h++){    
             if (h==(int) (calagedate+YEARM*cpt)) {    pp=vector(1,nlstate);
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    prop=matrix(1,nlstate,iagemin,iagemax+3);
             }    strcpy(fileresp,"p");
             for(j=1; j<=nlstate+ndeath;j++) {    strcat(fileresp,fileres);
               kk1=0.;kk2=0;    if((ficresp=fopen(fileresp,"w"))==NULL) {
               for(i=1; i<=nlstate;i++) {                    printf("Problem with prevalence resultfile: %s\n", fileresp);
                 if (mobilav==1)      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      exit(0);
                 else {    }
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
                 }    j1=0;
               }    
               if (h==(int)(calagedate+12*cpt)){    j=cptcoveff;
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
                   /*fprintf(ficrespop," %.3f", kk1);  
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/    first=1;
               }  
             }    /* for(k1=1; k1<=j ; k1++){ */  /* Loop on covariates */
             for(i=1; i<=nlstate;i++){    /*  for(i1=1; i1<=ncodemax[k1];i1++){ */ /* Now it is 2 */
               kk1=0.;    /*    j1++; */
                 for(j=1; j<=nlstate;j++){    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
                 }          scanf("%d", i);*/
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];        for (i=-5; i<=nlstate+ndeath; i++)  
             }          for (jk=-5; jk<=nlstate+ndeath; jk++)  
             for(m=iagemin; m <= iagemax+3; m++)
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)              freq[i][jk][m]=0;
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);        
           }        for (i=1; i<=nlstate; i++)  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for(m=iagemin; m <= iagemax+3; m++)
         }            prop[i][m]=0;
       }        
          dateintsum=0;
   /******/        k2cpt=0;
         for (i=1; i<=imx; i++) {
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {          bool=1;
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);            if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){            for (z1=1; z1<=cptcoveff; z1++)       
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
           nhstepm = nhstepm/hstepm;                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
                          bool=0;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                /* 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", 
           oldm=oldms;savm=savms;                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                    j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
           for (h=0; h<=nhstepm; h++){                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
             if (h==(int) (calagedate+YEARM*cpt)) {              } 
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);          }
             }   
             for(j=1; j<=nlstate+ndeath;j++) {          if (bool==1){
               kk1=0.;kk2=0;            for(m=firstpass; m<=lastpass; m++){
               for(i=1; i<=nlstate;i++) {                            k2=anint[m][i]+(mint[m][i]/12.);
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];                  /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
               }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
             }                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
           }                if (m<lastpass) {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
         }                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
       }                }
    }                
   }                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                    dateintsum=dateintsum+k2;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                  k2cpt++;
                 }
   if (popforecast==1) {                /*}*/
     free_ivector(popage,0,AGESUP);            }
     free_vector(popeffectif,0,AGESUP);          }
     free_vector(popcount,0,AGESUP);        } /* end i */
   }         
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        pstamp(ficresp);
   fclose(ficrespop);        if  (cptcovn>0) {
 }          fprintf(ficresp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 /***********************************************/          fprintf(ficresp, "**********\n#");
 /**************** Main Program *****************/          fprintf(ficlog, "\n#********** Variable "); 
 /***********************************************/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficlog, "**********\n#");
 int main(int argc, char *argv[])        }
 {        for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;        fprintf(ficresp, "\n");
   double agedeb, agefin,hf;        
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;        for(i=iagemin; i <= iagemax+3; i++){
           if(i==iagemax+3){
   double fret;            fprintf(ficlog,"Total");
   double **xi,tmp,delta;          }else{
             if(first==1){
   double dum; /* Dummy variable */              first=0;
   double ***p3mat;              printf("See log file for details...\n");
   int *indx;            }
   char line[MAXLINE], linepar[MAXLINE];            fprintf(ficlog,"Age %d", i);
   char title[MAXLINE];          }
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];          for(jk=1; jk <=nlstate ; jk++){
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                pp[jk] += freq[jk][m][i]; 
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];          }
           for(jk=1; jk <=nlstate ; jk++){
   char filerest[FILENAMELENGTH];            for(m=-1, pos=0; m <=0 ; m++)
   char fileregp[FILENAMELENGTH];              pos += freq[jk][m][i];
   char popfile[FILENAMELENGTH];            if(pp[jk]>=1.e-10){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];              if(first==1){
   int firstobs=1, lastobs=10;                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   int sdeb, sfin; /* Status at beginning and end */              }
   int c,  h , cpt,l;              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   int ju,jl, mi;            }else{
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;              if(first==1)
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   int mobilav=0,popforecast=0;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   int hstepm, nhstepm;            }
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;          }
   
   double bage, fage, age, agelim, agebase;          for(jk=1; jk <=nlstate ; jk++){
   double ftolpl=FTOL;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   double **prlim;              pp[jk] += freq[jk][m][i];
   double *severity;          }       
   double ***param; /* Matrix of parameters */          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
   double  *p;            pos += pp[jk];
   double **matcov; /* Matrix of covariance */            posprop += prop[jk][i];
   double ***delti3; /* Scale */          }
   double *delti; /* Scale */          for(jk=1; jk <=nlstate ; jk++){
   double ***eij, ***vareij;            if(pos>=1.e-5){
   double **varpl; /* Variances of prevalence limits by age */              if(first==1)
   double *epj, vepp;                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   double kk1, kk2;              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;            }else{
                if(first==1)
                 printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   char version[80]="Imach version 0.8d, May 2002, INED-EUROREVES ";              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   char *alph[]={"a","a","b","c","d","e"}, str[4];            }
             if( i <= iagemax){
               if(pos>=1.e-5){
   char z[1]="c", occ;                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
 #include <sys/time.h>                /*probs[i][jk][j1]= pp[jk]/pos;*/
 #include <time.h>                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];              }
                else
   /* long total_usecs;                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   struct timeval start_time, end_time;            }
            }
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */          
   getcwd(pathcd, size);          for(jk=-1; jk <=nlstate+ndeath; jk++)
             for(m=-1; m <=nlstate+ndeath; m++)
   printf("\n%s",version);              if(freq[jk][m][i] !=0 ) {
   if(argc <=1){              if(first==1)
     printf("\nEnter the parameter file name: ");                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
     scanf("%s",pathtot);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   }              }
   else{          if(i <= iagemax)
     strcpy(pathtot,argv[1]);            fprintf(ficresp,"\n");
   }          if(first==1)
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/            printf("Others in log...\n");
   /*cygwin_split_path(pathtot,path,optionfile);          fprintf(ficlog,"\n");
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/        }
   /* cutv(path,optionfile,pathtot,'\\');*/        /*}*/
     }
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    dateintmean=dateintsum/k2cpt; 
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);   
   chdir(path);    fclose(ficresp);
   replace(pathc,path);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     free_vector(pp,1,nlstate);
 /*-------- arguments in the command line --------*/    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     /* End of Freq */
   strcpy(fileres,"r");  }
   strcat(fileres, optionfilefiname);  
   strcat(fileres,".txt");    /* Other files have txt extension */  /************ 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)
   /*---------arguments file --------*/  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   if((ficpar=fopen(optionfile,"r"))==NULL)    {       in each health status at the date of interview (if between dateprev1 and dateprev2).
     printf("Problem with optionfile %s\n",optionfile);       We still use firstpass and lastpass as another selection.
     goto end;    */
   }   
     int i, m, jk, j1, bool, z1,j;
   strcpy(filereso,"o");  
   strcat(filereso,fileres);    double **prop;
   if((ficparo=fopen(filereso,"w"))==NULL) {    double posprop; 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    double  y2; /* in fractional years */
   }    int iagemin, iagemax;
     int first; /** to stop verbosity which is redirected to log file */
   /* Reads comments: lines beginning with '#' */  
   while((c=getc(ficpar))=='#' && c!= EOF){    iagemin= (int) agemin;
     ungetc(c,ficpar);    iagemax= (int) agemax;
     fgets(line, MAXLINE, ficpar);    /*pp=vector(1,nlstate);*/
     puts(line);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     fputs(line,ficparo);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   }    j1=0;
   ungetc(c,ficpar);    
     /*j=cptcoveff;*/
   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);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   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);    first=1;
 while((c=getc(ficpar))=='#' && c!= EOF){    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
     ungetc(c,ficpar);      /*for(i1=1; i1<=ncodemax[k1];i1++){
     fgets(line, MAXLINE, ficpar);        j1++;*/
     puts(line);        
     fputs(line,ficparo);        for (i=1; i<=nlstate; i++)  
   }          for(m=iagemin; m <= iagemax+3; m++)
   ungetc(c,ficpar);            prop[i][m]=0.0;
         
            for (i=1; i<=imx; i++) { /* Each individual */
   covar=matrix(0,NCOVMAX,1,n);          bool=1;
   cptcovn=0;          if  (cptcovn>0) {
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;            for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   ncovmodel=2+cptcovn;                bool=0;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */          } 
            if (bool==1) { 
   /* Read guess parameters */            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
   /* Reads comments: lines beginning with '#' */              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
   while((c=getc(ficpar))=='#' && c!= EOF){              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     ungetc(c,ficpar);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     fgets(line, MAXLINE, ficpar);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     puts(line);                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); 
     fputs(line,ficparo);                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]]);*/
   ungetc(c,ficpar);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
                    prop[s[m][i]][iagemax+3] += weight[i]; 
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);                } 
     for(i=1; i <=nlstate; i++)              }
     for(j=1; j <=nlstate+ndeath-1; j++){            } /* end selection of waves */
       fscanf(ficpar,"%1d%1d",&i1,&j1);          }
       fprintf(ficparo,"%1d%1d",i1,j1);        }
       printf("%1d%1d",i,j);        for(i=iagemin; i <= iagemax+3; i++){  
       for(k=1; k<=ncovmodel;k++){          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
         fscanf(ficpar," %lf",&param[i][j][k]);            posprop += prop[jk][i]; 
         printf(" %lf",param[i][j][k]);          } 
         fprintf(ficparo," %lf",param[i][j][k]);          
       }          for(jk=1; jk <=nlstate ; jk++){     
       fscanf(ficpar,"\n");            if( i <=  iagemax){ 
       printf("\n");              if(posprop>=1.e-5){ 
       fprintf(ficparo,"\n");                probs[i][jk][j1]= prop[jk][i]/posprop;
     }              } else{
                  if(first==1){
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;                  first=0;
                   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]);
   p=param[1][1];                }
                }
   /* Reads comments: lines beginning with '#' */            } 
   while((c=getc(ficpar))=='#' && c!= EOF){          }/* end jk */ 
     ungetc(c,ficpar);        }/* end i */ 
     fgets(line, MAXLINE, ficpar);      /*} *//* end i1 */
     puts(line);    } /* end j1 */
     fputs(line,ficparo);    
   }    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
   ungetc(c,ficpar);    /*free_vector(pp,1,nlstate);*/
     free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  }  /* End of prevalence */
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */  
   for(i=1; i <=nlstate; i++){  /************* Waves Concatenation ***************/
     for(j=1; j <=nlstate+ndeath-1; j++){  
       fscanf(ficpar,"%1d%1d",&i1,&j1);  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)
       printf("%1d%1d",i,j);  {
       fprintf(ficparo,"%1d%1d",i1,j1);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       for(k=1; k<=ncovmodel;k++){       Death is a valid wave (if date is known).
         fscanf(ficpar,"%le",&delti3[i][j][k]);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
         printf(" %le",delti3[i][j][k]);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
         fprintf(ficparo," %le",delti3[i][j][k]);       and mw[mi+1][i]. dh depends on stepm.
       }       */
       fscanf(ficpar,"\n");  
       printf("\n");    int i, mi, m;
       fprintf(ficparo,"\n");    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
     }       double sum=0., jmean=0.;*/
   }    int first;
   delti=delti3[1][1];    int j, k=0,jk, ju, jl;
      double sum=0.;
   /* Reads comments: lines beginning with '#' */    first=0;
   while((c=getc(ficpar))=='#' && c!= EOF){    jmin=100000;
     ungetc(c,ficpar);    jmax=-1;
     fgets(line, MAXLINE, ficpar);    jmean=0.;
     puts(line);    for(i=1; i<=imx; i++){
     fputs(line,ficparo);      mi=0;
   }      m=firstpass;
   ungetc(c,ficpar);      while(s[m][i] <= nlstate){
          if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
   matcov=matrix(1,npar,1,npar);          mw[++mi][i]=m;
   for(i=1; i <=npar; i++){        if(m >=lastpass)
     fscanf(ficpar,"%s",&str);          break;
     printf("%s",str);        else
     fprintf(ficparo,"%s",str);          m++;
     for(j=1; j <=i; j++){      }/* end while */
       fscanf(ficpar," %le",&matcov[i][j]);      if (s[m][i] > nlstate){
       printf(" %.5le",matcov[i][j]);        mi++;     /* Death is another wave */
       fprintf(ficparo," %.5le",matcov[i][j]);        /* if(mi==0)  never been interviewed correctly before death */
     }           /* Only death is a correct wave */
     fscanf(ficpar,"\n");        mw[mi][i]=m;
     printf("\n");      }
     fprintf(ficparo,"\n");  
   }      wav[i]=mi;
   for(i=1; i <=npar; i++)      if(mi==0){
     for(j=i+1;j<=npar;j++)        nbwarn++;
       matcov[i][j]=matcov[j][i];        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);
   printf("\n");          first=1;
         }
         if(first==1){
     /*-------- Rewriting paramater file ----------*/          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
      strcpy(rfileres,"r");    /* "Rparameterfile */        }
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/      } /* end mi==0 */
      strcat(rfileres,".");    /* */    } /* End individuals */
      strcat(rfileres,optionfilext);    /* Other files have txt extension */  
     if((ficres =fopen(rfileres,"w"))==NULL) {    for(i=1; i<=imx; i++){
       printf("Problem writing new parameter file: %s\n", fileres);goto end;      for(mi=1; mi<wav[i];mi++){
     }        if (stepm <=0)
     fprintf(ficres,"#%s\n",version);          dh[mi][i]=1;
            else{
     /*-------- data file ----------*/          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     if((fic=fopen(datafile,"r"))==NULL)    {            if (agedc[i] < 2*AGESUP) {
       printf("Problem with datafile: %s\n", datafile);goto end;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     }              if(j==0) j=1;  /* Survives at least one month after exam */
               else if(j<0){
     n= lastobs;                nberr++;
     severity = vector(1,maxwav);                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]);
     outcome=imatrix(1,maxwav+1,1,n);                j=1; /* Temporary Dangerous patch */
     num=ivector(1,n);                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);
     moisnais=vector(1,n);                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]);
     annais=vector(1,n);                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);
     moisdc=vector(1,n);              }
     andc=vector(1,n);              k=k+1;
     agedc=vector(1,n);              if (j >= jmax){
     cod=ivector(1,n);                jmax=j;
     weight=vector(1,n);                ijmax=i;
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */              }
     mint=matrix(1,maxwav,1,n);              if (j <= jmin){
     anint=matrix(1,maxwav,1,n);                jmin=j;
     s=imatrix(1,maxwav+1,1,n);                ijmin=i;
     adl=imatrix(1,maxwav+1,1,n);                  }
     tab=ivector(1,NCOVMAX);              sum=sum+j;
     ncodemax=ivector(1,8);              /*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);*/
     i=1;            }
     while (fgets(line, MAXLINE, fic) != NULL)    {          }
       if ((i >= firstobs) && (i <=lastobs)) {          else{
                    j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
         for (j=maxwav;j>=1;j--){  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  
           strcpy(line,stra);            k=k+1;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);            if (j >= jmax) {
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);              jmax=j;
         }              ijmax=i;
                    }
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            else if (j <= jmin){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);              jmin=j;
               ijmin=i;
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);            }
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);            /*        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]);*/
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);            if(j<0){
         for (j=ncovcol;j>=1;j--){              nberr++;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
         }              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
         num[i]=atol(stra);            }
                    sum=sum+j;
         /*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;}*/          jk= j/stepm;
           jl= j -jk*stepm;
         i=i+1;          ju= j -(jk+1)*stepm;
       }          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
     }            if(jl==0){
     /* printf("ii=%d", ij);              dh[mi][i]=jk;
        scanf("%d",i);*/              bh[mi][i]=0;
   imx=i-1; /* Number of individuals */            }else{ /* We want a negative bias in order to only have interpolation ie
                     * to avoid the price of an extra matrix product in likelihood */
   /* for (i=1; i<=imx; i++){              dh[mi][i]=jk+1;
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;              bh[mi][i]=ju;
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;            }
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;          }else{
     }*/            if(jl <= -ju){
    /*  for (i=1; i<=imx; i++){              dh[mi][i]=jk;
      if (s[4][i]==9)  s[4][i]=-1;              bh[mi][i]=jl;       /* bias is positive if real duration
      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]));}*/                                   * is higher than the multiple of stepm and negative otherwise.
                                     */
              }
   /* Calculation of the number of parameter from char model*/            else{
   Tvar=ivector(1,15);              dh[mi][i]=jk+1;
   Tprod=ivector(1,15);              bh[mi][i]=ju;
   Tvaraff=ivector(1,15);            }
   Tvard=imatrix(1,15,1,2);            if(dh[mi][i]==0){
   Tage=ivector(1,15);                    dh[mi][i]=1; /* At least one step */
                  bh[mi][i]=ju; /* At least one step */
   if (strlen(model) >1){              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
     j=0, j1=0, k1=1, k2=1;            }
     j=nbocc(model,'+');          } /* end if mle */
     j1=nbocc(model,'*');        }
     cptcovn=j+1;      } /* end wave */
     cptcovprod=j1;    }
        jmean=sum/k;
     strcpy(modelsav,model);    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);
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    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);
       printf("Error. Non available option model=%s ",model);   }
       goto end;  
     }  /*********** Tricode ****************************/
      void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
     for(i=(j+1); i>=1;i--){  {
       cutv(stra,strb,modelsav,'+');    /**< Uses cptcovn+2*cptcovprod as the number of covariates */
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/     * Boring subroutine which should only output nbcode[Tvar[j]][k]
       /*scanf("%d",i);*/     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
       if (strchr(strb,'*')) {     * nbcode[Tvar[j]][1]= 
         cutv(strd,strc,strb,'*');    */
         if (strcmp(strc,"age")==0) {  
           cptcovprod--;    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
           cutv(strb,stre,strd,'V');    int modmaxcovj=0; /* Modality max of covariates j */
           Tvar[i]=atoi(stre);    int cptcode=0; /* Modality max of covariates j */
           cptcovage++;    int modmincovj=0; /* Modality min of covariates j */
             Tage[cptcovage]=i;  
             /*printf("stre=%s ", stre);*/  
         }    cptcoveff=0; 
         else if (strcmp(strd,"age")==0) {   
           cptcovprod--;    for (k=-1; k < maxncov; k++) Ndum[k]=0;
           cutv(strb,stre,strc,'V');    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
           Tvar[i]=atoi(stre);  
           cptcovage++;    /* Loop on covariates without age and products */
           Tage[cptcovage]=i;    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
         }      for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
         else {                                 modality of this covariate Vj*/ 
           cutv(strb,stre,strc,'V');        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
           Tvar[i]=ncovcol+k1;                                      * If product of Vn*Vm, still boolean *:
           cutv(strb,strc,strd,'V');                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
           Tprod[k1]=i;                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
           Tvard[k1][1]=atoi(strc);        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
           Tvard[k1][2]=atoi(stre);                                        modality of the nth covariate of individual i. */
           Tvar[cptcovn+k2]=Tvard[k1][1];        if (ij > modmaxcovj)
           Tvar[cptcovn+k2+1]=Tvard[k1][2];          modmaxcovj=ij; 
           for (k=1; k<=lastobs;k++)        else if (ij < modmincovj) 
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];          modmincovj=ij; 
           k1++;        if ((ij < -1) && (ij > NCOVMAX)){
           k2=k2+2;          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
         }          exit(1);
       }        }else
       else {        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
        /*  scanf("%d",i);*/        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
       cutv(strd,strc,strb,'V');        /* getting the maximum value of the modality of the covariate
       Tvar[i]=atoi(strc);           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
       }           female is 1, then modmaxcovj=1.*/
       strcpy(modelsav,stra);        }
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
         scanf("%d",i);*/      cptcode=modmaxcovj;
     }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
 }     /*for (i=0; i<=cptcode; i++) {*/
        for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
   printf("cptcovprod=%d ", cptcovprod);        if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
   scanf("%d ",i);*/          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
     fclose(fic);        }
         /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
     /*  if(mle==1){*/           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
     if (weightopt != 1) { /* Maximisation without weights*/      } /* Ndum[-1] number of undefined modalities */
       for(i=1;i<=n;i++) weight[i]=1.0;  
     }      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
     /*-calculation of age at interview from date of interview and age at death -*/      /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
     agev=matrix(1,maxwav,1,imx);      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
          modmincovj=3; modmaxcovj = 7;
     for (i=1; i<=imx; i++) {         There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
       for(m=2; (m<= maxwav); m++) {         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){         variables V1_1 and V1_2.
          anint[m][i]=9999;         nbcode[Tvar[j]][ij]=k;
          s[m][i]=-1;         nbcode[Tvar[j]][1]=0;
        }         nbcode[Tvar[j]][2]=1;
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;         nbcode[Tvar[j]][3]=2;
       }      */
     }      ij=1; /* ij is similar to i but can jumps over null modalities */
       for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
     for (i=1; i<=imx; i++)  {        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          /*recode from 0 */
       for(m=1; (m<= maxwav); m++){          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
         if(s[m][i] >0){            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
           if (s[m][i] >= nlstate+1) {                                       k is a modality. If we have model=V1+V1*sex 
             if(agedc[i]>0)                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
               if(moisdc[i]!=99 && andc[i]!=9999)            ij++;
                 agev[m][i]=agedc[i];          }
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/          if (ij > ncodemax[j]) break; 
            else {        }  /* end of loop on */
               if (andc[i]!=9999){      } /* end of loop on modality */ 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
               agev[m][i]=-1;    
               }   for (k=-1; k< maxncov; k++) Ndum[k]=0; 
             }    
           }    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
           else if(s[m][i] !=9){ /* Should no more exist */     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
             if(mint[m][i]==99 || anint[m][i]==9999)     Ndum[ij]++; 
               agev[m][i]=1;   } 
             else if(agev[m][i] <agemin){  
               agemin=agev[m][i];   ij=1;
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
             }     /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
             else if(agev[m][i] >agemax){     if((Ndum[i]!=0) && (i<=ncovcol)){
               agemax=agev[m][i];       /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/       Tvaraff[ij]=i; /*For printing (unclear) */
             }       ij++;
             /*agev[m][i]=anint[m][i]-annais[i];*/     }else
             /*   agev[m][i] = age[i]+2*m;*/         Tvaraff[ij]=0;
           }   }
           else { /* =9 */   ij--;
             agev[m][i]=1;   cptcoveff=ij; /*Number of total covariates*/
             s[m][i]=-1;  
           }  }
         }  
         else /*= 0 Unknown */  
           agev[m][i]=1;  /*********** 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[] )
     }  
     for (i=1; i<=imx; i++)  {  {
       for(m=1; (m<= maxwav); m++){    /* Health expectancies, no variances */
         if (s[m][i] > (nlstate+ndeath)) {    int i, j, nhstepm, hstepm, h, nstepm;
           printf("Error: Wrong value in nlstate or ndeath\n");      int nhstepma, nstepma; /* Decreasing with age */
           goto end;    double age, agelim, hf;
         }    double ***p3mat;
       }    double eip;
     }  
     pstamp(ficreseij);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
     fprintf(ficreseij,"# Age");
     free_vector(severity,1,maxwav);    for(i=1; i<=nlstate;i++){
     free_imatrix(outcome,1,maxwav+1,1,n);      for(j=1; j<=nlstate;j++){
     free_vector(moisnais,1,n);        fprintf(ficreseij," e%1d%1d ",i,j);
     free_vector(annais,1,n);      }
     /* free_matrix(mint,1,maxwav,1,n);      fprintf(ficreseij," e%1d. ",i);
        free_matrix(anint,1,maxwav,1,n);*/    }
     free_vector(moisdc,1,n);    fprintf(ficreseij,"\n");
     free_vector(andc,1,n);  
     
        if(estepm < stepm){
     wav=ivector(1,imx);      printf ("Problem %d lower than %d\n",estepm, stepm);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    }
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    else  hstepm=estepm;   
        /* We compute the life expectancy from trapezoids spaced every estepm months
     /* Concatenates waves */     * This is mainly to measure the difference between two models: for example
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);     * 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
       Tcode=ivector(1,100);     * to the curvature of the survival function. If, for the same date, we 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       ncodemax[1]=1;     * to compare the new estimate of Life expectancy with the same linear 
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);     * hypothesis. A more precise result, taking into account a more precise
           * curvature will be obtained if estepm is as small as stepm. */
    codtab=imatrix(1,100,1,10);  
    h=0;    /* For example we decided to compute the life expectancy with the smallest unit */
    m=pow(2,cptcoveff);    /* 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 
    for(k=1;k<=cptcoveff; k++){       nstepm is the number of stepm from age to agelin. 
      for(i=1; i <=(m/pow(2,k));i++){       Look at hpijx to understand the reason of that which relies in memory size
        for(j=1; j <= ncodemax[k]; j++){       and note for a fixed period like estepm months */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
            h++;       survival function given by stepm (the optimization length). Unfortunately it
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;       means that if the survival funtion is printed only each two years of age and if
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/       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 */ 
    }  
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);    agelim=AGESUP;
       codtab[1][2]=1;codtab[2][2]=2; */    /* If stepm=6 months */
    /* for(i=1; i <=m ;i++){      /* Computed by stepm unit matrices, product of hstepm matrices, stored
       for(k=1; k <=cptcovn; k++){         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);      
       }  /* nhstepm age range expressed in number of stepm */
       printf("\n");    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       scanf("%d",i);*/    /* if (stepm >= YEARM) hstepm=1;*/
        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
    /* Calculates basic frequencies. Computes observed prevalence at single age    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        and prints on file fileres'p'. */  
     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 */ 
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* if (stepm >= YEARM) hstepm=1;*/
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      /* If stepm=6 months */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      /* Computed by stepm unit matrices, product of hstepma matrices, stored
               in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     /* 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] */      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     if(mle==1){      
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      printf("%d|",(int)age);fflush(stdout);
     }      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
          
     /*--------- results files --------------*/      /* Computing expectancies */
     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);      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++){
    jk=1;            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");            
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");            /* 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]);*/
    for(i=1,jk=1; i <=nlstate; i++){  
      for(k=1; k <=(nlstate+ndeath); k++){          }
        if (k != i)  
          {      fprintf(ficreseij,"%3.0f",age );
            printf("%d%d ",i,k);      for(i=1; i<=nlstate;i++){
            fprintf(ficres,"%1d%1d ",i,k);        eip=0;
            for(j=1; j <=ncovmodel; j++){        for(j=1; j<=nlstate;j++){
              printf("%f ",p[jk]);          eip +=eij[i][j][(int)age];
              fprintf(ficres,"%f ",p[jk]);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
              jk++;        }
            }        fprintf(ficreseij,"%9.4f", eip );
            printf("\n");      }
            fprintf(ficres,"\n");      fprintf(ficreseij,"\n");
          }      
      }    }
    }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  if(mle==1){    printf("\n");
     /* Computing hessian and covariance matrix */    fprintf(ficlog,"\n");
     ftolhess=ftol; /* Usually correct */    
     hesscov(matcov, p, npar, delti, ftolhess, func);  }
  }  
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
     printf("# Scales (for hessian or gradient estimation)\n");  
      for(i=1,jk=1; i <=nlstate; i++){  {
       for(j=1; j <=nlstate+ndeath; j++){    /* Covariances of health expectancies eij and of total life expectancies according
         if (j!=i) {     to initial status i, ei. .
           fprintf(ficres,"%1d%1d",i,j);    */
           printf("%1d%1d",i,j);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
           for(k=1; k<=ncovmodel;k++){    int nhstepma, nstepma; /* Decreasing with age */
             printf(" %.5e",delti[jk]);    double age, agelim, hf;
             fprintf(ficres," %.5e",delti[jk]);    double ***p3matp, ***p3matm, ***varhe;
             jk++;    double **dnewm,**doldm;
           }    double *xp, *xm;
           printf("\n");    double **gp, **gm;
           fprintf(ficres,"\n");    double ***gradg, ***trgradg;
         }    int theta;
       }  
      }    double eip, vip;
      
     k=1;    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     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");    xp=vector(1,npar);
     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");    xm=vector(1,npar);
     for(i=1;i<=npar;i++){    dnewm=matrix(1,nlstate*nlstate,1,npar);
       /*  if (k>nlstate) k=1;    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
       i1=(i-1)/(ncovmodel*nlstate)+1;    
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    pstamp(ficresstdeij);
       printf("%s%d%d",alph[k],i1,tab[i]);*/    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
       fprintf(ficres,"%3d",i);    fprintf(ficresstdeij,"# Age");
       printf("%3d",i);    for(i=1; i<=nlstate;i++){
       for(j=1; j<=i;j++){      for(j=1; j<=nlstate;j++)
         fprintf(ficres," %.5e",matcov[i][j]);        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
         printf(" %.5e",matcov[i][j]);      fprintf(ficresstdeij," e%1d. ",i);
       }    }
       fprintf(ficres,"\n");    fprintf(ficresstdeij,"\n");
       printf("\n");  
       k++;    pstamp(ficrescveij);
     }    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
        fprintf(ficrescveij,"# Age");
     while((c=getc(ficpar))=='#' && c!= EOF){    for(i=1; i<=nlstate;i++)
       ungetc(c,ficpar);      for(j=1; j<=nlstate;j++){
       fgets(line, MAXLINE, ficpar);        cptj= (j-1)*nlstate+i;
       puts(line);        for(i2=1; i2<=nlstate;i2++)
       fputs(line,ficparo);          for(j2=1; j2<=nlstate;j2++){
     }            cptj2= (j2-1)*nlstate+i2;
     ungetc(c,ficpar);            if(cptj2 <= cptj)
     estepm=0;              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
     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) {    fprintf(ficrescveij,"\n");
       bage = ageminpar;    
       fage = agemaxpar;    if(estepm < stepm){
     }      printf ("Problem %d lower than %d\n",estepm, stepm);
        }
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    else  hstepm=estepm;   
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);    /* We compute the life expectancy from trapezoids spaced every estepm months
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);     * 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
     while((c=getc(ficpar))=='#' && c!= EOF){     * we are calculating an estimate of the Life Expectancy assuming a linear 
     ungetc(c,ficpar);     * progression in between and thus overestimating or underestimating according
     fgets(line, MAXLINE, ficpar);     * to the curvature of the survival function. If, for the same date, we 
     puts(line);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     fputs(line,ficparo);     * to compare the new estimate of Life expectancy with the same linear 
   }     * hypothesis. A more precise result, taking into account a more precise
   ungetc(c,ficpar);     * curvature will be obtained if estepm is as small as stepm. */
    
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    /* For example we decided to compute the life expectancy with the smallest unit */
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);       nhstepm is the number of hstepm from age to agelim 
             nstepm is the number of stepm from age to agelin. 
   while((c=getc(ficpar))=='#' && c!= EOF){       Look at hpijx to understand the reason of that which relies in memory size
     ungetc(c,ficpar);       and note for a fixed period like estepm months */
     fgets(line, MAXLINE, ficpar);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     puts(line);       survival function given by stepm (the optimization length). Unfortunately it
     fputs(line,ficparo);       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 
   ungetc(c,ficpar);       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 */ 
    dateprev1=anprev1+mprev1/12.+jprev1/365.;  
    dateprev2=anprev2+mprev2/12.+jprev2/365.;    /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
   fscanf(ficpar,"pop_based=%d\n",&popbased);    agelim=AGESUP;
   fprintf(ficparo,"pop_based=%d\n",popbased);      nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
   fprintf(ficres,"pop_based=%d\n",popbased);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      /* if (stepm >= YEARM) hstepm=1;*/
   while((c=getc(ficpar))=='#' && c!= EOF){    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     ungetc(c,ficpar);    
     fgets(line, MAXLINE, ficpar);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     puts(line);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     fputs(line,ficparo);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
   }    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
   ungetc(c,ficpar);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     gm=matrix(0,nhstepm,1,nlstate*nlstate);
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);  
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);    for (age=bage; age<=fage; age ++){ 
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
 while((c=getc(ficpar))=='#' && c!= EOF){      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);      /* If stepm=6 months */
     puts(line);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     fputs(line,ficparo);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   }      
   ungetc(c,ficpar);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);      /* Computing  Variances of health expectancies */
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);         decrease memory allocation */
       for(theta=1; theta <=npar; theta++){
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
 /*------------ gnuplot -------------*/          xm[i] = x[i] - (i==theta ?delti[theta]:0);
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);        }
          hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
 /*------------ free_vector  -------------*/        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
  chdir(path);    
          for(j=1; j<= nlstate; j++){
  free_ivector(wav,1,imx);          for(i=1; i<=nlstate; i++){
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);            for(h=0; h<=nhstepm-1; h++){
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);                gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
  free_ivector(num,1,n);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
  free_vector(agedc,1,n);            }
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          }
  fclose(ficparo);        }
  fclose(ficres);       
         for(ij=1; ij<= nlstate*nlstate; ij++)
 /*--------- index.htm --------*/          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm);          }
       }/* End theta */
        
   /*--------------- Prevalence limit --------------*/      
        for(h=0; h<=nhstepm-1; h++)
   strcpy(filerespl,"pl");        for(j=1; j<=nlstate*nlstate;j++)
   strcat(filerespl,fileres);          for(theta=1; theta <=npar; theta++)
   if((ficrespl=fopen(filerespl,"w"))==NULL) {            trgradg[h][j][theta]=gradg[h][theta][j];
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      
   }  
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);       for(ij=1;ij<=nlstate*nlstate;ij++)
   fprintf(ficrespl,"#Prevalence limit\n");        for(ji=1;ji<=nlstate*nlstate;ji++)
   fprintf(ficrespl,"#Age ");          varhe[ij][ji][(int)age] =0.;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");       printf("%d|",(int)age);fflush(stdout);
         fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   prlim=matrix(1,nlstate,1,nlstate);       for(h=0;h<=nhstepm-1;h++){
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(k=0;k<=nhstepm-1;k++){
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          for(ij=1;ij<=nlstate*nlstate;ij++)
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */            for(ji=1;ji<=nlstate*nlstate;ji++)
   k=0;              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   agebase=ageminpar;        }
   agelim=agemaxpar;      }
   ftolpl=1.e-10;  
   i1=cptcoveff;      /* Computing expectancies */
   if (cptcovn < 1){i1=1;}      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
   for(cptcov=1;cptcov<=i1;cptcov++){        for(j=1; j<=nlstate;j++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
         k=k+1;            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/            
         fprintf(ficrespl,"\n#******");            /* 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]);*/
         for(j=1;j<=cptcoveff;j++)  
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          }
         fprintf(ficrespl,"******\n");  
              fprintf(ficresstdeij,"%3.0f",age );
         for (age=agebase; age<=agelim; age++){      for(i=1; i<=nlstate;i++){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        eip=0.;
           fprintf(ficrespl,"%.0f",age );        vip=0.;
           for(i=1; i<=nlstate;i++)        for(j=1; j<=nlstate;j++){
           fprintf(ficrespl," %.5f", prlim[i][i]);          eip += eij[i][j][(int)age];
           fprintf(ficrespl,"\n");          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]) );
     }        }
   fclose(ficrespl);        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }
   /*------------- h Pij x at various ages ------------*/      fprintf(ficresstdeij,"\n");
    
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      fprintf(ficrescveij,"%3.0f",age );
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      for(i=1; i<=nlstate;i++)
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;        for(j=1; j<=nlstate;j++){
   }          cptj= (j-1)*nlstate+i;
   printf("Computing pij: result on file '%s' \n", filerespij);          for(i2=1; i2<=nlstate;i2++)
              for(j2=1; j2<=nlstate;j2++){
   stepsize=(int) (stepm+YEARM-1)/YEARM;              cptj2= (j2-1)*nlstate+i2;
   /*if (stepm<=24) stepsize=2;*/              if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   agelim=AGESUP;            }
   hstepm=stepsize*YEARM; /* Every year of age */        }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */      fprintf(ficrescveij,"\n");
       
   k=0;    }
   for(cptcov=1;cptcov<=i1;cptcov++){    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
       k=k+1;    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
         fprintf(ficrespij,"\n#****** ");    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
         for(j=1;j<=cptcoveff;j++)    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fprintf(ficrespij,"******\n");    printf("\n");
            fprintf(ficlog,"\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 */    free_vector(xm,1,npar);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    free_vector(xp,1,npar);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
           oldm=oldms;savm=savms;    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
           fprintf(ficrespij,"# Age");  }
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)  /************ Variance ******************/
               fprintf(ficrespij," %1d-%1d",i,j);  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
           fprintf(ficrespij,"\n");  {
            for (h=0; h<=nhstepm; h++){    /* Variance of health expectancies */
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
             for(i=1; i<=nlstate;i++)    /* double **newm;*/
               for(j=1; j<=nlstate+ndeath;j++)    /* int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav)*/
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    
             fprintf(ficrespij,"\n");    int movingaverage();
              }    double **dnewm,**doldm;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double **dnewmp,**doldmp;
           fprintf(ficrespij,"\n");    int i, j, nhstepm, hstepm, h, nstepm ;
         }    int k;
     }    double *xp;
   }    double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);    double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
   fclose(ficrespij);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
     double age,agelim, hf;
   /*---------- Forecasting ------------------*/    double ***mobaverage;
   if((stepm == 1) && (strcmp(model,".")==0)){    int theta;
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);    char digit[4];
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    char digitp[25];
   }  
   else{    char fileresprobmorprev[FILENAMELENGTH];
     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);    if(popbased==1){
   }      if(mobilav!=0)
          strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
   /*---------- Health expectancies and variances ------------*/    }
     else 
   strcpy(filerest,"t");      strcpy(digitp,"-stablbased-");
   strcat(filerest,fileres);  
   if((ficrest=fopen(filerest,"w"))==NULL) {    if (mobilav!=0) {
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   }      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   printf("Computing Total LEs with variances: file '%s' \n", filerest);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
   strcpy(filerese,"e");    }
   strcat(filerese,fileres);  
   if((ficreseij=fopen(filerese,"w"))==NULL) {    strcpy(fileresprobmorprev,"prmorprev"); 
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    sprintf(digit,"%-d",ij);
   }    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
  strcpy(fileresv,"v");    strcat(fileresprobmorprev,fileres);
   strcat(fileresv,fileres);    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   if((ficresvij=fopen(fileresv,"w"))==NULL) {      printf("Problem with resultfile: %s\n", fileresprobmorprev);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   }    }
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   calagedate=-1;   
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     pstamp(ficresprobmorprev);
   k=0;    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
   for(cptcov=1;cptcov<=i1;cptcov++){    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       k=k+1;      fprintf(ficresprobmorprev," p.%-d SE",j);
       fprintf(ficrest,"\n#****** ");      for(i=1; i<=nlstate;i++)
       for(j=1;j<=cptcoveff;j++)        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    }  
       fprintf(ficrest,"******\n");    fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
       fprintf(ficreseij,"\n#****** ");    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
       for(j=1;j<=cptcoveff;j++)    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(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       fprintf(ficreseij,"******\n");  /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fprintf(ficresvij,"\n#****** ");    pstamp(ficresvij);
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    if(popbased==1)
       fprintf(ficresvij,"******\n");      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
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
       oldm=oldms;savm=savms;    fprintf(ficresvij,"# Age");
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);      for(i=1; i<=nlstate;i++)
        for(j=1; j<=nlstate;j++)
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
       oldm=oldms;savm=savms;    fprintf(ficresvij,"\n");
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);  
        xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
      doldm=matrix(1,nlstate,1,nlstate);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fprintf(ficrest,"\n");  
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       epj=vector(1,nlstate+1);    gpp=vector(nlstate+1,nlstate+ndeath);
       for(age=bage; age <=fage ;age++){    gmp=vector(nlstate+1,nlstate+ndeath);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
         if (popbased==1) {    
           for(i=1; i<=nlstate;i++)    if(estepm < stepm){
             prlim[i][i]=probs[(int)age][i][k];      printf ("Problem %d lower than %d\n",estepm, stepm);
         }    }
            else  hstepm=estepm;   
         fprintf(ficrest," %4.0f",age);    /* For example we decided to compute the life expectancy with the smallest unit */
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           for(i=1, epj[j]=0.;i <=nlstate;i++) {       nhstepm is the number of hstepm from age to agelim 
             epj[j] += prlim[i][i]*eij[i][j][(int)age];       nstepm is the number of stepm from age to agelin. 
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/       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
           epj[nlstate+1] +=epj[j];       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 
         for(i=1, vepp=0.;i <=nlstate;i++)       results. So we changed our mind and took the option of the best precision.
           for(j=1;j <=nlstate;j++)    */
             vepp += vareij[i][j][(int)age];    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));    agelim = AGESUP;
         for(j=1;j <=nlstate;j++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));      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 */
         fprintf(ficrest,"\n");      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);
 free_matrix(mint,1,maxwav,1,n);  
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);  
     free_vector(weight,1,n);      for(theta=1; theta <=npar; theta++){
   fclose(ficreseij);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   fclose(ficresvij);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   fclose(ficrest);        }
   fclose(ficpar);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   free_vector(epj,1,nlstate+1);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    
   /*------- Variance limit prevalence------*/          if (popbased==1) {
           if(mobilav ==0){
   strcpy(fileresvpl,"vpl");            for(i=1; i<=nlstate;i++)
   strcat(fileresvpl,fileres);              prlim[i][i]=probs[(int)age][i][ij];
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {          }else{ /* mobilav */ 
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);            for(i=1; i<=nlstate;i++)
     exit(0);              prlim[i][i]=mobaverage[(int)age][i][ij];
   }          }
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);        }
     
   k=0;        for(j=1; j<= nlstate; j++){
   for(cptcov=1;cptcov<=i1;cptcov++){          for(h=0; h<=nhstepm; h++){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       k=k+1;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
       fprintf(ficresvpl,"\n#****** ");          }
       for(j=1;j<=cptcoveff;j++)        }
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        /* This for computing probability of death (h=1 means
       fprintf(ficresvpl,"******\n");           computed over hstepm matrices product = hstepm*stepm months) 
                 as a weighted average of prlim.
       varpl=matrix(1,nlstate,(int) bage, (int) fage);        */
       oldm=oldms;savm=savms;        for(j=nlstate+1;j<=nlstate+ndeath;j++){
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
     }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
  }        }    
         /* end probability of death */
   fclose(ficresvpl);  
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
   /*---------- End : free ----------------*/          xp[i] = x[i] - (i==theta ?delti[theta]:0);
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
          prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);   
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);        if (popbased==1) {
            if(mobilav ==0){
              for(i=1; i<=nlstate;i++)
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);              prlim[i][i]=probs[(int)age][i][ij];
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);          }else{ /* mobilav */ 
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);            for(i=1; i<=nlstate;i++)
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);              prlim[i][i]=mobaverage[(int)age][i][ij];
            }
   free_matrix(matcov,1,npar,1,npar);        }
   free_vector(delti,1,npar);  
   free_matrix(agev,1,maxwav,1,imx);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
   if(erreur >0)              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
     printf("End of Imach with error or warning %d\n",erreur);          }
   else   printf("End of Imach\n");        }
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        /* This for computing probability of death (h=1 means
             computed over hstepm matrices product = hstepm*stepm months) 
   /* 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);*/           as a weighted average of prlim.
   /*printf("Total time was %d uSec.\n", total_usecs);*/        */
   /*------ End -----------*/        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:        }    
 #ifdef windows        /* end probability of death */
   /* chdir(pathcd);*/  
 #endif        for(j=1; j<= nlstate; j++) /* vareij */
  /*system("wgnuplot graph.plt");*/          for(h=0; h<=nhstepm; h++){
  /*system("../gp37mgw/wgnuplot graph.plt");*/            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
  /*system("cd ../gp37mgw");*/          }
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/  
  strcpy(plotcmd,GNUPLOTPROGRAM);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
  strcat(plotcmd," ");          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
  strcat(plotcmd,optionfilegnuplot);        }
  system(plotcmd);  
       } /* End theta */
 #ifdef windows  
   while (z[0] != 'q') {      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     /* chdir(path); */  
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");      for(h=0; h<=nhstepm; h++) /* veij */
     scanf("%s",z);        for(j=1; j<=nlstate;j++)
     if (z[0] == 'c') system("./imach");          for(theta=1; theta <=npar; theta++)
     else if (z[0] == 'e') system(optionfilehtm);            trgradg[h][j][theta]=gradg[h][theta][j];
     else if (z[0] == 'g') system(plotcmd);  
     else if (z[0] == 'q') exit(0);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   }        for(theta=1; theta <=npar; theta++)
 #endif          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;
           for (k=1; k<=cptcovn;k++) {
             cov[2+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<=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(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]]);
          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>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance 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 */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
     /*goto avoid;*/
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d_%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small size 320, 240\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  /* if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /\* Bug valgrind *\/ */
                  /*        /\*fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);*\/ */
                  /*        ij++; */
                  /* } */
                  /* else */
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    /* if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { */
                    /*   fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]); */
                    /*   ij++; */
                    /* } */
                    /* else */
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
    /* avoid: */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   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
      * - cptcovt total number of covariates of the model nbocc(+)+1 = 8
      * - cptcovn or number of covariates k of the models excluding age*products =6
      * - cptcovage number of covariates with age*products =2
      * - cptcovs number of simple covariates
      * - Tvar[k] is the id of the kth covariate Tvar[1]@12 {1, 2, 3, 8, 10, 11, 8, 3, 7, 8, 5, 6}, thus Tvar[5=V7*V8]=10
      *     which is a new column after the 9 (ncovcol) variables. 
      * - if k is a product Vn*Vm covar[k][i] is filled with correct values for each individual
      * - Tprod[l] gives the kth covariates of the product Vn*Vm l=1 to cptcovprod-cptcovage
      *    Tprod[1]@2 {5, 6}: position of first product V7*V8 is 5, and second V5*V6 is 6.
      * - Tvard[k]  p Tvard[1][1]@4 {7, 8, 5, 6} for V7*V8 and V5*V6 .
    */
   {
     int i, j, k, ks;
     int  j1, k1, k2;
     char modelsav[80];
     char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     /*removespace(model);*/
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=0, k2=-1, ks=0, cptcovn=0;
       j=nbocc(model,'+'); /**< j=Number of '+' */
       j1=nbocc(model,'*'); /**< j1=Number of '*' */
       cptcovs=j+1-j1; /**<  Number of simple covariates V1+V2*age+V3 +V3*V4=> V1 + V3 =2  */
       cptcovt= j+1; /* Number of total covariates in the model V1 + V2*age+ V3 + V3*V4=> 4*/
                     /* including age products which are counted in cptcovage.
                     * but the covariates which are products must be treated separately: ncovn=4- 2=2 (V1+V3). */
       cptcovprod=j1; /**< Number of products  V1*V2 +v3*age = 2 */
       cptcovprodnoage=0; /**< Number of covariate products without age: V3*V4 =1  */
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /*   Design
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9 Weight
        *  <          ncovcol=8                >
        * Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8
        *   k=  1    2      3       4     5       6      7        8
        *  cptcovn number of covariates (not including constant and age ) = # of + plus 1 = 7+1=8
        *  covar[k,i], value of kth covariate if not including age for individual i:
        *       covar[1][i]= (V2), covar[4][i]=(V3), covar[8][i]=(V8)
        *  Tvar[k] # of the kth covariate:  Tvar[1]=2  Tvar[4]=3 Tvar[8]=8
        *       if multiplied by age: V3*age Tvar[3=V3*age]=3 (V3) Tvar[7]=8 and 
        *  Tage[++cptcovage]=k
        *       if products, new covar are created after ncovcol with k1
        *  Tvar[k]=ncovcol+k1; # of the kth covariate product:  Tvar[5]=ncovcol+1=10  Tvar[6]=ncovcol+1=11
        *  Tprod[k1]=k; Tprod[1]=5 Tprod[2]= 6; gives the position of the k1th product
        *  Tvard[k1][1]=m Tvard[k1][2]=m; Tvard[1][1]=5 (V5) Tvard[1][2]=6 Tvard[2][1]=7 (V7) Tvard[2][2]=8
        *  Tvar[cptcovn+k2]=Tvard[k1][1];Tvar[cptcovn+k2+1]=Tvard[k1][2];
        *  Tvar[8+1]=5;Tvar[8+2]=6;Tvar[8+3]=7;Tvar[8+4]=8 inverted
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9  V10  V11
        *  <          ncovcol=8                >
        *       Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8    d1   d1   d2  d2
        *          k=  1    2      3       4     5       6      7        8    9   10   11  12
        *     Tvar[k]= 2    1      3       3    10      11      8        8    5    6    7   8
        * p Tvar[1]@12={2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        * p Tprod[1]@2={                         6, 5}
        *p Tvard[1][1]@4= {7, 8, 5, 6}
        * covar[k][i]= V2   V1      ?      V3    V5*V6?   V7*V8?  ?       V8   
        *  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
        *How to reorganize?
        * Model V1 + V2 + V3 + V8 + V5*V6 + V7*V8 + V3*age + V8*age
        * Tvars {2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        *       {2,   1,     4,      8,    5,      6,     3,       7}
        * Struct []
        */
   
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       /*
        * Treating invertedly V2+V1+V3*age+V2*V4 is as if written V2*V4 +V3*age + V1 + V2 */
       for(k=cptcovt; k>=1;k--) /**< Number of covariates */
           Tvar[k]=0;
       cptcovage=0;
       for(k=1; k<=cptcovt;k++){ /* Loop on total covariates of the model */
         cutl(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /**< Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutl(strc,strd,strb,'*'); /**< strd*strc  Vm*Vn: strb=V3*age(input) strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /**< Model includes age: Vn*age */
             /* covar is not filled and then is empty */
             cptcovprod--;
             cutl(stre,strb,strd,'V'); /* strd=V3(input): stre="3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=3 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutl(stre,strb,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cptcovn++;
             cptcovprodnoage++;k1++;
             cutl(stre,strb,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1; /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutl(strc,strb,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1] =atoi(strc); /* m 1 for V1*/
             Tvard[k1][2] =atoi(stre); /* n 4 for V4*/
             k2=k2+2;
             Tvar[cptcovt+k2]=Tvard[k1][1]; /* Tvar[(cptcovt=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovt+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovt=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 May not be defined */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutl(strd,strc,strb,'V');
           ks++; /**< Number of simple covariates */
           cptcovn++;
           Tvar[k]=atoi(strd);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     /*endread:*/
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   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);
   }
   
   void syscompilerinfo()
    {
      /* #include "syscompilerinfo.h"*/
      /* #include <gnu/libc-version.h> */ /* Only on gnu */
   
      printf("Compiled with:");fprintf(ficlog,"Compiled with:");
   #if defined(__clang__)
      printf(" Clang/LLVM");fprintf(ficlog," Clang/LLVM"); /* Clang/LLVM. ---------------------------------------------- */
   #endif
   #if defined(__ICC) || defined(__INTEL_COMPILER)
      printf(" Intel ICC/ICPC");fprintf(ficlog," Intel ICC/ICPC");/* Intel ICC/ICPC. ------------------------------------------ */
   #endif
   #if defined(__GNUC__) || defined(__GNUG__)
      printf(" GNU GCC/G++");fprintf(ficlog," GNU GCC/G++");/* GNU GCC/G++. --------------------------------------------- */
   #endif
   #if defined(__HP_cc) || defined(__HP_aCC)
      printf(" Hewlett-Packard C/aC++");fprintf(fcilog," Hewlett-Packard C/aC++"); /* Hewlett-Packard C/aC++. ---------------------------------- */
   #endif
   #if defined(__IBMC__) || defined(__IBMCPP__)
      printf(" IBM XL C/C++"); fprintf(ficlog," IBM XL C/C++");/* IBM XL C/C++. -------------------------------------------- */
   #endif
   #if defined(_MSC_VER)
      printf(" Microsoft Visual Studio");fprintf(ficlog," Microsoft Visual Studio");/* Microsoft Visual Studio. --------------------------------- */
   #endif
   #if defined(__PGI)
      printf(" Portland Group PGCC/PGCPP");fprintf(ficlog," Portland Group PGCC/PGCPP");/* Portland Group PGCC/PGCPP. ------------------------------- */
   #endif
   #if defined(__SUNPRO_C) || defined(__SUNPRO_CC)
      printf(" Oracle Solaris Studio");fprintf(ficlog," Oracle Solaris Studio\n");/* Oracle Solaris Studio. ----------------------------------- */
   #endif
      printf(". ");fprintf(ficlog,". ");
      
   // 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)
   #elif __unix__ // all unices, not all compilers
       // Unix
   #elif __linux__
       // linux
   #elif __APPLE__
       // Mac OS, not sure if this is covered by __posix__ and/or __unix__ though...
   #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. */
   #include <stdint.h>
   #if UINTPTR_MAX == 0xffffffff
      printf(" 32-bit."); /* 32-bit */
   #elif UINTPTR_MAX == 0xffffffffffffffff
     printf(" 64-bit.");/* 64-bit */
   #else
    printf(" wtf-bit."); /* wtf */
   #endif
   
   struct utsname sysInfo;
   
      if (uname(&sysInfo) != -1) {
        printf(" %s %s %s %s %s\n",sysInfo.sysname, sysInfo.nodename, sysInfo.release, sysInfo.version, sysInfo.machine);
        fprintf(ficlog," %s %s %s %s %s\n ",sysInfo.sysname, sysInfo.nodename, sysInfo.release, sysInfo.version, sysInfo.machine);
      }
      else
         perror("uname() error");
   #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("GNU C version %d.\n", __GNUC_VERSION__);
      fprintf(ficlog, "GNU C version %d.\n", __GNUC_VERSION__);
   #endif
   #if defined(_MSC_VER)
      printf("Visual C++ compiler: %s \n;", _MSC_FULL_VER);
      fprintf(ficlog, "Visual C++ compiler: %s \n;", _MSC_FULL_VER);
   #endif
      
     /* printf("GNU libc version: %s\n", gnu_get_libc_version()); */
   
    }
   
   /***********************************************/
   /**************** 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;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double dum; /* 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;
     int i1, j1, jk, stepsize;
     int *tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage=0, fage=110, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
   
     double 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;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
       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);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("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 --------*/
   
     /* 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();
   
     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 */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile '%s' with errno='%s'\n",optionfile,strerror(errno));
       fprintf(ficlog,"Problem with optionfile '%s' with errno='%s'\n",optionfile,strerror(errno));
       fflush(ficlog);
       /* goto end; */
       exit(70); 
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line,stdout);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n);  /**< used in readdata */
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       ncovmodel=2+nbocc(model,'+')+1; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     else
       ncovmodel=2;
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guessed parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       /* Reads scales values */
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ( (i1-i) * (j1-j) != 0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       /* Reads covariance matrix */
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,NCOVMAX); /* Number of code per covariate; if O and 1 only, 2**ncov; V1+V2+V3+V4=>16 */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,NCOVMAX); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,NCOVMAX); /* Unclear */
     Tvard=imatrix(1,NCOVMAX,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,NCOVMAX); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
     /* */
     
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
     /* */
    
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     Ndum =ivector(-1,NCOVMAX);  
     if (ncovmodel > 2)
       tricode(Tvar,nbcode,imx, Ndum); /**< Fills nbcode[Tvar[j]][l]; */
   
     codtab=imatrix(1,100,1,10); /* codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) */
     /*printf(" codtab[1,1],codtab[100,10]=%d,%d\n", codtab[1][1],codtab[100][10]);*/
     h=0;
   
   
     /*if (cptcovn > 0) */
         
    
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=pow(2,cptcoveff-k);i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             /**< codtab(h,k)  k   = codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) + 1
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     1
              */
             codtab[h][k]=j;
             /*codtab[h][Tvar[k]]=j;*/
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
   
    free_ivector(Ndum,-1,NCOVMAX);
   
   
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       fprintf(ficgp,"set datafile missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       /*p[1]=0.0268; p[NDIM]=0.083;*/
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #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]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
        /* freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint); */
       /* ,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2); */
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
   #include "prevlim.h"  /* Use ficrespl, ficlog */
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
   #include "hpijx.h"
       fclose(ficrespij);
   
     /*-------------- Variance of one-step probabilities---*/
       k=1;
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
           /*
            */
           /* goto endfree; */
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
   
   
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms; /* Segmentation fault */
             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(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);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #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.1.42  
changed lines
  Added in v.1.170


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