Diff for /imach/src/imach.c between versions 1.44 and 1.167

version 1.44, 2002/05/24 13:01:48 version 1.167, 2014/12/22 13:50:56
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.167  2014/12/22 13:50:56  brouard
      Summary: Testing uname and compiler version and if compiled 32 or 64
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    Testing on Linux 64
   first survey ("cross") where individuals from different ages are  
   interviewed on their health status or degree of disability (in the    Revision 1.166  2014/12/22 11:40:47  brouard
   case of a health survey which is our main interest) -2- at least a    *** empty log message ***
   second wave of interviews ("longitudinal") which measure each change  
   (if any) in individual health status.  Health expectancies are    Revision 1.165  2014/12/16 11:20:36  brouard
   computed from the time spent in each health state according to a    Summary: After compiling on Visual C
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    * imach.c (Module): Merging 1.61 to 1.162
   simplest model is the multinomial logistic model where pij is the  
   probability to be observed in state j at the second wave    Revision 1.164  2014/12/16 10:52:11  brouard
   conditional to be observed in state i at the first wave. Therefore    Summary: Merging with Visual C after suppressing some warnings for unused variables. Also fixing Saito's bug 0.98Xn
   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    * imach.c (Module): Merging 1.61 to 1.162
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.163  2014/12/16 10:30:11  brouard
   you to do it.  More covariates you add, slower the    * imach.c (Module): Merging 1.61 to 1.162
   convergence.  
     Revision 1.162  2014/09/25 11:43:39  brouard
   The advantage of this computer programme, compared to a simple    Summary: temporary backup 0.99!
   multinomial logistic model, is clear when the delay between waves is not  
   identical for each individual. Also, if a individual missed an    Revision 1.1  2014/09/16 11:06:58  brouard
   intermediate interview, the information is lost, but taken into    Summary: With some code (wrong) for nlopt
   account using an interpolation or extrapolation.    
     Author:
   hPijx is the probability to be observed in state i at age x+h  
   conditional to the observed state i at age x. The delay 'h' can be    Revision 1.161  2014/09/15 20:41:41  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    Summary: Problem with macro SQR on Intel compiler
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.160  2014/09/02 09:24:05  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    *** empty log message ***
   and the contribution of each individual to the likelihood is simply  
   hPijx.    Revision 1.159  2014/09/01 10:34:10  brouard
     Summary: WIN32
   Also this programme outputs the covariance matrix of the parameters but also    Author: Brouard
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.158  2014/08/27 17:11:51  brouard
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    *** empty log message ***
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.157  2014/08/27 16:26:55  brouard
   from the European Union.    Summary: Preparing windows Visual studio version
   It is copyrighted identically to a GNU software product, ie programme and    Author: Brouard
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    In order to compile on Visual studio, time.h is now correct and time_t
   **********************************************************************/    and tm struct should be used. difftime should be used but sometimes I
      just make the differences in raw time format (time(&now).
 #include <math.h>    Trying to suppress #ifdef LINUX
 #include <stdio.h>    Add xdg-open for __linux in order to open default browser.
 #include <stdlib.h>  
 #include <unistd.h>    Revision 1.156  2014/08/25 20:10:10  brouard
     *** empty log message ***
 #define MAXLINE 256  
 #define GNUPLOTPROGRAM "gnuplot"    Revision 1.155  2014/08/25 18:32:34  brouard
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    Summary: New compile, minor changes
 #define FILENAMELENGTH 80    Author: Brouard
 /*#define DEBUG*/  
 #define windows    Revision 1.154  2014/06/20 17:32:08  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Summary: Outputs now all graphs of convergence to period prevalence
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     Revision 1.153  2014/06/20 16:45:46  brouard
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Summary: If 3 live state, convergence to period prevalence on same graph
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Author: Brouard
   
 #define NINTERVMAX 8    Revision 1.152  2014/06/18 17:54:09  brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Summary: open browser, use gnuplot on same dir than imach if not found in the path
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  
 #define NCOVMAX 8 /* Maximum number of covariates */    Revision 1.151  2014/06/18 16:43:30  brouard
 #define MAXN 20000    *** empty log message ***
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.150  2014/06/18 16:42:35  brouard
 #define AGEBASE 40    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
     Author: brouard
   
 int erreur; /* Error number */    Revision 1.149  2014/06/18 15:51:14  brouard
 int nvar;    Summary: Some fixes in parameter files errors
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Author: Nicolas Brouard
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.148  2014/06/17 17:38:48  brouard
 int ndeath=1; /* Number of dead states */    Summary: Nothing new
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Author: Brouard
 int popbased=0;  
     Just a new packaging for OS/X version 0.98nS
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.147  2014/06/16 10:33:11  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    *** empty log message ***
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.146  2014/06/16 10:20:28  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Summary: Merge
 double jmean; /* Mean space between 2 waves */    Author: Brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Merge, before building revised version.
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficgp,*ficresprob,*ficpop;    Revision 1.145  2014/06/10 21:23:15  brouard
 FILE *ficreseij;    Summary: Debugging with valgrind
   char filerese[FILENAMELENGTH];    Author: Nicolas Brouard
  FILE  *ficresvij;  
   char fileresv[FILENAMELENGTH];    Lot of changes in order to output the results with some covariates
  FILE  *ficresvpl;    After the Edimburgh REVES conference 2014, it seems mandatory to
   char fileresvpl[FILENAMELENGTH];    improve the code.
     No more memory valgrind error but a lot has to be done in order to
 #define NR_END 1    continue the work of splitting the code into subroutines.
 #define FREE_ARG char*    Also, decodemodel has been improved. Tricode is still not
 #define FTOL 1.0e-10    optimal. nbcode should be improved. Documentation has been added in
     the source code.
 #define NRANSI  
 #define ITMAX 200    Revision 1.143  2014/01/26 09:45:38  brouard
     Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 #define TOL 2.0e-4  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define CGOLD 0.3819660    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.142  2014/01/26 03:57:36  brouard
     Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define GOLD 1.618034  
 #define GLIMIT 100.0    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define TINY 1.0e-20  
     Revision 1.141  2014/01/26 02:42:01  brouard
 static double maxarg1,maxarg2;    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.140  2011/09/02 10:37:54  brouard
      Summary: times.h is ok with mingw32 now.
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.139  2010/06/14 07:50:17  brouard
     After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 static double sqrarg;    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.138  2010/04/30 18:19:40  brouard
     *** empty log message ***
 int imx;  
 int stepm;    Revision 1.137  2010/04/29 18:11:38  brouard
 /* Stepm, step in month: minimum step interpolation*/    (Module): Checking covariates for more complex models
     than V1+V2. A lot of change to be done. Unstable.
 int estepm;  
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    Revision 1.136  2010/04/26 20:30:53  brouard
     (Module): merging some libgsl code. Fixing computation
 int m,nb;    of likelione (using inter/intrapolation if mle = 0) in order to
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    get same likelihood as if mle=1.
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Some cleaning of code and comments added.
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.135  2009/10/29 15:33:14  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 double *weight;  
 int **s; /* Status */    Revision 1.134  2009/10/29 13:18:53  brouard
 double *agedc, **covar, idx;    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.133  2009/07/06 10:21:25  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    just nforces
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.132  2009/07/06 08:22:05  brouard
 /**************** split *************************/    Many tings
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.131  2009/06/20 16:22:47  brouard
    char *s;                             /* pointer */    Some dimensions resccaled
    int  l1, l2;                         /* length counters */  
     Revision 1.130  2009/05/26 06:44:34  brouard
    l1 = strlen( path );                 /* length of path */    (Module): Max Covariate is now set to 20 instead of 8. A
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    lot of cleaning with variables initialized to 0. Trying to make
 #ifdef windows    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
    s = strrchr( path, '\\' );           /* find last / */  
 #else    Revision 1.129  2007/08/31 13:49:27  lievre
    s = strrchr( path, '/' );            /* find last / */    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 #endif  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.128  2006/06/30 13:02:05  brouard
 #if     defined(__bsd__)                /* get current working directory */    (Module): Clarifications on computing e.j
       extern char       *getwd( );  
     Revision 1.127  2006/04/28 18:11:50  brouard
       if ( getwd( dirc ) == NULL ) {    (Module): Yes the sum of survivors was wrong since
 #else    imach-114 because nhstepm was no more computed in the age
       extern char       *getcwd( );    loop. Now we define nhstepma in the age loop.
     (Module): In order to speed up (in case of numerous covariates) we
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    compute health expectancies (without variances) in a first step
 #endif    and then all the health expectancies with variances or standard
          return( GLOCK_ERROR_GETCWD );    deviation (needs data from the Hessian matrices) which slows the
       }    computation.
       strcpy( name, path );             /* we've got it */    In the future we should be able to stop the program is only health
    } else {                             /* strip direcotry from path */    expectancies and graph are needed without standard deviations.
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.126  2006/04/28 17:23:28  brouard
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): Yes the sum of survivors was wrong since
       strcpy( name, s );                /* save file name */    imach-114 because nhstepm was no more computed in the age
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    loop. Now we define nhstepma in the age loop.
       dirc[l1-l2] = 0;                  /* add zero */    Version 0.98h
    }  
    l1 = strlen( dirc );                 /* length of directory */    Revision 1.125  2006/04/04 15:20:31  lievre
 #ifdef windows    Errors in calculation of health expectancies. Age was not initialized.
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    Forecasting file added.
 #else  
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    Revision 1.124  2006/03/22 17:13:53  lievre
 #endif    Parameters are printed with %lf instead of %f (more numbers after the comma).
    s = strrchr( name, '.' );            /* find last / */    The log-likelihood is printed in the log file
    s++;  
    strcpy(ext,s);                       /* save extension */    Revision 1.123  2006/03/20 10:52:43  brouard
    l1= strlen( name);    * imach.c (Module): <title> changed, corresponds to .htm file
    l2= strlen( s)+1;    name. <head> headers where missing.
    strncpy( finame, name, l1-l2);  
    finame[l1-l2]= 0;    * imach.c (Module): Weights can have a decimal point as for
    return( 0 );                         /* we're done */    English (a comma might work with a correct LC_NUMERIC environment,
 }    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
     1.
 /******************************************/    Version 0.98g
   
 void replace(char *s, char*t)    Revision 1.122  2006/03/20 09:45:41  brouard
 {    (Module): Weights can have a decimal point as for
   int i;    English (a comma might work with a correct LC_NUMERIC environment,
   int lg=20;    otherwise the weight is truncated).
   i=0;    Modification of warning when the covariates values are not 0 or
   lg=strlen(t);    1.
   for(i=0; i<= lg; i++) {    Version 0.98g
     (s[i] = t[i]);  
     if (t[i]== '\\') s[i]='/';    Revision 1.121  2006/03/16 17:45:01  lievre
   }    * imach.c (Module): Comments concerning covariates added
 }  
     * imach.c (Module): refinements in the computation of lli if
 int nbocc(char *s, char occ)    status=-2 in order to have more reliable computation if stepm is
 {    not 1 month. Version 0.98f
   int i,j=0;  
   int lg=20;    Revision 1.120  2006/03/16 15:10:38  lievre
   i=0;    (Module): refinements in the computation of lli if
   lg=strlen(s);    status=-2 in order to have more reliable computation if stepm is
   for(i=0; i<= lg; i++) {    not 1 month. Version 0.98f
   if  (s[i] == occ ) j++;  
   }    Revision 1.119  2006/03/15 17:42:26  brouard
   return j;    (Module): Bug if status = -2, the loglikelihood was
 }    computed as likelihood omitting the logarithm. Version O.98e
   
 void cutv(char *u,char *v, char*t, char occ)    Revision 1.118  2006/03/14 18:20:07  brouard
 {    (Module): varevsij Comments added explaining the second
   int i,lg,j,p=0;    table of variances if popbased=1 .
   i=0;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   for(j=0; j<=strlen(t)-1; j++) {    (Module): Function pstamp added
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    (Module): Version 0.98d
   }  
     Revision 1.117  2006/03/14 17:16:22  brouard
   lg=strlen(t);    (Module): varevsij Comments added explaining the second
   for(j=0; j<p; j++) {    table of variances if popbased=1 .
     (u[j] = t[j]);    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   }    (Module): Function pstamp added
      u[p]='\0';    (Module): Version 0.98d
   
    for(j=0; j<= lg; j++) {    Revision 1.116  2006/03/06 10:29:27  brouard
     if (j>=(p+1))(v[j-p-1] = t[j]);    (Module): Variance-covariance wrong links and
   }    varian-covariance of ej. is needed (Saito).
 }  
     Revision 1.115  2006/02/27 12:17:45  brouard
 /********************** nrerror ********************/    (Module): One freematrix added in mlikeli! 0.98c
   
 void nrerror(char error_text[])    Revision 1.114  2006/02/26 12:57:58  brouard
 {    (Module): Some improvements in processing parameter
   fprintf(stderr,"ERREUR ...\n");    filename with strsep.
   fprintf(stderr,"%s\n",error_text);  
   exit(1);    Revision 1.113  2006/02/24 14:20:24  brouard
 }    (Module): Memory leaks checks with valgrind and:
 /*********************** vector *******************/    datafile was not closed, some imatrix were not freed and on matrix
 double *vector(int nl, int nh)    allocation too.
 {  
   double *v;    Revision 1.112  2006/01/30 09:55:26  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   if (!v) nrerror("allocation failure in vector");  
   return v-nl+NR_END;    Revision 1.111  2006/01/25 20:38:18  brouard
 }    (Module): Lots of cleaning and bugs added (Gompertz)
     (Module): Comments can be added in data file. Missing date values
 /************************ free vector ******************/    can be a simple dot '.'.
 void free_vector(double*v, int nl, int nh)  
 {    Revision 1.110  2006/01/25 00:51:50  brouard
   free((FREE_ARG)(v+nl-NR_END));    (Module): Lots of cleaning and bugs added (Gompertz)
 }  
     Revision 1.109  2006/01/24 19:37:15  brouard
 /************************ivector *******************************/    (Module): Comments (lines starting with a #) are allowed in data.
 int *ivector(long nl,long nh)  
 {    Revision 1.108  2006/01/19 18:05:42  lievre
   int *v;    Gnuplot problem appeared...
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    To be fixed
   if (!v) nrerror("allocation failure in ivector");  
   return v-nl+NR_END;    Revision 1.107  2006/01/19 16:20:37  brouard
 }    Test existence of gnuplot in imach path
   
 /******************free ivector **************************/    Revision 1.106  2006/01/19 13:24:36  brouard
 void free_ivector(int *v, long nl, long nh)    Some cleaning and links added in html output
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.105  2006/01/05 20:23:19  lievre
 }    *** empty log message ***
   
 /******************* imatrix *******************************/    Revision 1.104  2005/09/30 16:11:43  lievre
 int **imatrix(long nrl, long nrh, long ncl, long nch)    (Module): sump fixed, loop imx fixed, and simplifications.
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    (Module): If the status is missing at the last wave but we know
 {    that the person is alive, then we can code his/her status as -2
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    (instead of missing=-1 in earlier versions) and his/her
   int **m;    contributions to the likelihood is 1 - Prob of dying from last
      health status (= 1-p13= p11+p12 in the easiest case of somebody in
   /* allocate pointers to rows */    the healthy state at last known wave). Version is 0.98
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    Revision 1.103  2005/09/30 15:54:49  lievre
   m += NR_END;    (Module): sump fixed, loop imx fixed, and simplifications.
   m -= nrl;  
      Revision 1.102  2004/09/15 17:31:30  brouard
      Add the possibility to read data file including tab characters.
   /* allocate rows and set pointers to them */  
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    Revision 1.101  2004/09/15 10:38:38  brouard
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Fix on curr_time
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.100  2004/07/12 18:29:06  brouard
      Add version for Mac OS X. Just define UNIX in Makefile
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
      Revision 1.99  2004/06/05 08:57:40  brouard
   /* return pointer to array of pointers to rows */    *** empty log message ***
   return m;  
 }    Revision 1.98  2004/05/16 15:05:56  brouard
     New version 0.97 . First attempt to estimate force of mortality
 /****************** free_imatrix *************************/    directly from the data i.e. without the need of knowing the health
 void free_imatrix(m,nrl,nrh,ncl,nch)    state at each age, but using a Gompertz model: log u =a + b*age .
       int **m;    This is the basic analysis of mortality and should be done before any
       long nch,ncl,nrh,nrl;    other analysis, in order to test if the mortality estimated from the
      /* free an int matrix allocated by imatrix() */    cross-longitudinal survey is different from the mortality estimated
 {    from other sources like vital statistic data.
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));    The same imach parameter file can be used but the option for mle should be -3.
 }  
     Agnès, who wrote this part of the code, tried to keep most of the
 /******************* matrix *******************************/    former routines in order to include the new code within the former code.
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {    The output is very simple: only an estimate of the intercept and of
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    the slope with 95% confident intervals.
   double **m;  
     Current limitations:
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    A) Even if you enter covariates, i.e. with the
   if (!m) nrerror("allocation failure 1 in matrix()");    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   m += NR_END;    B) There is no computation of Life Expectancy nor Life Table.
   m -= nrl;  
     Revision 1.97  2004/02/20 13:25:42  lievre
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    Version 0.96d. Population forecasting command line is (temporarily)
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    suppressed.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.96  2003/07/15 15:38:55  brouard
     * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    rewritten within the same printf. Workaround: many printfs.
   return m;  
 }    Revision 1.95  2003/07/08 07:54:34  brouard
     * imach.c (Repository):
 /*************************free matrix ************************/    (Repository): Using imachwizard code to output a more meaningful covariance
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    matrix (cov(a12,c31) instead of numbers.
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.94  2003/06/27 13:00:02  brouard
   free((FREE_ARG)(m+nrl-NR_END));    Just cleaning
 }  
     Revision 1.93  2003/06/25 16:33:55  brouard
 /******************* ma3x *******************************/    (Module): On windows (cygwin) function asctime_r doesn't
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    exist so I changed back to asctime which exists.
 {    (Module): Version 0.96b
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  
   double ***m;    Revision 1.92  2003/06/25 16:30:45  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    exist so I changed back to asctime which exists.
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.91  2003/06/25 15:30:29  brouard
   m -= nrl;    * imach.c (Repository): Duplicated warning errors corrected.
     (Repository): Elapsed time after each iteration is now output. It
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    helps to forecast when convergence will be reached. Elapsed time
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    is stamped in powell.  We created a new html file for the graphs
   m[nrl] += NR_END;    concerning matrix of covariance. It has extension -cov.htm.
   m[nrl] -= ncl;  
     Revision 1.90  2003/06/24 12:34:15  brouard
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    of the covariance matrix to be input.
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  
   m[nrl][ncl] += NR_END;    Revision 1.89  2003/06/24 12:30:52  brouard
   m[nrl][ncl] -= nll;    (Module): Some bugs corrected for windows. Also, when
   for (j=ncl+1; j<=nch; j++)    mle=-1 a template is output in file "or"mypar.txt with the design
     m[nrl][j]=m[nrl][j-1]+nlay;    of the covariance matrix to be input.
    
   for (i=nrl+1; i<=nrh; i++) {    Revision 1.88  2003/06/23 17:54:56  brouard
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    * 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.
     for (j=ncl+1; j<=nch; j++)  
       m[i][j]=m[i][j-1]+nlay;    Revision 1.87  2003/06/18 12:26:01  brouard
   }    Version 0.96
   return m;  
 }    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 /*************************free ma3x ************************/    routine fileappend.
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  
 {    Revision 1.85  2003/06/17 13:12:43  brouard
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    * imach.c (Repository): Check when date of death was earlier that
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    current date of interview. It may happen when the death was just
   free((FREE_ARG)(m+nrl-NR_END));    prior to the death. In this case, dh was negative and likelihood
 }    was wrong (infinity). We still send an "Error" but patch by
     assuming that the date of death was just one stepm after the
 /***************** f1dim *************************/    interview.
 extern int ncom;    (Repository): Because some people have very long ID (first column)
 extern double *pcom,*xicom;    we changed int to long in num[] and we added a new lvector for
 extern double (*nrfunc)(double []);    memory allocation. But we also truncated to 8 characters (left
      truncation)
 double f1dim(double x)    (Repository): No more line truncation errors.
 {  
   int j;    Revision 1.84  2003/06/13 21:44:43  brouard
   double f;    * imach.c (Repository): Replace "freqsummary" at a correct
   double *xt;    place. It differs from routine "prevalence" which may be called
      many times. Probs is memory consuming and must be used with
   xt=vector(1,ncom);    parcimony.
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   f=(*nrfunc)(xt);  
   free_vector(xt,1,ncom);    Revision 1.83  2003/06/10 13:39:11  lievre
   return f;    *** empty log message ***
 }  
     Revision 1.82  2003/06/05 15:57:20  brouard
 /*****************brent *************************/    Add log in  imach.c and  fullversion number is now printed.
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {  */
   int iter;  /*
   double a,b,d,etemp;     Interpolated Markov Chain
   double fu,fv,fw,fx;  
   double ftemp;    Short summary of the programme:
   double p,q,r,tol1,tol2,u,v,w,x,xm;    
   double e=0.0;    This program computes Healthy Life Expectancies from
      cross-longitudinal data. Cross-longitudinal data consist in: -1- a
   a=(ax < cx ? ax : cx);    first survey ("cross") where individuals from different ages are
   b=(ax > cx ? ax : cx);    interviewed on their health status or degree of disability (in the
   x=w=v=bx;    case of a health survey which is our main interest) -2- at least a
   fw=fv=fx=(*f)(x);    second wave of interviews ("longitudinal") which measure each change
   for (iter=1;iter<=ITMAX;iter++) {    (if any) in individual health status.  Health expectancies are
     xm=0.5*(a+b);    computed from the time spent in each health state according to a
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    model. More health states you consider, more time is necessary to reach the
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    Maximum Likelihood of the parameters involved in the model.  The
     printf(".");fflush(stdout);    simplest model is the multinomial logistic model where pij is the
 #ifdef DEBUG    probability to be observed in state j at the second wave
     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);    conditional to be observed in state i at the first wave. Therefore
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 #endif    'age' is age and 'sex' is a covariate. If you want to have a more
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    complex model than "constant and age", you should modify the program
       *xmin=x;    where the markup *Covariates have to be included here again* invites
       return fx;    you to do it.  More covariates you add, slower the
     }    convergence.
     ftemp=fu;  
     if (fabs(e) > tol1) {    The advantage of this computer programme, compared to a simple
       r=(x-w)*(fx-fv);    multinomial logistic model, is clear when the delay between waves is not
       q=(x-v)*(fx-fw);    identical for each individual. Also, if a individual missed an
       p=(x-v)*q-(x-w)*r;    intermediate interview, the information is lost, but taken into
       q=2.0*(q-r);    account using an interpolation or extrapolation.  
       if (q > 0.0) p = -p;  
       q=fabs(q);    hPijx is the probability to be observed in state i at age x+h
       etemp=e;    conditional to the observed state i at age x. The delay 'h' can be
       e=d;    split into an exact number (nh*stepm) of unobserved intermediate
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    states. This elementary transition (by month, quarter,
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    semester or year) is modelled as a multinomial logistic.  The hPx
       else {    matrix is simply the matrix product of nh*stepm elementary matrices
         d=p/q;    and the contribution of each individual to the likelihood is simply
         u=x+d;    hPijx.
         if (u-a < tol2 || b-u < tol2)  
           d=SIGN(tol1,xm-x);    Also this programme outputs the covariance matrix of the parameters but also
       }    of the life expectancies. It also computes the period (stable) prevalence. 
     } else {    
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
     }             Institut national d'études démographiques, Paris.
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    This software have been partly granted by Euro-REVES, a concerted action
     fu=(*f)(u);    from the European Union.
     if (fu <= fx) {    It is copyrighted identically to a GNU software product, ie programme and
       if (u >= x) a=x; else b=x;    software can be distributed freely for non commercial use. Latest version
       SHFT(v,w,x,u)    can be accessed at http://euroreves.ined.fr/imach .
         SHFT(fv,fw,fx,fu)  
         } else {    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
           if (u < x) a=u; else b=u;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
           if (fu <= fw || w == x) {    
             v=w;    **********************************************************************/
             w=u;  /*
             fv=fw;    main
             fw=fu;    read parameterfile
           } else if (fu <= fv || v == x || v == w) {    read datafile
             v=u;    concatwav
             fv=fu;    freqsummary
           }    if (mle >= 1)
         }      mlikeli
   }    print results files
   nrerror("Too many iterations in brent");    if mle==1 
   *xmin=x;       computes hessian
   return fx;    read end of parameter file: agemin, agemax, bage, fage, estepm
 }        begin-prev-date,...
     open gnuplot file
 /****************** mnbrak ***********************/    open html file
     period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
             double (*func)(double))                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
 {      freexexit2 possible for memory heap.
   double ulim,u,r,q, dum;  
   double fu;    h Pij x                         | pij_nom  ficrestpij
       # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
   *fa=(*func)(*ax);         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
   *fb=(*func)(*bx);         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
   if (*fb > *fa) {  
     SHFT(dum,*ax,*bx,dum)         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
       SHFT(dum,*fb,*fa,dum)         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
       }    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
   *cx=(*bx)+GOLD*(*bx-*ax);     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
   *fc=(*func)(*cx);     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
   while (*fb > *fc) {  
     r=(*bx-*ax)*(*fb-*fc);    forecasting if prevfcast==1 prevforecast call prevalence()
     q=(*bx-*cx)*(*fb-*fa);    health expectancies
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    Variance-covariance of DFLE
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    prevalence()
     ulim=(*bx)+GLIMIT*(*cx-*bx);     movingaverage()
     if ((*bx-u)*(u-*cx) > 0.0) {    varevsij() 
       fu=(*func)(u);    if popbased==1 varevsij(,popbased)
     } else if ((*cx-u)*(u-ulim) > 0.0) {    total life expectancies
       fu=(*func)(u);    Variance of period (stable) prevalence
       if (fu < *fc) {   end
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  */
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  #define POWELL /* Instead of NLOPT */
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  #include <math.h>
       fu=(*func)(u);  #include <stdio.h>
     } else {  #include <stdlib.h>
       u=(*cx)+GOLD*(*cx-*bx);  #include <string.h>
       fu=(*func)(u);  
     }  #ifdef _WIN32
     SHFT(*ax,*bx,*cx,u)  #include <io.h>
       SHFT(*fa,*fb,*fc,fu)  #else
       }  #include <unistd.h>
 }  #endif
   
 /*************** linmin ************************/  #include <limits.h>
   #include <sys/types.h>
 int ncom;  #include <sys/utsname.h>
 double *pcom,*xicom;  #include <sys/stat.h>
 double (*nrfunc)(double []);  #include <errno.h>
    /* extern int errno; */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  /* #ifdef LINUX */
   double brent(double ax, double bx, double cx,  /* #include <time.h> */
                double (*f)(double), double tol, double *xmin);  /* #include "timeval.h" */
   double f1dim(double x);  /* #else */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  /* #include <sys/time.h> */
               double *fc, double (*func)(double));  /* #endif */
   int j;  
   double xx,xmin,bx,ax;  #include <time.h>
   double fx,fb,fa;  
    #ifdef GSL
   ncom=n;  #include <gsl/gsl_errno.h>
   pcom=vector(1,n);  #include <gsl/gsl_multimin.h>
   xicom=vector(1,n);  #endif
   nrfunc=func;  
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  #ifdef NLOPT
     xicom[j]=xi[j];  #include <nlopt.h>
   }  typedef struct {
   ax=0.0;    double (* function)(double [] );
   xx=1.0;  } myfunc_data ;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  #endif
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG  /* #include <libintl.h> */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  /* #define _(String) gettext (String) */
 #endif  
   for (j=1;j<=n;j++) {  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
     xi[j] *= xmin;  
     p[j] += xi[j];  #define GNUPLOTPROGRAM "gnuplot"
   }  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   free_vector(xicom,1,n);  #define FILENAMELENGTH 132
   free_vector(pcom,1,n);  
 }  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 /*************** powell ************************/  
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
             double (*func)(double []))  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
 {  
   void linmin(double p[], double xi[], int n, double *fret,  #define NINTERVMAX 8
               double (*func)(double []));  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
   int i,ibig,j;  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
   double del,t,*pt,*ptt,*xit;  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
   double fp,fptt;  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
   double *xits;  #define MAXN 20000
   pt=vector(1,n);  #define YEARM 12. /**< Number of months per year */
   ptt=vector(1,n);  #define AGESUP 130
   xit=vector(1,n);  #define AGEBASE 40
   xits=vector(1,n);  #define AGEGOMP 10 /**< Minimal age for Gompertz adjustment */
   *fret=(*func)(p);  #ifdef _WIN32
   for (j=1;j<=n;j++) pt[j]=p[j];  #define DIRSEPARATOR '\\'
   for (*iter=1;;++(*iter)) {  #define CHARSEPARATOR "\\"
     fp=(*fret);  #define ODIRSEPARATOR '/'
     ibig=0;  #else
     del=0.0;  #define DIRSEPARATOR '/'
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #define CHARSEPARATOR "/"
     for (i=1;i<=n;i++)  #define ODIRSEPARATOR '\\'
       printf(" %d %.12f",i, p[i]);  #endif
     printf("\n");  
     for (i=1;i<=n;i++) {  /* $Id$ */
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  /* $State$ */
       fptt=(*fret);  
 #ifdef DEBUG  char version[]="Imach version 0.99, September 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
       printf("fret=%lf \n",*fret);  char fullversion[]="$Revision$ $Date$"; 
 #endif  char strstart[80];
       printf("%d",i);fflush(stdout);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       linmin(p,xit,n,fret,func);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       if (fabs(fptt-(*fret)) > del) {  int nvar=0, nforce=0; /* Number of variables, number of forces */
         del=fabs(fptt-(*fret));  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
         ibig=i;  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
       }  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
 #ifdef DEBUG  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
       printf("%d %.12e",i,(*fret));  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
       for (j=1;j<=n;j++) {  int cptcovprodnoage=0; /**< Number of covariate products without age */   
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  int cptcoveff=0; /* Total number of covariates to vary for printing results */
         printf(" x(%d)=%.12e",j,xit[j]);  int cptcov=0; /* Working variable */
       }  int npar=NPARMAX;
       for(j=1;j<=n;j++)  int nlstate=2; /* Number of live states */
         printf(" p=%.12e",p[j]);  int ndeath=1; /* Number of dead states */
       printf("\n");  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 #endif  int popbased=0;
     }  
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  int *wav; /* Number of waves for this individuual 0 is possible */
 #ifdef DEBUG  int maxwav=0; /* Maxim number of waves */
       int k[2],l;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       k[0]=1;  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       k[1]=-1;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       printf("Max: %.12e",(*func)(p));                     to the likelihood and the sum of weights (done by funcone)*/
       for (j=1;j<=n;j++)  int mle=1, weightopt=0;
         printf(" %.12e",p[j]);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       printf("\n");  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       for(l=0;l<=1;l++) {  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
         for (j=1;j<=n;j++) {             * wave mi and wave mi+1 is not an exact multiple of stepm. */
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  int countcallfunc=0;  /* Count the number of calls to func */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  double jmean=1; /* Mean space between 2 waves */
         }  double **matprod2(); /* test */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  double **oldm, **newm, **savm; /* Working pointers to matrices */
       }  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 #endif  /*FILE *fic ; */ /* Used in readdata only */
   FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   FILE *ficlog, *ficrespow;
       free_vector(xit,1,n);  int globpr=0; /* Global variable for printing or not */
       free_vector(xits,1,n);  double fretone; /* Only one call to likelihood */
       free_vector(ptt,1,n);  long ipmx=0; /* Number of contributions */
       free_vector(pt,1,n);  double sw; /* Sum of weights */
       return;  char filerespow[FILENAMELENGTH];
     }  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  FILE *ficresilk;
     for (j=1;j<=n;j++) {  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       ptt[j]=2.0*p[j]-pt[j];  FILE *ficresprobmorprev;
       xit[j]=p[j]-pt[j];  FILE *fichtm, *fichtmcov; /* Html File */
       pt[j]=p[j];  FILE *ficreseij;
     }  char filerese[FILENAMELENGTH];
     fptt=(*func)(ptt);  FILE *ficresstdeij;
     if (fptt < fp) {  char fileresstde[FILENAMELENGTH];
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  FILE *ficrescveij;
       if (t < 0.0) {  char filerescve[FILENAMELENGTH];
         linmin(p,xit,n,fret,func);  FILE  *ficresvij;
         for (j=1;j<=n;j++) {  char fileresv[FILENAMELENGTH];
           xi[j][ibig]=xi[j][n];  FILE  *ficresvpl;
           xi[j][n]=xit[j];  char fileresvpl[FILENAMELENGTH];
         }  char title[MAXLINE];
 #ifdef DEBUG  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
         for(j=1;j<=n;j++)  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
           printf(" %.12e",xit[j]);  char command[FILENAMELENGTH];
         printf("\n");  int  outcmd=0;
 #endif  
       }  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     }  
   }  char filelog[FILENAMELENGTH]; /* Log file */
 }  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 /**** Prevalence limit ****************/  char popfile[FILENAMELENGTH];
   
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
 {  
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  /* struct timeval start_time, end_time, curr_time, last_time, forecast_time; */
      matrix by transitions matrix until convergence is reached */  /* struct timezone tzp; */
   /* extern int gettimeofday(); */
   int i, ii,j,k;  struct tm tml, *gmtime(), *localtime();
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();  extern time_t time();
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  struct tm start_time, end_time, curr_time, last_time, forecast_time;
   double agefin, delaymax=50 ; /* Max number of years to converge */  time_t  rstart_time, rend_time, rcurr_time, rlast_time, rforecast_time; /* raw time */
   struct tm tm;
   for (ii=1;ii<=nlstate+ndeath;ii++)  
     for (j=1;j<=nlstate+ndeath;j++){  char strcurr[80], strfor[80];
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  char *endptr;
   long lval;
    cov[1]=1.;  double dval;
    
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  #define NR_END 1
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  #define FREE_ARG char*
     newm=savm;  #define FTOL 1.0e-10
     /* Covariates have to be included here again */  
      cov[2]=agefin;  #define NRANSI 
    #define ITMAX 200 
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  #define TOL 2.0e-4 
         /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/  
       }  #define CGOLD 0.3819660 
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  #define ZEPS 1.0e-10 
       for (k=1; k<=cptcovprod;k++)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  
   #define GOLD 1.618034 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  #define GLIMIT 100.0 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  #define TINY 1.0e-20 
       /*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);  static double maxarg1,maxarg2;
   #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
     savm=oldm;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     oldm=newm;    
     maxmax=0.;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
     for(j=1;j<=nlstate;j++){  #define rint(a) floor(a+0.5)
       min=1.;  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/myutils_8h-source.html */
       max=0.;  /* #define mytinydouble 1.0e-16 */
       for(i=1; i<=nlstate; i++) {  /* #define DEQUAL(a,b) (fabs((a)-(b))<mytinydouble) */
         sumnew=0;  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/mynrutils_8h-source.html */
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  /* static double dsqrarg; */
         prlim[i][j]= newm[i][j]/(1-sumnew);  /* #define DSQR(a) (DEQUAL((dsqrarg=(a)),0.0) ? 0.0 : dsqrarg*dsqrarg) */
         max=FMAX(max,prlim[i][j]);  static double sqrarg;
         min=FMIN(min,prlim[i][j]);  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
       maxmin=max-min;  int agegomp= AGEGOMP;
       maxmax=FMAX(maxmax,maxmin);  
     }  int imx; 
     if(maxmax < ftolpl){  int stepm=1;
       return prlim;  /* Stepm, step in month: minimum step interpolation*/
     }  
   }  int estepm;
 }  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
 /*************** transition probabilities ***************/  int m,nb;
   long *num;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
 {  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double s1, s2;  double **pmmij, ***probs;
   /*double t34;*/  double *ageexmed,*agecens;
   int i,j,j1, nc, ii, jj;  double dateintmean=0;
   
     for(i=1; i<= nlstate; i++){  double *weight;
     for(j=1; j<i;j++){  int **s; /* Status */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  double *agedc;
         /*s2 += param[i][j][nc]*cov[nc];*/  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];                    * covar=matrix(0,NCOVMAX,1,n); 
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
       }  double  idx; 
       ps[i][j]=s2;  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  int *Ndum; /** Freq of modality (tricode */
     }  int **codtab; /**< codtab=imatrix(1,100,1,10); */
     for(j=i+1; j<=nlstate+ndeath;j++){  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  double *lsurv, *lpop, *tpop;
         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 ftol=FTOL; /**< Tolerance for computing Max Likelihood */
       }  double ftolhess; /**< Tolerance for computing hessian */
       ps[i][j]=s2;  
     }  /**************** split *************************/
   }  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     /*ps[3][2]=1;*/  {
     /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   for(i=1; i<= nlstate; i++){       the name of the file (name), its extension only (ext) and its first part of the name (finame)
      s1=0;    */ 
     for(j=1; j<i; j++)    char  *ss;                            /* pointer */
       s1+=exp(ps[i][j]);    int   l1, l2;                         /* length counters */
     for(j=i+1; j<=nlstate+ndeath; j++)  
       s1+=exp(ps[i][j]);    l1 = strlen(path );                   /* length of path */
     ps[i][i]=1./(s1+1.);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     for(j=1; j<i; j++)    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       ps[i][j]= exp(ps[i][j])*ps[i][i];    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     for(j=i+1; j<=nlstate+ndeath; j++)      strcpy( name, path );               /* we got the fullname name because no directory */
       ps[i][j]= exp(ps[i][j])*ps[i][i];      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   } /* end i */      /* get current working directory */
       /*    extern  char* getcwd ( char *buf , int len);*/
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     for(jj=1; jj<= nlstate+ndeath; jj++){        return( GLOCK_ERROR_GETCWD );
       ps[ii][jj]=0;      }
       ps[ii][ii]=1;      /* got dirc from getcwd*/
     }      printf(" DIRC = %s \n",dirc);
   }    } else {                              /* strip direcotry from path */
       ss++;                               /* after this, the filename */
       l2 = strlen( ss );                  /* length of filename */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     for(jj=1; jj<= nlstate+ndeath; jj++){      strcpy( name, ss );         /* save file name */
      printf("%lf ",ps[ii][jj]);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
    }      dirc[l1-l2] = 0;                    /* add zero */
     printf("\n ");      printf(" DIRC2 = %s \n",dirc);
     }    }
     printf("\n ");printf("%lf ",cov[2]);*/    /* We add a separator at the end of dirc if not exists */
 /*    l1 = strlen( dirc );                  /* length of directory */
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    if( dirc[l1-1] != DIRSEPARATOR ){
   goto end;*/      dirc[l1] =  DIRSEPARATOR;
     return ps;      dirc[l1+1] = 0; 
 }      printf(" DIRC3 = %s \n",dirc);
     }
 /**************** Product of 2 matrices ******************/    ss = strrchr( name, '.' );            /* find last / */
     if (ss >0){
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      ss++;
 {      strcpy(ext,ss);                     /* save extension */
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times      l1= strlen( name);
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */      l2= strlen(ss)+1;
   /* in, b, out are matrice of pointers which should have been initialized      strncpy( finame, name, l1-l2);
      before: only the contents of out is modified. The function returns      finame[l1-l2]= 0;
      a pointer to pointers identical to out */    }
   long i, j, k;  
   for(i=nrl; i<= nrh; i++)    return( 0 );                          /* we're done */
     for(k=ncolol; k<=ncoloh; k++)  }
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  
         out[i][k] +=in[i][j]*b[j][k];  
   /******************************************/
   return out;  
 }  void replace_back_to_slash(char *s, char*t)
   {
     int i;
 /************* Higher Matrix Product ***************/    int lg=0;
     i=0;
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    lg=strlen(t);
 {    for(i=0; i<= lg; i++) {
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month      (s[i] = t[i]);
      duration (i.e. until      if (t[i]== '\\') s[i]='/';
      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  char *trimbb(char *out, char *in)
      included manually here.  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
     char *s;
      */    s=out;
     while (*in != '\0'){
   int i, j, d, h, k;      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
   double **out, cov[NCOVMAX];        in++;
   double **newm;      }
       *out++ = *in++;
   /* Hstepm could be zero and should return the unit matrix */    }
   for (i=1;i<=nlstate+ndeath;i++)    *out='\0';
     for (j=1;j<=nlstate+ndeath;j++){    return s;
       oldm[i][j]=(i==j ? 1.0 : 0.0);  }
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }  char *cutl(char *blocc, char *alocc, char *in, char occ)
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  {
   for(h=1; h <=nhstepm; h++){    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
     for(d=1; d <=hstepm; d++){       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
       newm=savm;       gives blocc="abcdef2ghi" and alocc="j".
       /* Covariates have to be included here again */       If occ is not found blocc is null and alocc is equal to in. Returns blocc
       cov[1]=1.;    */
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    char *s, *t;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    t=in;s=in;
       for (k=1; k<=cptcovage;k++)    while ((*in != occ) && (*in != '\0')){
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];      *alocc++ = *in++;
       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]]];    if( *in == occ){
       *(alocc)='\0';
       s=++in;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    }
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/   
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    if (s == t) {/* occ not found */
                    pmij(pmmij,cov,ncovmodel,x,nlstate));      *(alocc-(in-s))='\0';
       savm=oldm;      in=s;
       oldm=newm;    }
     }    while ( *in != '\0'){
     for(i=1; i<=nlstate+ndeath; i++)      *blocc++ = *in++;
       for(j=1;j<=nlstate+ndeath;j++) {    }
         po[i][j][h]=newm[i][j];  
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    *blocc='\0';
          */    return t;
       }  }
   } /* end h */  char *cutv(char *blocc, char *alocc, char *in, char occ)
   return po;  {
 }    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
        and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
        gives blocc="abcdef2ghi" and alocc="j".
 /*************** log-likelihood *************/       If occ is not found blocc is null and alocc is equal to in. Returns alocc
 double func( double *x)    */
 {    char *s, *t;
   int i, ii, j, k, mi, d, kk;    t=in;s=in;
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    while (*in != '\0'){
   double **out;      while( *in == occ){
   double sw; /* Sum of weights */        *blocc++ = *in++;
   double lli; /* Individual log likelihood */        s=in;
   long ipmx;      }
   /*extern weight */      *blocc++ = *in++;
   /* We are differentiating ll according to initial status */    }
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    if (s == t) /* occ not found */
   /*for(i=1;i<imx;i++)      *(blocc-(in-s))='\0';
     printf(" %d\n",s[4][i]);    else
   */      *(blocc-(in-s)-1)='\0';
   cov[1]=1.;    in=s;
     while ( *in != '\0'){
   for(k=1; k<=nlstate; k++) ll[k]=0.;      *alocc++ = *in++;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    }
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  
     for(mi=1; mi<= wav[i]-1; mi++){    *alocc='\0';
       for (ii=1;ii<=nlstate+ndeath;ii++)    return s;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  }
       for(d=0; d<dh[mi][i]; d++){  
         newm=savm;  int nbocc(char *s, char occ)
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  {
         for (kk=1; kk<=cptcovage;kk++) {    int i,j=0;
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    int lg=20;
         }    i=0;
            lg=strlen(s);
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    for(i=0; i<= lg; i++) {
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    if  (s[i] == occ ) j++;
         savm=oldm;    }
         oldm=newm;    return j;
          }
          
       } /* end mult */  /* void cutv(char *u,char *v, char*t, char occ) */
        /* { */
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       ipmx +=1;  /*      gives u="abcdef2ghi" and v="j" *\/ */
       sw += weight[i];  /*   int i,lg,j,p=0; */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  /*   i=0; */
     } /* end of wave */  /*   lg=strlen(t); */
   } /* end of individual */  /*   for(j=0; j<=lg-1; j++) { */
   /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   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 */  /*   for(j=0; j<p; j++) { */
   return -l;  /*     (u[j] = t[j]); */
 }  /*   } */
   /*      u[p]='\0'; */
   
 /*********** Maximum Likelihood Estimation ***************/  /*    for(j=0; j<= lg; j++) { */
   /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  /*   } */
 {  /* } */
   int i,j, iter;  
   double **xi,*delti;  #ifdef _WIN32
   double fret;  char * strsep(char **pp, const char *delim)
   xi=matrix(1,npar,1,npar);  {
   for (i=1;i<=npar;i++)    char *p, *q;
     for (j=1;j<=npar;j++)           
       xi[i][j]=(i==j ? 1.0 : 0.0);    if ((p = *pp) == NULL)
   printf("Powell\n");      return 0;
   powell(p,xi,npar,ftol,&iter,&fret,func);    if ((q = strpbrk (p, delim)) != NULL)
     {
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));      *pp = q + 1;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));      *q = '\0';
     }
 }    else
       *pp = 0;
 /**** Computes Hessian and covariance matrix ***/    return p;
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  }
 {  #endif
   double  **a,**y,*x,pd;  
   double **hess;  /********************** nrerror ********************/
   int i, j,jk;  
   int *indx;  void nrerror(char error_text[])
   {
   double hessii(double p[], double delta, int theta, double delti[]);    fprintf(stderr,"ERREUR ...\n");
   double hessij(double p[], double delti[], int i, int j);    fprintf(stderr,"%s\n",error_text);
   void lubksb(double **a, int npar, int *indx, double b[]) ;    exit(EXIT_FAILURE);
   void ludcmp(double **a, int npar, int *indx, double *d) ;  }
   /*********************** vector *******************/
   hess=matrix(1,npar,1,npar);  double *vector(int nl, int nh)
   {
   printf("\nCalculation of the hessian matrix. Wait...\n");    double *v;
   for (i=1;i<=npar;i++){    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     printf("%d",i);fflush(stdout);    if (!v) nrerror("allocation failure in vector");
     hess[i][i]=hessii(p,ftolhess,i,delti);    return v-nl+NR_END;
     /*printf(" %f ",p[i]);*/  }
     /*printf(" %lf ",hess[i][i]);*/  
   }  /************************ free vector ******************/
    void free_vector(double*v, int nl, int nh)
   for (i=1;i<=npar;i++) {  {
     for (j=1;j<=npar;j++)  {    free((FREE_ARG)(v+nl-NR_END));
       if (j>i) {  }
         printf(".%d%d",i,j);fflush(stdout);  
         hess[i][j]=hessij(p,delti,i,j);  /************************ivector *******************************/
         hess[j][i]=hess[i][j];      int *ivector(long nl,long nh)
         /*printf(" %lf ",hess[i][j]);*/  {
       }    int *v;
     }    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   }    if (!v) nrerror("allocation failure in ivector");
   printf("\n");    return v-nl+NR_END;
   }
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  
    /******************free ivector **************************/
   a=matrix(1,npar,1,npar);  void free_ivector(int *v, long nl, long nh)
   y=matrix(1,npar,1,npar);  {
   x=vector(1,npar);    free((FREE_ARG)(v+nl-NR_END));
   indx=ivector(1,npar);  }
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  /************************lvector *******************************/
   ludcmp(a,npar,indx,&pd);  long *lvector(long nl,long nh)
   {
   for (j=1;j<=npar;j++) {    long *v;
     for (i=1;i<=npar;i++) x[i]=0;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     x[j]=1;    if (!v) nrerror("allocation failure in ivector");
     lubksb(a,npar,indx,x);    return v-nl+NR_END;
     for (i=1;i<=npar;i++){  }
       matcov[i][j]=x[i];  
     }  /******************free lvector **************************/
   }  void free_lvector(long *v, long nl, long nh)
   {
   printf("\n#Hessian matrix#\n");    free((FREE_ARG)(v+nl-NR_END));
   for (i=1;i<=npar;i++) {  }
     for (j=1;j<=npar;j++) {  
       printf("%.3e ",hess[i][j]);  /******************* imatrix *******************************/
     }  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     printf("\n");       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   }  { 
     long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   /* Recompute Inverse */    int **m; 
   for (i=1;i<=npar;i++)    
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    /* allocate pointers to rows */ 
   ludcmp(a,npar,indx,&pd);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     if (!m) nrerror("allocation failure 1 in matrix()"); 
   /*  printf("\n#Hessian matrix recomputed#\n");    m += NR_END; 
     m -= nrl; 
   for (j=1;j<=npar;j++) {    
     for (i=1;i<=npar;i++) x[i]=0;    
     x[j]=1;    /* allocate rows and set pointers to them */ 
     lubksb(a,npar,indx,x);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     for (i=1;i<=npar;i++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       y[i][j]=x[i];    m[nrl] += NR_END; 
       printf("%.3e ",y[i][j]);    m[nrl] -= ncl; 
     }    
     printf("\n");    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   }    
   */    /* return pointer to array of pointers to rows */ 
     return m; 
   free_matrix(a,1,npar,1,npar);  } 
   free_matrix(y,1,npar,1,npar);  
   free_vector(x,1,npar);  /****************** free_imatrix *************************/
   free_ivector(indx,1,npar);  void free_imatrix(m,nrl,nrh,ncl,nch)
   free_matrix(hess,1,npar,1,npar);        int **m;
         long nch,ncl,nrh,nrl; 
        /* free an int matrix allocated by imatrix() */ 
 }  { 
     free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
 /*************** hessian matrix ****************/    free((FREE_ARG) (m+nrl-NR_END)); 
 double hessii( double x[], double delta, int theta, double delti[])  } 
 {  
   int i;  /******************* matrix *******************************/
   int l=1, lmax=20;  double **matrix(long nrl, long nrh, long ncl, long nch)
   double k1,k2;  {
   double p2[NPARMAX+1];    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   double res;    double **m;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  
   double fx;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   int k=0,kmax=10;    if (!m) nrerror("allocation failure 1 in matrix()");
   double l1;    m += NR_END;
     m -= nrl;
   fx=func(x);  
   for (i=1;i<=npar;i++) p2[i]=x[i];    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   for(l=0 ; l <=lmax; l++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     l1=pow(10,l);    m[nrl] += NR_END;
     delts=delt;    m[nrl] -= ncl;
     for(k=1 ; k <kmax; k=k+1){  
       delt = delta*(l1*k);    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       p2[theta]=x[theta] +delt;    return m;
       k1=func(p2)-fx;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
       p2[theta]=x[theta]-delt;  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
       k2=func(p2)-fx;  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
       /*res= (k1-2.0*fx+k2)/delt/delt; */     */
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  }
        
 #ifdef DEBUG  /*************************free matrix ************************/
       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);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
 #endif  {
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    free((FREE_ARG)(m+nrl-NR_END));
         k=kmax;  }
       }  
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  /******************* ma3x *******************************/
         k=kmax; l=lmax*10.;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       }  {
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
         delts=delt;    double ***m;
       }  
     }    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   }    if (!m) nrerror("allocation failure 1 in matrix()");
   delti[theta]=delts;    m += NR_END;
   return res;    m -= nrl;
    
 }    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 double hessij( double x[], double delti[], int thetai,int thetaj)    m[nrl] += NR_END;
 {    m[nrl] -= ncl;
   int i;  
   int l=1, l1, lmax=20;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   double k1,k2,k3,k4,res,fx;  
   double p2[NPARMAX+1];    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   int k;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     m[nrl][ncl] += NR_END;
   fx=func(x);    m[nrl][ncl] -= nll;
   for (k=1; k<=2; k++) {    for (j=ncl+1; j<=nch; j++) 
     for (i=1;i<=npar;i++) p2[i]=x[i];      m[nrl][j]=m[nrl][j-1]+nlay;
     p2[thetai]=x[thetai]+delti[thetai]/k;    
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    for (i=nrl+1; i<=nrh; i++) {
     k1=func(p2)-fx;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
        for (j=ncl+1; j<=nch; j++) 
     p2[thetai]=x[thetai]+delti[thetai]/k;        m[i][j]=m[i][j-1]+nlay;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    }
     k2=func(p2)-fx;    return m; 
      /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
     p2[thetai]=x[thetai]-delti[thetai]/k;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    */
     k3=func(p2)-fx;  }
    
     p2[thetai]=x[thetai]-delti[thetai]/k;  /*************************free ma3x ************************/
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     k4=func(p2)-fx;  {
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
 #ifdef DEBUG    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     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);    free((FREE_ARG)(m+nrl-NR_END));
 #endif  }
   }  
   return res;  /*************** function subdirf ***********/
 }  char *subdirf(char fileres[])
   {
 /************** Inverse of matrix **************/    /* Caution optionfilefiname is hidden */
 void ludcmp(double **a, int n, int *indx, double *d)    strcpy(tmpout,optionfilefiname);
 {    strcat(tmpout,"/"); /* Add to the right */
   int i,imax,j,k;    strcat(tmpout,fileres);
   double big,dum,sum,temp;    return tmpout;
   double *vv;  }
    
   vv=vector(1,n);  /*************** function subdirf2 ***********/
   *d=1.0;  char *subdirf2(char fileres[], char *preop)
   for (i=1;i<=n;i++) {  {
     big=0.0;    
     for (j=1;j<=n;j++)    /* Caution optionfilefiname is hidden */
       if ((temp=fabs(a[i][j])) > big) big=temp;    strcpy(tmpout,optionfilefiname);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    strcat(tmpout,"/");
     vv[i]=1.0/big;    strcat(tmpout,preop);
   }    strcat(tmpout,fileres);
   for (j=1;j<=n;j++) {    return tmpout;
     for (i=1;i<j;i++) {  }
       sum=a[i][j];  
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  /*************** function subdirf3 ***********/
       a[i][j]=sum;  char *subdirf3(char fileres[], char *preop, char *preop2)
     }  {
     big=0.0;    
     for (i=j;i<=n;i++) {    /* Caution optionfilefiname is hidden */
       sum=a[i][j];    strcpy(tmpout,optionfilefiname);
       for (k=1;k<j;k++)    strcat(tmpout,"/");
         sum -= a[i][k]*a[k][j];    strcat(tmpout,preop);
       a[i][j]=sum;    strcat(tmpout,preop2);
       if ( (dum=vv[i]*fabs(sum)) >= big) {    strcat(tmpout,fileres);
         big=dum;    return tmpout;
         imax=i;  }
       }  
     }  char *asc_diff_time(long time_sec, char ascdiff[])
     if (j != imax) {  {
       for (k=1;k<=n;k++) {    long sec_left, days, hours, minutes;
         dum=a[imax][k];    days = (time_sec) / (60*60*24);
         a[imax][k]=a[j][k];    sec_left = (time_sec) % (60*60*24);
         a[j][k]=dum;    hours = (sec_left) / (60*60) ;
       }    sec_left = (sec_left) %(60*60);
       *d = -(*d);    minutes = (sec_left) /60;
       vv[imax]=vv[j];    sec_left = (sec_left) % (60);
     }    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     indx[j]=imax;    return ascdiff;
     if (a[j][j] == 0.0) a[j][j]=TINY;  }
     if (j != n) {  
       dum=1.0/(a[j][j]);  /***************** f1dim *************************/
       for (i=j+1;i<=n;i++) a[i][j] *= dum;  extern int ncom; 
     }  extern double *pcom,*xicom;
   }  extern double (*nrfunc)(double []); 
   free_vector(vv,1,n);  /* Doesn't work */   
 ;  double f1dim(double x) 
 }  { 
     int j; 
 void lubksb(double **a, int n, int *indx, double b[])    double f;
 {    double *xt; 
   int i,ii=0,ip,j;   
   double sum;    xt=vector(1,ncom); 
      for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   for (i=1;i<=n;i++) {    f=(*nrfunc)(xt); 
     ip=indx[i];    free_vector(xt,1,ncom); 
     sum=b[ip];    return f; 
     b[ip]=b[i];  } 
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  /*****************brent *************************/
     else if (sum) ii=i;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     b[i]=sum;  { 
   }    int iter; 
   for (i=n;i>=1;i--) {    double a,b,d,etemp;
     sum=b[i];    double fu=0,fv,fw,fx;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    double ftemp=0.;
     b[i]=sum/a[i][i];    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   }    double e=0.0; 
 }   
     a=(ax < cx ? ax : cx); 
 /************ Frequencies ********************/    b=(ax > cx ? ax : cx); 
 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)    x=w=v=bx; 
 {  /* Some frequencies */    fw=fv=fx=(*f)(x); 
      for (iter=1;iter<=ITMAX;iter++) { 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;      xm=0.5*(a+b); 
   double ***freq; /* Frequencies */      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
   double *pp;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   double pos, k2, dateintsum=0,k2cpt=0;      printf(".");fflush(stdout);
   FILE *ficresp;      fprintf(ficlog,".");fflush(ficlog);
   char fileresp[FILENAMELENGTH];  #ifdef DEBUGBRENT
        printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   pp=vector(1,nlstate);      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);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   strcpy(fileresp,"p");  #endif
   strcat(fileresp,fileres);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   if((ficresp=fopen(fileresp,"w"))==NULL) {        *xmin=x; 
     printf("Problem with prevalence resultfile: %s\n", fileresp);        return fx; 
     exit(0);      } 
   }      ftemp=fu;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      if (fabs(e) > tol1) { 
   j1=0;        r=(x-w)*(fx-fv); 
          q=(x-v)*(fx-fw); 
   j=cptcoveff;        p=(x-v)*q-(x-w)*r; 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        q=2.0*(q-r); 
          if (q > 0.0) p = -p; 
   for(k1=1; k1<=j;k1++){        q=fabs(q); 
     for(i1=1; i1<=ncodemax[k1];i1++){        etemp=e; 
       j1++;        e=d; 
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
         scanf("%d", i);*/          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       for (i=-1; i<=nlstate+ndeath; i++)          else { 
         for (jk=-1; jk<=nlstate+ndeath; jk++)            d=p/q; 
           for(m=agemin; m <= agemax+3; m++)          u=x+d; 
             freq[i][jk][m]=0;          if (u-a < tol2 || b-u < tol2) 
                  d=SIGN(tol1,xm-x); 
       dateintsum=0;        } 
       k2cpt=0;      } else { 
       for (i=1; i<=imx; i++) {        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         bool=1;      } 
         if  (cptcovn>0) {      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
           for (z1=1; z1<=cptcoveff; z1++)      fu=(*f)(u); 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      if (fu <= fx) { 
               bool=0;        if (u >= x) a=x; else b=x; 
         }        SHFT(v,w,x,u) 
         if (bool==1) {          SHFT(fv,fw,fx,fu) 
           for(m=firstpass; m<=lastpass; m++){          } else { 
             k2=anint[m][i]+(mint[m][i]/12.);            if (u < x) a=u; else b=u; 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {            if (fu <= fw || w == x) { 
               if(agev[m][i]==0) agev[m][i]=agemax+1;              v=w; 
               if(agev[m][i]==1) agev[m][i]=agemax+2;              w=u; 
               if (m<lastpass) {              fv=fw; 
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];              fw=fu; 
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];            } else if (fu <= fv || v == x || v == w) { 
               }              v=u; 
                            fv=fu; 
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {            } 
                 dateintsum=dateintsum+k2;          } 
                 k2cpt++;    } 
               }    nrerror("Too many iterations in brent"); 
             }    *xmin=x; 
           }    return fx; 
         }  } 
       }  
          /****************** mnbrak ***********************/
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
       if  (cptcovn>0) {              double (*func)(double)) 
         fprintf(ficresp, "\n#********** Variable ");  { 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    double ulim,u,r,q, dum;
         fprintf(ficresp, "**********\n#");    double fu; 
       }   
       for(i=1; i<=nlstate;i++)    *fa=(*func)(*ax); 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    *fb=(*func)(*bx); 
       fprintf(ficresp, "\n");    if (*fb > *fa) { 
            SHFT(dum,*ax,*bx,dum) 
       for(i=(int)agemin; i <= (int)agemax+3; i++){        SHFT(dum,*fb,*fa,dum) 
         if(i==(int)agemax+3)        } 
           printf("Total");    *cx=(*bx)+GOLD*(*bx-*ax); 
         else    *fc=(*func)(*cx); 
           printf("Age %d", i);    while (*fb > *fc) { /* Declining fa, fb, fc */
         for(jk=1; jk <=nlstate ; jk++){      r=(*bx-*ax)*(*fb-*fc); 
           for(m=-1, 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). */
         for(jk=1; jk <=nlstate ; jk++){      ulim=(*bx)+GLIMIT*(*cx-*bx); /* Maximum abscisse where function can be evaluated */
           for(m=-1, pos=0; m <=0 ; m++)      if ((*bx-u)*(u-*cx) > 0.0) { /* if u between b and c */
             pos += freq[jk][m][i];        fu=(*func)(u); 
           if(pp[jk]>=1.e-10)  #ifdef DEBUG
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        /* f(x)=A(x-u)**2+f(u) */
           else        double A, fparabu; 
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        A= (*fb - *fa)/(*bx-*ax)/(*bx+*ax-2*u);
         }        fparabu= *fa - A*(*ax-u)*(*ax-u);
         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);
         for(jk=1; jk <=nlstate ; jk++){        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);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  #endif 
             pp[jk] += freq[jk][m][i];      } else if ((*cx-u)*(u-ulim) > 0.0) { /* u is after c but before ulim */
         }        fu=(*func)(u); 
         if (fu < *fc) { 
         for(jk=1,pos=0; jk <=nlstate ; jk++)          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
           pos += pp[jk];            SHFT(*fb,*fc,fu,(*func)(u)) 
         for(jk=1; jk <=nlstate ; jk++){            } 
           if(pos>=1.e-5)      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { /* u outside ulim (verifying that ulim is beyond c) */
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        u=ulim; 
           else        fu=(*func)(u); 
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);      } else { 
           if( i <= (int) agemax){        u=(*cx)+GOLD*(*cx-*bx); 
             if(pos>=1.e-5){        fu=(*func)(u); 
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      } 
               probs[i][jk][j1]= pp[jk]/pos;      SHFT(*ax,*bx,*cx,u) 
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/        SHFT(*fa,*fb,*fc,fu) 
             }        } 
             else  } 
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  
           }  /*************** linmin ************************/
         }  /* Given an n -dimensional point p[1..n] and an n -dimensional direction xi[1..n] , moves and
          resets p to where the function func(p) takes on a minimum along the direction xi from p ,
         for(jk=-1; jk <=nlstate+ndeath; jk++)  and replaces xi by the actual vector displacement that p was moved. Also returns as fret
           for(m=-1; m <=nlstate+ndeath; m++)  the value of func at the returned location p . This is actually all accomplished by calling the
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);  routines mnbrak and brent .*/
         if(i <= (int) agemax)  int ncom; 
           fprintf(ficresp,"\n");  double *pcom,*xicom;
         printf("\n");  double (*nrfunc)(double []); 
       }   
     }  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   }  { 
   dateintmean=dateintsum/k2cpt;    double brent(double ax, double bx, double cx, 
                   double (*f)(double), double tol, double *xmin); 
   fclose(ficresp);    double f1dim(double x); 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   free_vector(pp,1,nlstate);                double *fc, double (*func)(double)); 
      int j; 
   /* End of Freq */    double xx,xmin,bx,ax; 
 }    double fx,fb,fa;
    
 /************ Prevalence ********************/    ncom=n; 
 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)    pcom=vector(1,n); 
 {  /* Some frequencies */    xicom=vector(1,n); 
      nrfunc=func; 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;    for (j=1;j<=n;j++) { 
   double ***freq; /* Frequencies */      pcom[j]=p[j]; 
   double *pp;      xicom[j]=xi[j]; 
   double pos, k2;    } 
     ax=0.0; 
   pp=vector(1,nlstate);    xx=1.0; 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); /* Find a bracket a,x,b in direction n=xi ie xicom */
      *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); /* Find a minimum P+lambda n in that direction (lambdamin), with TOL between abscisses */
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  #ifdef DEBUG
   j1=0;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
      fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   j=cptcoveff;  #endif
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    for (j=1;j<=n;j++) { 
        xi[j] *= xmin; 
   for(k1=1; k1<=j;k1++){      p[j] += xi[j]; 
     for(i1=1; i1<=ncodemax[k1];i1++){    } 
       j1++;    free_vector(xicom,1,n); 
          free_vector(pcom,1,n); 
       for (i=-1; i<=nlstate+ndeath; i++)    } 
         for (jk=-1; jk<=nlstate+ndeath; jk++)    
           for(m=agemin; m <= agemax+3; m++)  
             freq[i][jk][m]=0;  /*************** powell ************************/
        /*
       for (i=1; i<=imx; i++) {  Minimization of a function func of n variables. Input consists of an initial starting point
         bool=1;  p[1..n] ; an initial matrix xi[1..n][1..n] , whose columns contain the initial set of di-
         if  (cptcovn>0) {  rections (usually the n unit vectors); and ftol , the fractional tolerance in the function value
           for (z1=1; z1<=cptcoveff; z1++)  such that failure to decrease by more than this amount on one iteration signals doneness. On
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  output, p is set to the best point found, xi is the then-current direction set, fret is the returned
               bool=0;  function value at p , and iter is the number of iterations taken. The routine linmin is used.
         }   */
         if (bool==1) {  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
           for(m=firstpass; m<=lastpass; m++){              double (*func)(double [])) 
             k2=anint[m][i]+(mint[m][i]/12.);  { 
             if ((k2>=dateprev1) && (k2<=dateprev2)) {    void linmin(double p[], double xi[], int n, double *fret, 
               if(agev[m][i]==0) agev[m][i]=agemax+1;                double (*func)(double [])); 
               if(agev[m][i]==1) agev[m][i]=agemax+2;    int i,ibig,j; 
               if (m<lastpass) {    double del,t,*pt,*ptt,*xit;
                 if (calagedate>0)    double fp,fptt;
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];    double *xits;
                 else    int niterf, itmp;
                   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];    pt=vector(1,n); 
               }    ptt=vector(1,n); 
             }    xit=vector(1,n); 
           }    xits=vector(1,n); 
         }    *fret=(*func)(p); 
       }    for (j=1;j<=n;j++) pt[j]=p[j]; 
       for(i=(int)agemin; i <= (int)agemax+3; i++){      rcurr_time = time(NULL);  
         for(jk=1; jk <=nlstate ; jk++){    for (*iter=1;;++(*iter)) { 
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      fp=(*fret); 
             pp[jk] += freq[jk][m][i];      ibig=0; 
         }      del=0.0; 
         for(jk=1; jk <=nlstate ; jk++){      rlast_time=rcurr_time;
           for(m=-1, pos=0; m <=0 ; m++)      /* (void) gettimeofday(&curr_time,&tzp); */
             pos += freq[jk][m][i];      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);
         for(jk=1; jk <=nlstate ; jk++){      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret,rcurr_time-rlast_time, rcurr_time-rstart_time); fflush(ficlog);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tm_sec-start_time.tm_sec); */
             pp[jk] += freq[jk][m][i];     for (i=1;i<=n;i++) {
         }        printf(" %d %.12f",i, p[i]);
                fprintf(ficlog," %d %.12lf",i, p[i]);
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];        fprintf(ficrespow," %.12lf", p[i]);
              }
         for(jk=1; jk <=nlstate ; jk++){          printf("\n");
           if( i <= (int) agemax){      fprintf(ficlog,"\n");
             if(pos>=1.e-5){      fprintf(ficrespow,"\n");fflush(ficrespow);
               probs[i][jk][j1]= pp[jk]/pos;      if(*iter <=3){
             }        tml = *localtime(&rcurr_time);
           }        strcpy(strcurr,asctime(&tml));
         }        rforecast_time=rcurr_time; 
                itmp = strlen(strcurr);
       }        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
     }          strcurr[itmp-1]='\0';
   }        printf("\nConsidering the time needed for the last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
         fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
          for(niterf=10;niterf<=30;niterf+=10){
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          rforecast_time=rcurr_time+(niterf-*iter)*(rcurr_time-rlast_time);
   free_vector(pp,1,nlstate);          forecast_time = *localtime(&rforecast_time);
            strcpy(strfor,asctime(&forecast_time));
 }  /* End of Freq */          itmp = strlen(strfor);
           if(strfor[itmp-1]=='\n')
 /************* Waves Concatenation ***************/          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);
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          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);
 {        }
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.      }
      Death is a valid wave (if date is known).      for (i=1;i<=n;i++) { 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        fptt=(*fret); 
      and mw[mi+1][i]. dh depends on stepm.  #ifdef DEBUG
      */            printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
             fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
   int i, mi, m;  #endif
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;        printf("%d",i);fflush(stdout);
      double sum=0., jmean=0.;*/        fprintf(ficlog,"%d",i);fflush(ficlog);
         linmin(p,xit,n,fret,func); 
   int j, k=0,jk, ju, jl;        if (fabs(fptt-(*fret)) > del) { 
   double sum=0.;          del=fabs(fptt-(*fret)); 
   jmin=1e+5;          ibig=i; 
   jmax=-1;        } 
   jmean=0.;  #ifdef DEBUG
   for(i=1; i<=imx; i++){        printf("%d %.12e",i,(*fret));
     mi=0;        fprintf(ficlog,"%d %.12e",i,(*fret));
     m=firstpass;        for (j=1;j<=n;j++) {
     while(s[m][i] <= nlstate){          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
       if(s[m][i]>=1)          printf(" x(%d)=%.12e",j,xit[j]);
         mw[++mi][i]=m;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
       if(m >=lastpass)        }
         break;        for(j=1;j<=n;j++) {
       else          printf(" p(%d)=%.12e",j,p[j]);
         m++;          fprintf(ficlog," p(%d)=%.12e",j,p[j]);
     }/* end while */        }
     if (s[m][i] > nlstate){        printf("\n");
       mi++;     /* Death is another wave */        fprintf(ficlog,"\n");
       /* if(mi==0)  never been interviewed correctly before death */  #endif
          /* Only death is a correct wave */      } /* end i */
       mw[mi][i]=m;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     }  #ifdef DEBUG
         int k[2],l;
     wav[i]=mi;        k[0]=1;
     if(mi==0)        k[1]=-1;
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        printf("Max: %.12e",(*func)(p));
   }        fprintf(ficlog,"Max: %.12e",(*func)(p));
         for (j=1;j<=n;j++) {
   for(i=1; i<=imx; i++){          printf(" %.12e",p[j]);
     for(mi=1; mi<wav[i];mi++){          fprintf(ficlog," %.12e",p[j]);
       if (stepm <=0)        }
         dh[mi][i]=1;        printf("\n");
       else{        fprintf(ficlog,"\n");
         if (s[mw[mi+1][i]][i] > nlstate) {        for(l=0;l<=1;l++) {
           if (agedc[i] < 2*AGESUP) {          for (j=1;j<=n;j++) {
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
           if(j==0) j=1;  /* Survives at least one month after exam */            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           k=k+1;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           if (j >= jmax) jmax=j;          }
           if (j <= jmin) jmin=j;          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           sum=sum+j;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           /*if (j<0) printf("j=%d num=%d \n",j,i); */        }
           }  #endif
         }  
         else{  
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));        free_vector(xit,1,n); 
           k=k+1;        free_vector(xits,1,n); 
           if (j >= jmax) jmax=j;        free_vector(ptt,1,n); 
           else if (j <= jmin)jmin=j;        free_vector(pt,1,n); 
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */        return; 
           sum=sum+j;      } 
         }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
         jk= j/stepm;      for (j=1;j<=n;j++) { /* Computes an extrapolated point */
         jl= j -jk*stepm;        ptt[j]=2.0*p[j]-pt[j]; 
         ju= j -(jk+1)*stepm;        xit[j]=p[j]-pt[j]; 
         if(jl <= -ju)        pt[j]=p[j]; 
           dh[mi][i]=jk;      } 
         else      fptt=(*func)(ptt); 
           dh[mi][i]=jk+1;      if (fptt < fp) { /* If extrapolated point is better, decide if we keep that new direction or not */
         if(dh[mi][i]==0)        /* (x1 f1=fp), (x2 f2=*fret), (x3 f3=fptt), (xm fm) */
           dh[mi][i]=1; /* At least one step */        /* From x1 (P0) distance of x2 is at h and x3 is 2h */
       }        /* Let f"(x2) be the 2nd derivative equal everywhere.  */
     }        /* Then the parabolic through (x1,f1), (x2,f2) and (x3,f3) */
   }        /* will reach at f3 = fm + h^2/2 f"m  ; f" = (f1 -2f2 +f3 ) / h**2 */
   jmean=sum/k;        /* f1-f3 = delta(2h) = 2 h**2 f'' = 2(f1- 2f2 +f3) */
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        /* Thus we compare delta(2h) with observed f1-f3 */
  }        /* or best gain on one ancient line 'del' with total  */
 /*********** Tricode ****************************/        /* gain f1-f2 = f1 - f2 - 'del' with del  */
 void tricode(int *Tvar, int **nbcode, int imx)        /* t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); */
 {  
   int Ndum[20],ij=1, k, j, i;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del);
   int cptcode=0;        t= t- del*SQR(fp-fptt);
   cptcoveff=0;        printf("t1= %.12lf, t2= %.12lf, t=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t);
          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);
   for (k=0; k<19; k++) Ndum[k]=0;  #ifdef DEBUG
   for (k=1; k<=7; k++) ncodemax[k]=0;        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));
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {        fprintf(ficlog,"t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
     for (i=1; i<=imx; i++) {               (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
       ij=(int)(covar[Tvar[j]][i]);        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);
       Ndum[ij]++;        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);
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/  #endif
       if (ij > cptcode) cptcode=ij;        if (t < 0.0) { /* Then we use it for last direction */
     }          linmin(p,xit,n,fret,func); /* computes mean on the extrapolated direction.*/
           for (j=1;j<=n;j++) { 
     for (i=0; i<=cptcode; i++) {            xi[j][ibig]=xi[j][n]; /* Replace the direction with biggest decrease by n */
       if(Ndum[i]!=0) ncodemax[j]++;            xi[j][n]=xit[j];      /* and nth direction by the extrapolated */
     }          }
     ij=1;          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 :\n",n,ibig);
   
     for (i=1; i<=ncodemax[j]; i++) {  #ifdef DEBUG
       for (k=0; k<=19; k++) {          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         if (Ndum[k] != 0) {          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           nbcode[Tvar[j]][ij]=k;          for(j=1;j<=n;j++){
                      printf(" %.12e",xit[j]);
           ij++;            fprintf(ficlog," %.12e",xit[j]);
         }          }
         if (ij > ncodemax[j]) break;          printf("\n");
       }            fprintf(ficlog,"\n");
     }  #endif
   }          } /* end of t negative */
       } /* end if (fptt < fp)  */
  for (k=0; k<19; k++) Ndum[k]=0;    } 
   } 
  for (i=1; i<=ncovmodel-2; i++) {  
       ij=Tvar[i];  /**** Prevalence limit (stable or period prevalence)  ****************/
       Ndum[ij]++;  
     }  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   {
  ij=1;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
  for (i=1; i<=10; i++) {       matrix by transitions matrix until convergence is reached */
    if((Ndum[i]!=0) && (i<=ncovcol)){  
      Tvaraff[ij]=i;    int i, ii,j,k;
      ij++;    double min, max, maxmin, maxmax,sumnew=0.;
    }    /* double **matprod2(); */ /* test */
  }    double **out, cov[NCOVMAX+1], **pmij();
      double **newm;
     cptcoveff=ij-1;    double agefin, delaymax=50 ; /* Max number of years to converge */
 }  
     for (ii=1;ii<=nlstate+ndeath;ii++)
 /*********** Health Expectancies ****************/      for (j=1;j<=nlstate+ndeath;j++){
         oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )      }
   
 {     cov[1]=1.;
   /* Health expectancies */   
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   double age, agelim, hf;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   double ***p3mat,***varhe;      newm=savm;
   double **dnewm,**doldm;      /* Covariates have to be included here again */
   double *xp;      cov[2]=agefin;
   double **gp, **gm;      
   double ***gradg, ***trgradg;      for (k=1; k<=cptcovn;k++) {
   int theta;        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         /*printf("prevalim ij=%d k=%d Tvar[%d]=%d nbcode=%d cov=%lf codtab[%d][Tvar[%d]]=%d \n",ij,k, k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], ij, k, codtab[ij][Tvar[k]]);*/
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);      }
   xp=vector(1,npar);      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
   dnewm=matrix(1,nlstate*2,1,npar);      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
   doldm=matrix(1,nlstate*2,1,nlstate*2);      /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
        
   fprintf(ficreseij,"# Health expectancies\n");      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   fprintf(ficreseij,"# Age");      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   for(i=1; i<=nlstate;i++)      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
     for(j=1; j<=nlstate;j++)      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
       fprintf(ficreseij," %1d-%1d (SE)",i,j);      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
   fprintf(ficreseij,"\n");      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
       
   if(estepm < stepm){      savm=oldm;
     printf ("Problem %d lower than %d\n",estepm, stepm);      oldm=newm;
   }      maxmax=0.;
   else  hstepm=estepm;        for(j=1;j<=nlstate;j++){
   /* We compute the life expectancy from trapezoids spaced every estepm months        min=1.;
    * This is mainly to measure the difference between two models: for example        max=0.;
    * if stepm=24 months pijx are given only every 2 years and by summing them        for(i=1; i<=nlstate; i++) {
    * we are calculating an estimate of the Life Expectancy assuming a linear          sumnew=0;
    * progression inbetween and thus overestimating or underestimating according          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
    * to the curvature of the survival function. If, for the same date, we          prlim[i][j]= newm[i][j]/(1-sumnew);
    * estimate the model with stepm=1 month, we can keep estepm to 24 months          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
    * to compare the new estimate of Life expectancy with the same linear          max=FMAX(max,prlim[i][j]);
    * hypothesis. A more precise result, taking into account a more precise          min=FMIN(min,prlim[i][j]);
    * curvature will be obtained if estepm is as small as stepm. */        }
         maxmin=max-min;
   /* For example we decided to compute the life expectancy with the smallest unit */        maxmax=FMAX(maxmax,maxmin);
   /* 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      if(maxmax < ftolpl){
      nstepm is the number of stepm from age to agelin.        return prlim;
      Look at hpijx to understand the reason of that which relies in memory size      }
      and note for a fixed period like estepm months */    }
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the  }
      survival function given by stepm (the optimization length). Unfortunately it  
      means that if the survival funtion is printed only each two years of age and if  /*************** transition probabilities ***************/ 
      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.  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   */  {
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    /* According to parameters values stored in x and the covariate's values stored in cov,
        computes the probability to be observed in state j being in state i by appying the
   agelim=AGESUP;       model to the ncovmodel covariates (including constant and age).
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
     /* nhstepm age range expressed in number of stepm */       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
     nstepm=(int) rint((agelim-age)*YEARM/stepm);       ncth covariate in the global vector x is given by the formula:
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
     /* if (stepm >= YEARM) hstepm=1;*/       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);       Outputs ps[i][j] the probability to be observed in j being in j according to
     gp=matrix(0,nhstepm,1,nlstate*2);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     gm=matrix(0,nhstepm,1,nlstate*2);    */
     double s1, lnpijopii;
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    /*double t34;*/
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    int i,j, nc, ii, jj;
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);    
        for(i=1; i<= nlstate; i++){
         for(j=1; j<i;j++){
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
             /*lnpijopii += param[i][j][nc]*cov[nc];*/
     /* Computing Variances of health expectancies */            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
      for(theta=1; theta <=npar; theta++){          }
       for(i=1; i<=npar; i++){          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
       }        }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          for(j=i+1; j<=nlstate+ndeath;j++){
            for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
       cptj=0;            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
       for(j=1; j<= nlstate; j++){            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
         for(i=1; i<=nlstate; i++){  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
           cptj=cptj+1;          }
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
             gp[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++){
       for(i=1; i<=npar; i++)          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          }
              for(j=i+1; j<=nlstate+ndeath; j++){
       cptj=0;          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
       for(j=1; j<= nlstate; j++){          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         for(i=1;i<=nlstate;i++){        }
           cptj=cptj+1;        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){        ps[i][i]=1./(s1+1.);
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;        /* Computing other pijs */
           }        for(j=1; j<i; j++)
         }          ps[i][j]= exp(ps[i][j])*ps[i][i];
       }        for(j=i+1; j<=nlstate+ndeath; j++)
                ps[i][j]= exp(ps[i][j])*ps[i][i];
            /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
       } /* end i */
       for(j=1; j<= nlstate*2; j++)      
         for(h=0; h<=nhstepm-1; h++){      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        for(jj=1; jj<= nlstate+ndeath; jj++){
         }          ps[ii][jj]=0;
           ps[ii][ii]=1;
      }        }
          }
 /* End theta */      
       
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
       /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
      for(h=0; h<=nhstepm-1; h++)      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
       for(j=1; j<=nlstate*2;j++)      /*   } */
         for(theta=1; theta <=npar; theta++)      /*   printf("\n "); */
         trgradg[h][j][theta]=gradg[h][theta][j];      /* } */
       /* printf("\n ");printf("%lf ",cov[2]);*/
       /*
      for(i=1;i<=nlstate*2;i++)        for(i=1; i<= npar; i++) printf("%f ",x[i]);
       for(j=1;j<=nlstate*2;j++)        goto end;*/
         varhe[i][j][(int)age] =0.;      return ps;
   }
      printf("%d|",(int)age);fflush(stdout);  
     for(h=0;h<=nhstepm-1;h++){  /**************** Product of 2 matrices ******************/
       for(k=0;k<=nhstepm-1;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);  {
         for(i=1;i<=nlstate*2;i++)    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
           for(j=1;j<=nlstate*2;j++)       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;    /* in, b, out are matrice of pointers which should have been initialized 
       }       before: only the contents of out is modified. The function returns
     }       a pointer to pointers identical to out */
     int i, j, k;
          for(i=nrl; i<= nrh; i++)
     /* Computing expectancies */      for(k=ncolol; k<=ncoloh; k++){
     for(i=1; i<=nlstate;i++)        out[i][k]=0.;
       for(j=1; j<=nlstate;j++)        for(j=ncl; j<=nch; j++)
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){          out[i][k] +=in[i][j]*b[j][k];
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;      }
              return out;
 /* 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]);*/  }
   
         }  
   /************* Higher Matrix Product ***************/
     fprintf(ficreseij,"%3.0f",age );  
     cptj=0;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
     for(i=1; i<=nlstate;i++)  {
       for(j=1; j<=nlstate;j++){    /* Computes the transition matrix starting at age 'age' over 
         cptj++;       'nhstepm*hstepm*stepm' months (i.e. until
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
       }       nhstepm*hstepm matrices. 
     fprintf(ficreseij,"\n");       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
           (typically every 2 years instead of every month which is too big 
     free_matrix(gm,0,nhstepm,1,nlstate*2);       for the memory).
     free_matrix(gp,0,nhstepm,1,nlstate*2);       Model is determined by parameters x and covariates have to be 
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);       included manually here. 
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);  
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       */
   }  
   free_vector(xp,1,npar);    int i, j, d, h, k;
   free_matrix(dnewm,1,nlstate*2,1,npar);    double **out, cov[NCOVMAX+1];
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);    double **newm;
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);  
 }    /* Hstepm could be zero and should return the unit matrix */
     for (i=1;i<=nlstate+ndeath;i++)
 /************ Variance ******************/      for (j=1;j<=nlstate+ndeath;j++){
 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)        oldm[i][j]=(i==j ? 1.0 : 0.0);
 {        po[i][j][0]=(i==j ? 1.0 : 0.0);
   /* Variance of health expectancies */      }
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   double **newm;    for(h=1; h <=nhstepm; h++){
   double **dnewm,**doldm;      for(d=1; d <=hstepm; d++){
   int i, j, nhstepm, hstepm, h, nstepm ;        newm=savm;
   int k, cptcode;        /* Covariates have to be included here again */
   double *xp;        cov[1]=1.;
   double **gp, **gm;        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   double ***gradg, ***trgradg;        for (k=1; k<=cptcovn;k++) 
   double ***p3mat;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   double age,agelim, hf;        for (k=1; k<=cptcovage;k++)
   int theta;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
         for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   fprintf(ficresvij,"# Age");  
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   fprintf(ficresvij,"\n");        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
                      pmij(pmmij,cov,ncovmodel,x,nlstate));
   xp=vector(1,npar);        savm=oldm;
   dnewm=matrix(1,nlstate,1,npar);        oldm=newm;
   doldm=matrix(1,nlstate,1,nlstate);      }
        for(i=1; i<=nlstate+ndeath; i++)
   if(estepm < stepm){        for(j=1;j<=nlstate+ndeath;j++) {
     printf ("Problem %d lower than %d\n",estepm, stepm);          po[i][j][h]=newm[i][j];
   }          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
   else  hstepm=estepm;          }
   /* For example we decided to compute the life expectancy with the smallest unit */      /*printf("h=%d ",h);*/
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.    } /* end h */
      nhstepm is the number of hstepm from age to agelim  /*     printf("\n H=%d \n",h); */
      nstepm is the number of stepm from age to agelin.    return po;
      Look at hpijx to understand the reason of that which relies in memory size  }
      and note for a fixed period like k years */  
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the  #ifdef NLOPT
      survival function given by stepm (the optimization length). Unfortunately it    double  myfunc(unsigned n, const double *p1, double *grad, void *pd){
      means that if the survival funtion is printed only each two years of age and if    double fret;
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    double *xt;
      results. So we changed our mind and took the option of the best precision.    int j;
   */    myfunc_data *d2 = (myfunc_data *) pd;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */  /* xt = (p1-1); */
   agelim = AGESUP;    xt=vector(1,n); 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    for (j=1;j<=n;j++)   xt[j]=p1[j-1]; /* xt[1]=p1[0] */
     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 */    fret=(d2->function)(xt); /*  p xt[1]@8 is fine */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /* fret=(*func)(xt); /\*  p xt[1]@8 is fine *\/ */
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    printf("Function = %.12lf ",fret);
     gp=matrix(0,nhstepm,1,nlstate);    for (j=1;j<=n;j++) printf(" %d %.8lf", j, xt[j]); 
     gm=matrix(0,nhstepm,1,nlstate);    printf("\n");
    free_vector(xt,1,n);
     for(theta=1; theta <=npar; theta++){    return fret;
       for(i=1; i<=npar; i++){ /* Computes gradient */  }
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  #endif
       }  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    /*************** log-likelihood *************/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  double func( double *x)
   {
       if (popbased==1) {    int i, ii, j, k, mi, d, kk;
         for(i=1; i<=nlstate;i++)    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
           prlim[i][i]=probs[(int)age][i][ij];    double **out;
       }    double sw; /* Sum of weights */
      double lli; /* Individual log likelihood */
       for(j=1; j<= nlstate; j++){    int s1, s2;
         for(h=0; h<=nhstepm; h++){    double bbh, survp;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    long ipmx;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    /*extern weight */
         }    /* We are differentiating ll according to initial status */
       }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
        /*for(i=1;i<imx;i++) 
       for(i=1; i<=npar; i++) /* Computes gradient */      printf(" %d\n",s[4][i]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    ++countcallfunc;
    
       if (popbased==1) {    cov[1]=1.;
         for(i=1; i<=nlstate;i++)  
           prlim[i][i]=probs[(int)age][i][ij];    for(k=1; k<=nlstate; k++) ll[k]=0.;
       }  
     if(mle==1){
       for(j=1; j<= nlstate; j++){      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(i=1, gm[h][j]=0.;i<=nlstate;i++)           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
         }           to be observed in j being in i according to the model.
       }         */
         for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
       for(j=1; j<= nlstate; j++)          cov[2+k]=covar[Tvar[k]][i];
         for(h=0; h<=nhstepm; h++){        }
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        /* 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] 
     } /* End theta */           has been calculated etc */
         for(mi=1; mi<= wav[i]-1; mi++){
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     for(h=0; h<=nhstepm; h++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate;j++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(theta=1; theta <=npar; theta++)            }
           trgradg[h][j][theta]=gradg[h][theta][j];          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for(i=1;i<=nlstate;i++)            for (kk=1; kk<=cptcovage;kk++) {
       for(j=1;j<=nlstate;j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
         vareij[i][j][(int)age] =0.;            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(h=0;h<=nhstepm;h++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(k=0;k<=nhstepm;k++){            savm=oldm;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);            oldm=newm;
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);          } /* end mult */
         for(i=1;i<=nlstate;i++)        
           for(j=1;j<=nlstate;j++)          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;          /* But now since version 0.9 we anticipate for bias at large stepm.
       }           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     }           * (in months) between two waves is not a multiple of stepm, we rounded to 
            * the nearest (and in case of equal distance, to the lowest) interval but now
     fprintf(ficresvij,"%.0f ",age );           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     for(i=1; i<=nlstate;i++)           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
       for(j=1; j<=nlstate;j++){           * probability in order to take into account the bias as a fraction of the way
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
       }           * -stepm/2 to stepm/2 .
     fprintf(ficresvij,"\n");           * For stepm=1 the results are the same as for previous versions of Imach.
     free_matrix(gp,0,nhstepm,1,nlstate);           * For stepm > 1 the results are less biased than in previous versions. 
     free_matrix(gm,0,nhstepm,1,nlstate);           */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);          s1=s[mw[mi][i]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);          s2=s[mw[mi+1][i]][i];
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          bbh=(double)bh[mi][i]/(double)stepm; 
   } /* End age */          /* bias bh is positive if real duration
             * is higher than the multiple of stepm and negative otherwise.
   free_vector(xp,1,npar);           */
   free_matrix(doldm,1,nlstate,1,npar);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   free_matrix(dnewm,1,nlstate,1,nlstate);          if( s2 > nlstate){ 
             /* i.e. if s2 is a death state and if the date of death is known 
 }               then the contribution to the likelihood is the probability to 
                die between last step unit time and current  step unit time, 
 /************ Variance of prevlim ******************/               which is also equal to probability to die before dh 
 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)               minus probability to die before dh-stepm . 
 {               In version up to 0.92 likelihood was computed
   /* Variance of prevalence limit */          as if date of death was unknown. Death was treated as any other
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          health state: the date of the interview describes the actual state
   double **newm;          and not the date of a change in health state. The former idea was
   double **dnewm,**doldm;          to consider that at each interview the state was recorded
   int i, j, nhstepm, hstepm;          (healthy, disable or death) and IMaCh was corrected; but when we
   int k, cptcode;          introduced the exact date of death then we should have modified
   double *xp;          the contribution of an exact death to the likelihood. This new
   double *gp, *gm;          contribution is smaller and very dependent of the step unit
   double **gradg, **trgradg;          stepm. It is no more the probability to die between last interview
   double age,agelim;          and month of death but the probability to survive from last
   int theta;          interview up to one month before death multiplied by the
              probability to die within a month. Thanks to Chris
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");          Jackson for correcting this bug.  Former versions increased
   fprintf(ficresvpl,"# Age");          mortality artificially. The bad side is that we add another loop
   for(i=1; i<=nlstate;i++)          which slows down the processing. The difference can be up to 10%
       fprintf(ficresvpl," %1d-%1d",i,i);          lower mortality.
   fprintf(ficresvpl,"\n");            */
             lli=log(out[s1][s2] - savm[s1][s2]);
   xp=vector(1,npar);  
   dnewm=matrix(1,nlstate,1,npar);  
   doldm=matrix(1,nlstate,1,nlstate);          } else if  (s2==-2) {
              for (j=1,survp=0. ; j<=nlstate; j++) 
   hstepm=1*YEARM; /* Every year of age */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            /*survp += out[s1][j]; */
   agelim = AGESUP;            lli= log(survp);
   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;          else if  (s2==-4) { 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            for (j=3,survp=0. ; j<=nlstate; j++)  
     gradg=matrix(1,npar,1,nlstate);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     gp=vector(1,nlstate);            lli= log(survp); 
     gm=vector(1,nlstate);          } 
   
     for(theta=1; theta <=npar; theta++){          else if  (s2==-5) { 
       for(i=1; i<=npar; i++){ /* Computes gradient */            for (j=1,survp=0. ; j<=2; j++)  
         xp[i] = x[i] + (i==theta ?delti[theta]:0);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       }            lli= log(survp); 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          } 
       for(i=1;i<=nlstate;i++)          
         gp[i] = prlim[i][i];          else{
                lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for(i=1; i<=npar; i++) /* Computes gradient */            /*  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 */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          } 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       for(i=1;i<=nlstate;i++)          /*if(lli ==000.0)*/
         gm[i] = prlim[i][i];          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
           ipmx +=1;
       for(i=1;i<=nlstate;i++)          sw += weight[i];
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     } /* End theta */        } /* end of wave */
       } /* end of individual */
     trgradg =matrix(1,nlstate,1,npar);    }  else if(mle==2){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     for(j=1; j<=nlstate;j++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(theta=1; theta <=npar; theta++)        for(mi=1; mi<= wav[i]-1; mi++){
         trgradg[j][theta]=gradg[theta][j];          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     for(i=1;i<=nlstate;i++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       varpl[i][(int)age] =0.;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);            }
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);          for(d=0; d<=dh[mi][i]; d++){
     for(i=1;i<=nlstate;i++)            newm=savm;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
     fprintf(ficresvpl,"%.0f ",age );              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(i=1; i<=nlstate;i++)            }
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     fprintf(ficresvpl,"\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     free_vector(gp,1,nlstate);            savm=oldm;
     free_vector(gm,1,nlstate);            oldm=newm;
     free_matrix(gradg,1,npar,1,nlstate);          } /* end mult */
     free_matrix(trgradg,1,nlstate,1,npar);        
   } /* End age */          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   free_vector(xp,1,npar);          bbh=(double)bh[mi][i]/(double)stepm; 
   free_matrix(doldm,1,nlstate,1,npar);          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 */
   free_matrix(dnewm,1,nlstate,1,nlstate);          ipmx +=1;
           sw += weight[i];
 }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
 /************ Variance of one-step probabilities  ******************/      } /* end of individual */
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)    }  else if(mle==3){  /* exponential inter-extrapolation */
 {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   int i, j, i1, k1, j1, z1;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int k=0, cptcode;        for(mi=1; mi<= wav[i]-1; mi++){
   double **dnewm,**doldm;          for (ii=1;ii<=nlstate+ndeath;ii++)
   double *xp;            for (j=1;j<=nlstate+ndeath;j++){
   double *gp, *gm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **gradg, **trgradg;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double age,agelim, cov[NCOVMAX];            }
   int theta;          for(d=0; d<dh[mi][i]; d++){
   char fileresprob[FILENAMELENGTH];            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   strcpy(fileresprob,"prob");            for (kk=1; kk<=cptcovage;kk++) {
   strcat(fileresprob,fileres);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {            }
     printf("Problem with resultfile: %s\n", fileresprob);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);            savm=oldm;
              oldm=newm;
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");          } /* end mult */
   fprintf(ficresprob,"# Age");        
   for(i=1; i<=nlstate;i++)          s1=s[mw[mi][i]][i];
     for(j=1; j<=(nlstate+ndeath);j++)          s2=s[mw[mi+1][i]][i];
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);          bbh=(double)bh[mi][i]/(double)stepm; 
           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 */
           ipmx +=1;
   fprintf(ficresprob,"\n");          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
   xp=vector(1,npar);      } /* end of individual */
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   cov[1]=1;        for(mi=1; mi<= wav[i]-1; mi++){
   j=cptcoveff;          for (ii=1;ii<=nlstate+ndeath;ii++)
   if (cptcovn<1) {j=1;ncodemax[1]=1;}            for (j=1;j<=nlstate+ndeath;j++){
   j1=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for(k1=1; k1<=1;k1++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i1=1; i1<=ncodemax[k1];i1++){            }
     j1++;          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
     if  (cptcovn>0) {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       fprintf(ficresprob, "\n#********** Variable ");            for (kk=1; kk<=cptcovage;kk++) {
       for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       fprintf(ficresprob, "**********\n#");            }
     }          
                out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       for (age=bage; age<=fage; age ++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         cov[2]=age;            savm=oldm;
         for (k=1; k<=cptcovn;k++) {            oldm=newm;
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];          } /* end mult */
                  
         }          s1=s[mw[mi][i]][i];
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          s2=s[mw[mi+1][i]][i];
         for (k=1; k<=cptcovprod;k++)          if( s2 > nlstate){ 
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];            lli=log(out[s1][s2] - savm[s1][s2]);
                  }else{
         gradg=matrix(1,npar,1,9);            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         trgradg=matrix(1,9,1,npar);          }
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          ipmx +=1;
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          sw += weight[i];
              ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(theta=1; theta <=npar; theta++){  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
           for(i=1; i<=npar; i++)        } /* end of wave */
             xp[i] = x[i] + (i==theta ?delti[theta]:0);      } /* end of individual */
              }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
                  for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           k=0;        for(mi=1; mi<= wav[i]-1; mi++){
           for(i=1; i<= (nlstate+ndeath); i++){          for (ii=1;ii<=nlstate+ndeath;ii++)
             for(j=1; j<=(nlstate+ndeath);j++){            for (j=1;j<=nlstate+ndeath;j++){
               k=k+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               gp[k]=pmmij[i][j];              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }            }
           }          for(d=0; d<dh[mi][i]; d++){
                      newm=savm;
           for(i=1; i<=npar; i++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);            for (kk=1; kk<=cptcovage;kk++) {
                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           pmij(pmmij,cov,ncovmodel,xp,nlstate);            }
           k=0;          
           for(i=1; i<=(nlstate+ndeath); i++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
             for(j=1; j<=(nlstate+ndeath);j++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
               k=k+1;            savm=oldm;
               gm[k]=pmmij[i][j];            oldm=newm;
             }          } /* end mult */
           }        
                s1=s[mw[mi][i]][i];
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)          s2=s[mw[mi+1][i]][i];
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         }          ipmx +=1;
           sw += weight[i];
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           for(theta=1; theta <=npar; theta++)          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
             trgradg[j][theta]=gradg[theta][j];        } /* end of wave */
              } /* end of individual */
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    } /* End of if */
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
            /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         pmij(pmmij,cov,ncovmodel,x,nlstate);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
            return -l;
         k=0;  }
         for(i=1; i<=(nlstate+ndeath); i++){  
           for(j=1; j<=(nlstate+ndeath);j++){  /*************** log-likelihood *************/
             k=k+1;  double funcone( double *x)
             gm[k]=pmmij[i][j];  {
           }    /* Same as likeli but slower because of a lot of printf and if */
         }    int i, ii, j, k, mi, d, kk;
          double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
      /*printf("\n%d ",(int)age);    double **out;
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    double lli; /* Individual log likelihood */
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    double llt;
      }*/    int s1, s2;
     double bbh, survp;
         fprintf(ficresprob,"\n%d ",(int)age);    /*extern weight */
     /* We are differentiating ll according to initial status */
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));    /*for(i=1;i<imx;i++) 
        printf(" %d\n",s[4][i]);
       }    */
     }    cov[1]=1.;
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));  
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    for(k=1; k<=nlstate; k++) ll[k]=0.;
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);  
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   free_vector(xp,1,npar);      for(mi=1; mi<= wav[i]-1; mi++){
   fclose(ficresprob);        for (ii=1;ii<=nlstate+ndeath;ii++)
            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);
 /******************* Printing html file ***********/          }
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \        for(d=0; d<dh[mi][i]; d++){
                   int lastpass, int stepm, int weightopt, char model[],\          newm=savm;
                   int imx,int jmin, int jmax, double jmeanint,char optionfile[], \          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                   char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\          for (kk=1; kk<=cptcovage;kk++) {
                   char version[], int popforecast, int estepm ,/* \ */            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
                   double jprev1, double mprev1,double anprev1, \          }
                   double jprev2, double mprev2,double anprev2){          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   int jj1, k1, i1, cpt;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   FILE *fichtm;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /*char optionfilehtm[FILENAMELENGTH];*/          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
           /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
   strcpy(optionfilehtm,optionfile);          savm=oldm;
   strcat(optionfilehtm,".htm");          oldm=newm;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        } /* end mult */
     printf("Problem with %s \n",optionfilehtm), exit(0);        
   }        s1=s[mw[mi][i]][i];
         s2=s[mw[mi+1][i]][i];
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n        bbh=(double)bh[mi][i]/(double)stepm; 
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n        /* bias is positive if real duration
 \n         * is higher than the multiple of stepm and negative otherwise.
 Total number of observations=%d <br>\n         */
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n        if( s2 > nlstate && (mle <5) ){  /* Jackson */
 <hr  size=\"2\" color=\"#EC5E5E\">          lli=log(out[s1][s2] - savm[s1][s2]);
  <ul><li>Parameter files<br>\n        } else if  (s2==-2) {
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n          for (j=1,survp=0. ; j<=nlstate; j++) 
  - Gnuplot file name: <a href=\"%s\">%s</a><br></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           lli= log(survp);
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n        }else if (mle==1){
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n        } else if(mle==2){
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n          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 */
  - Life expectancies by age and initial health status (estepm=%2d months):        } else if(mle==3){  /* exponential inter-extrapolation */
    <a href=\"e%s\">e%s</a> <br>\n</li>", \          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 */
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);        } else if (mle==4){  /* mle=4 no inter-extrapolation */
           lli=log(out[s1][s2]); /* Original formula */
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n        } else{  /* mle=0 back to 1 */
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n          /*lli=log(out[s1][s2]); */ /* Original formula */
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n        } /* End of if */
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n        ipmx +=1;
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);        sw += weight[i];
         ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
  if(popforecast==1) fprintf(fichtm,"\n        /*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]); */
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n        if(globpr){
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
         <br>",fileres,fileres,fileres,fileres);   %11.6f %11.6f %11.6f ", \
  else                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
 fprintf(fichtm," <li>Graphs</li><p>");          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
             llt +=ll[k]*gipmx/gsw;
  m=cptcoveff;            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}          }
           fprintf(ficresilk," %10.6f\n", -llt);
  jj1=0;        }
  for(k1=1; k1<=m;k1++){      } /* end of wave */
    for(i1=1; i1<=ncodemax[k1];i1++){    } /* end of individual */
        jj1++;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
        if (cptcovn > 0) {    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
          for (cpt=1; cpt<=cptcoveff;cpt++)    if(globpr==0){ /* First time we count the contributions and weights */
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);      gipmx=ipmx;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      gsw=sw;
        }    }
        /* Pij */    return -l;
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>  }
 <img src=\"pe%s%d1.png\">",strtok(optionfile, "."),jj1,stepm,strtok(optionfile, "."),jj1);      
        /* Quasi-incidences */  
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: pe%s%d2.png<br>  /*************** function likelione ***********/
 <img src=\"pe%s%d2.png\">",strtok(optionfile, "."),jj1,stepm,strtok(optionfile, "."),jj1);      void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
        /* Stable prevalence in each health state */  {
        for(cpt=1; cpt<nlstate;cpt++){    /* This routine should help understanding what is done with 
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>       the selection of individuals/waves and
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);       to check the exact contribution to the likelihood.
        }       Plotting could be done.
     for(cpt=1; cpt<=nlstate;cpt++) {     */
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    int k;
 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);      if(*globpri !=0){ /* Just counts and sums, no printings */
      }      strcpy(fileresilk,"ilk"); 
      for(cpt=1; cpt<=nlstate;cpt++) {      strcat(fileresilk,fileres);
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);        printf("Problem with resultfile: %s\n", fileresilk);
      }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      }
 health expectancies in states (1) and (2): e%s%d.png<br>      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");
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
 fprintf(fichtm,"\n</body>");      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
    }      for(k=1; k<=nlstate; k++) 
    }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
 fclose(fichtm);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
 }    }
   
 /******************* Gnuplot file **************/    *fretone=(*funcone)(p);
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){    if(*globpri !=0){
       fclose(ficresilk);
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   int ng;      fflush(fichtm); 
   strcpy(optionfilegnuplot,optionfilefiname);    } 
   strcat(optionfilegnuplot,".gp.txt");    return;
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {  }
     printf("Problem with file %s",optionfilegnuplot);  
   }  
   /*********** Maximum Likelihood Estimation ***************/
 #ifdef windows  
     fprintf(ficgp,"cd \"%s\" \n",pathc);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
 #endif  {
 m=pow(2,cptcoveff);    int i,j, iter=0;
      double **xi;
  /* 1eme*/    double fret;
   for (cpt=1; cpt<= nlstate ; cpt ++) {    double fretone; /* Only one call to likelihood */
    for (k1=1; k1<= m ; k1 ++) {    /*  char filerespow[FILENAMELENGTH];*/
   
 #ifdef windows  #ifdef NLOPT
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);    int creturn;
      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);    nlopt_opt opt;
 #endif    /* double lb[9] = { -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL }; /\* lower bounds *\/ */
 #ifdef unix    double *lb;
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);    double minf; /* the minimum objective value, upon return */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);    double * p1; /* Shifted parameters from 0 instead of 1 */
 #endif    myfunc_data dinst, *d = &dinst;
   #endif
 for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    xi=matrix(1,npar,1,npar);
 }    for (i=1;i<=npar;i++)
     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 (j=1;j<=npar;j++)
     for (i=1; i<= nlstate ; i ++) {        xi[i][j]=(i==j ? 1.0 : 0.0);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    printf("Powell\n");  fprintf(ficlog,"Powell\n");
   else fprintf(ficgp," \%%*lf (\%%*lf)");    strcpy(filerespow,"pow"); 
 }    strcat(filerespow,fileres);
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
      for (i=1; i<= nlstate ; i ++) {      printf("Problem with resultfile: %s\n", filerespow);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    }
 }      fprintf(ficrespow,"# Powell\n# iter -2*LL");
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    for (i=1;i<=nlstate;i++)
 #ifdef unix      for(j=1;j<=nlstate+ndeath;j++)
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
 #endif    fprintf(ficrespow,"\n");
    }  #ifdef POWELL
   }    powell(p,xi,npar,ftol,&iter,&fret,func);
   /*2 eme*/  #endif
   
   for (k1=1; k1<= m ; k1 ++) {  #ifdef NLOPT
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);  #ifdef NEWUOA
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    opt = nlopt_create(NLOPT_LN_NEWUOA,npar);
      #else
     for (i=1; i<= nlstate+1 ; i ++) {    opt = nlopt_create(NLOPT_LN_BOBYQA,npar);
       k=2*i;  #endif
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    lb=vector(0,npar-1);
       for (j=1; j<= nlstate+1 ; j ++) {    for (i=0;i<npar;i++) lb[i]= -HUGE_VAL;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    nlopt_set_lower_bounds(opt, lb);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    nlopt_set_initial_step1(opt, 0.1);
 }      
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    p1= (p+1); /*  p *(p+1)@8 and p *(p1)@8 are equal p1[0]=p[1] */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    d->function = func;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    printf(" Func %.12lf \n",myfunc(npar,p1,NULL,d));
       for (j=1; j<= nlstate+1 ; j ++) {    nlopt_set_min_objective(opt, myfunc, d);
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    nlopt_set_xtol_rel(opt, ftol);
         else fprintf(ficgp," \%%*lf (\%%*lf)");    if ((creturn=nlopt_optimize(opt, p1, &minf)) < 0) {
 }        printf("nlopt failed! %d\n",creturn); 
       fprintf(ficgp,"\" t\"\" w l 0,");    }
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    else {
       for (j=1; j<= nlstate+1 ; j ++) {      printf("found minimum after %d evaluations (NLOPT=%d)\n", countcallfunc ,NLOPT);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      printf("found minimum at f(%g,%g) = %0.10g\n", p[0], p[1], minf);
   else fprintf(ficgp," \%%*lf (\%%*lf)");      iter=1; /* not equal */
 }      }
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    nlopt_destroy(opt);
       else fprintf(ficgp,"\" t\"\" w l 0,");  #endif
     }    free_matrix(xi,1,npar,1,npar);
   }    fclose(ficrespow);
      printf("\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   /*3eme*/    fprintf(ficlog,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
     fprintf(ficres,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<= nlstate ; cpt ++) {  }
       k=2+nlstate*(2*cpt-2);  
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);  /**** Computes Hessian and covariance matrix ***/
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);  {
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    double  **a,**y,*x,pd;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);    double **hess;
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    int i, j;
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    int *indx;
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);  
     double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
 */    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
       for (i=1; i< nlstate ; i ++) {    void lubksb(double **a, int npar, int *indx, double b[]) ;
         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);    void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
       }    hess=matrix(1,npar,1,npar);
     }  
   }    printf("\nCalculation of the hessian matrix. Wait...\n");
      fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   /* CV preval stat */    for (i=1;i<=npar;i++){
     for (k1=1; k1<= m ; k1 ++) {      printf("%d",i);fflush(stdout);
     for (cpt=1; cpt<nlstate ; cpt ++) {      fprintf(ficlog,"%d",i);fflush(ficlog);
       k=3;     
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
       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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);      
       /*  printf(" %f ",p[i]);
       for (i=1; i< nlstate ; i ++)          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
         fprintf(ficgp,"+$%d",k+i+1);    }
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    
          for (i=1;i<=npar;i++) {
       l=3+(nlstate+ndeath)*cpt;      for (j=1;j<=npar;j++)  {
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);        if (j>i) { 
       for (i=1; i< nlstate ; i ++) {          printf(".%d%d",i,j);fflush(stdout);
         l=3+(nlstate+ndeath)*cpt;          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
         fprintf(ficgp,"+$%d",l+i+1);          hess[i][j]=hessij(p,delti,i,j,func,npar);
       }          
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);            hess[j][i]=hess[i][j];    
     }          /*printf(" %lf ",hess[i][j]);*/
   }          }
        }
   /* proba elementaires */    }
    for(i=1,jk=1; i <=nlstate; i++){    printf("\n");
     for(k=1; k <=(nlstate+ndeath); k++){    fprintf(ficlog,"\n");
       if (k != i) {  
         for(j=1; j <=ncovmodel; j++){    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
            fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    
           jk++;    a=matrix(1,npar,1,npar);
           fprintf(ficgp,"\n");    y=matrix(1,npar,1,npar);
         }    x=vector(1,npar);
       }    indx=ivector(1,npar);
     }    for (i=1;i<=npar;i++)
    }      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     ludcmp(a,npar,indx,&pd);
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/  
      for(jk=1; jk <=m; jk++) {    for (j=1;j<=npar;j++) {
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);      for (i=1;i<=npar;i++) x[i]=0;
        if (ng==2)      x[j]=1;
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");      lubksb(a,npar,indx,x);
        else      for (i=1;i<=npar;i++){ 
          fprintf(ficgp,"\nset title \"Probability\"\n");        matcov[i][j]=x[i];
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);      }
        i=1;    }
        for(k2=1; k2<=nlstate; k2++) {  
          k3=i;    printf("\n#Hessian matrix#\n");
          for(k=1; k<=(nlstate+ndeath); k++) {    fprintf(ficlog,"\n#Hessian matrix#\n");
            if (k != k2){    for (i=1;i<=npar;i++) { 
              if(ng==2)      for (j=1;j<=npar;j++) { 
                fprintf(ficgp," %f*exp(p%d+p%d*x",stepm/YEARM,i,i+1);        printf("%.3e ",hess[i][j]);
              else        fprintf(ficlog,"%.3e ",hess[i][j]);
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);      }
              ij=1;      printf("\n");
              for(j=3; j <=ncovmodel; j++) {      fprintf(ficlog,"\n");
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    }
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);  
                  ij++;    /* Recompute Inverse */
                }    for (i=1;i<=npar;i++)
                else      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    ludcmp(a,npar,indx,&pd);
              }  
              fprintf(ficgp,")/(1");    /*  printf("\n#Hessian matrix recomputed#\n");
                
              for(k1=1; k1 <=nlstate; k1++){      for (j=1;j<=npar;j++) {
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);      for (i=1;i<=npar;i++) x[i]=0;
                ij=1;      x[j]=1;
                for(j=3; j <=ncovmodel; j++){      lubksb(a,npar,indx,x);
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {      for (i=1;i<=npar;i++){ 
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        y[i][j]=x[i];
                    ij++;        printf("%.3e ",y[i][j]);
                  }        fprintf(ficlog,"%.3e ",y[i][j]);
                  else      }
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);      printf("\n");
                }      fprintf(ficlog,"\n");
                fprintf(ficgp,")");    }
              }    */
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);  
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    free_matrix(a,1,npar,1,npar);
              i=i+ncovmodel;    free_matrix(y,1,npar,1,npar);
            }    free_vector(x,1,npar);
          }    free_ivector(indx,1,npar);
        }    free_matrix(hess,1,npar,1,npar);
      }  
    }  
    fclose(ficgp);  }
 }  /* end gnuplot */  
   /*************** hessian matrix ****************/
   double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
 /*************** Moving average **************/  {
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){    int i;
     int l=1, lmax=20;
   int i, cpt, cptcod;    double k1,k2;
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)    double p2[MAXPARM+1]; /* identical to x */
       for (i=1; i<=nlstate;i++)    double res;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
           mobaverage[(int)agedeb][i][cptcod]=0.;    double fx;
        int k=0,kmax=10;
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){    double l1;
       for (i=1; i<=nlstate;i++){  
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    fx=func(x);
           for (cpt=0;cpt<=4;cpt++){    for (i=1;i<=npar;i++) p2[i]=x[i];
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
           }      l1=pow(10,l);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      delts=delt;
         }      for(k=1 ; k <kmax; k=k+1){
       }        delt = delta*(l1*k);
     }        p2[theta]=x[theta] +delt;
            k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
 }        p2[theta]=x[theta]-delt;
         k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
 /************** Forecasting ******************/        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
 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){        
    #ifdef DEBUGHESS
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   int *popage;        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  #endif
   double *popeffectif,*popcount;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   double ***p3mat;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   char fileresf[FILENAMELENGTH];          k=kmax;
         }
  agelim=AGESUP;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;          k=kmax; l=lmax*10;
         }
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            delts=delt;
          }
   strcpy(fileresf,"f");      }
   strcat(fileresf,fileres);    }
   if((ficresf=fopen(fileresf,"w"))==NULL) {    delti[theta]=delts;
     printf("Problem with forecast resultfile: %s\n", fileresf);    return res; 
   }    
   printf("Computing forecasting: result on file '%s' \n", fileresf);  }
   
   if (cptcoveff==0) ncodemax[cptcoveff]=1;  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   {
   if (mobilav==1) {    int i;
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    int l=1, lmax=20;
     movingaverage(agedeb, fage, ageminpar, mobaverage);    double k1,k2,k3,k4,res,fx;
   }    double p2[MAXPARM+1];
     int k;
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=12) stepsize=1;    fx=func(x);
      for (k=1; k<=2; k++) {
   agelim=AGESUP;      for (i=1;i<=npar;i++) p2[i]=x[i];
        p2[thetai]=x[thetai]+delti[thetai]/k;
   hstepm=1;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   hstepm=hstepm/stepm;      k1=func(p2)-fx;
   yp1=modf(dateintmean,&yp);    
   anprojmean=yp;      p2[thetai]=x[thetai]+delti[thetai]/k;
   yp2=modf((yp1*12),&yp);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   mprojmean=yp;      k2=func(p2)-fx;
   yp1=modf((yp2*30.5),&yp);    
   jprojmean=yp;      p2[thetai]=x[thetai]-delti[thetai]/k;
   if(jprojmean==0) jprojmean=1;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   if(mprojmean==0) jprojmean=1;      k3=func(p2)-fx;
      
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);      p2[thetai]=x[thetai]-delti[thetai]/k;
        p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   for(cptcov=1;cptcov<=i2;cptcov++){      k4=func(p2)-fx;
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
       k=k+1;  #ifdef DEBUG
       fprintf(ficresf,"\n#******");      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
       for(j=1;j<=cptcoveff;j++) {      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);
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  #endif
       }    }
       fprintf(ficresf,"******\n");    return res;
       fprintf(ficresf,"# StartingAge FinalAge");  }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  
        /************** Inverse of matrix **************/
        void ludcmp(double **a, int n, int *indx, double *d) 
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {  { 
         fprintf(ficresf,"\n");    int i,imax,j,k; 
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      double big,dum,sum,temp; 
     double *vv; 
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){   
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    vv=vector(1,n); 
           nhstepm = nhstepm/hstepm;    *d=1.0; 
              for (i=1;i<=n;i++) { 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      big=0.0; 
           oldm=oldms;savm=savms;      for (j=1;j<=n;j++) 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          if ((temp=fabs(a[i][j])) > big) big=temp; 
              if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
           for (h=0; h<=nhstepm; h++){      vv[i]=1.0/big; 
             if (h==(int) (calagedate+YEARM*cpt)) {    } 
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);    for (j=1;j<=n;j++) { 
             }      for (i=1;i<j;i++) { 
             for(j=1; j<=nlstate+ndeath;j++) {        sum=a[i][j]; 
               kk1=0.;kk2=0;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
               for(i=1; i<=nlstate;i++) {                      a[i][j]=sum; 
                 if (mobilav==1)      } 
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];      big=0.0; 
                 else {      for (i=j;i<=n;i++) { 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];        sum=a[i][j]; 
                 }        for (k=1;k<j;k++) 
                          sum -= a[i][k]*a[k][j]; 
               }        a[i][j]=sum; 
               if (h==(int)(calagedate+12*cpt)){        if ( (dum=vv[i]*fabs(sum)) >= big) { 
                 fprintf(ficresf," %.3f", kk1);          big=dum; 
                                  imax=i; 
               }        } 
             }      } 
           }      if (j != imax) { 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for (k=1;k<=n;k++) { 
         }          dum=a[imax][k]; 
       }          a[imax][k]=a[j][k]; 
     }          a[j][k]=dum; 
   }        } 
                *d = -(*d); 
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        vv[imax]=vv[j]; 
       } 
   fclose(ficresf);      indx[j]=imax; 
 }      if (a[j][j] == 0.0) a[j][j]=TINY; 
 /************** Forecasting ******************/      if (j != n) { 
 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){        dum=1.0/(a[j][j]); 
          for (i=j+1;i<=n;i++) a[i][j] *= dum; 
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      } 
   int *popage;    } 
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    free_vector(vv,1,n);  /* Doesn't work */
   double *popeffectif,*popcount;  ;
   double ***p3mat,***tabpop,***tabpopprev;  } 
   char filerespop[FILENAMELENGTH];  
   void lubksb(double **a, int n, int *indx, double b[]) 
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  { 
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    int i,ii=0,ip,j; 
   agelim=AGESUP;    double sum; 
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;   
      for (i=1;i<=n;i++) { 
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      ip=indx[i]; 
        sum=b[ip]; 
        b[ip]=b[i]; 
   strcpy(filerespop,"pop");      if (ii) 
   strcat(filerespop,fileres);        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   if((ficrespop=fopen(filerespop,"w"))==NULL) {      else if (sum) ii=i; 
     printf("Problem with forecast resultfile: %s\n", filerespop);      b[i]=sum; 
   }    } 
   printf("Computing forecasting: result on file '%s' \n", filerespop);    for (i=n;i>=1;i--) { 
       sum=b[i]; 
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       b[i]=sum/a[i][i]; 
   if (mobilav==1) {    } 
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  } 
     movingaverage(agedeb, fage, ageminpar, mobaverage);  
   }  void pstamp(FILE *fichier)
   {
   stepsize=(int) (stepm+YEARM-1)/YEARM;    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   if (stepm<=12) stepsize=1;  }
    
   agelim=AGESUP;  /************ 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[])
   hstepm=1;  {  /* Some frequencies */
   hstepm=hstepm/stepm;    
      int i, m, jk, j1, bool, z1,j;
   if (popforecast==1) {    int first;
     if((ficpop=fopen(popfile,"r"))==NULL) {    double ***freq; /* Frequencies */
       printf("Problem with population file : %s\n",popfile);exit(0);    double *pp, **prop;
     }    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     popage=ivector(0,AGESUP);    char fileresp[FILENAMELENGTH];
     popeffectif=vector(0,AGESUP);    
     popcount=vector(0,AGESUP);    pp=vector(1,nlstate);
        prop=matrix(1,nlstate,iagemin,iagemax+3);
     i=1;      strcpy(fileresp,"p");
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;    strcat(fileresp,fileres);
        if((ficresp=fopen(fileresp,"w"))==NULL) {
     imx=i;      printf("Problem with prevalence resultfile: %s\n", fileresp);
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
   }      exit(0);
     }
   for(cptcov=1;cptcov<=i2;cptcov++){    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    j1=0;
       k=k+1;    
       fprintf(ficrespop,"\n#******");    j=cptcoveff;
       for(j=1;j<=cptcoveff;j++) {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       }    first=1;
       fprintf(ficrespop,"******\n");  
       fprintf(ficrespop,"# Age");    /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
       if (popforecast==1)  fprintf(ficrespop," [Population]");    /*    j1++;
        */
       for (cpt=0; cpt<=0;cpt++) {    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);          /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
                  scanf("%d", i);*/
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        for (i=-5; i<=nlstate+ndeath; i++)  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           nhstepm = nhstepm/hstepm;            for(m=iagemin; m <= iagemax+3; m++)
                        freq[i][jk][m]=0;
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        
           oldm=oldms;savm=savms;        for (i=1; i<=nlstate; i++)  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            for(m=iagemin; m <= iagemax+3; m++)
                    prop[i][m]=0;
           for (h=0; h<=nhstepm; h++){        
             if (h==(int) (calagedate+YEARM*cpt)) {        dateintsum=0;
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);        k2cpt=0;
             }        for (i=1; i<=imx; i++) {
             for(j=1; j<=nlstate+ndeath;j++) {          bool=1;
               kk1=0.;kk2=0;          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
               for(i=1; i<=nlstate;i++) {                          for (z1=1; z1<=cptcoveff; z1++)       
                 if (mobilav==1)              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
                 else {                bool=0;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];                /* printf("bool=%d i=%d, z1=%d, Tvaraff[%d]=%d, covar[Tvarff][%d]=%2f, codtab[%d][%d]=%d, nbcode[Tvaraff][codtab[%d][%d]=%d, j1=%d\n", 
                 }                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
               }                  j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
               if (h==(int)(calagedate+12*cpt)){                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;              } 
                   /*fprintf(ficrespop," %.3f", kk1);          }
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/   
               }          if (bool==1){
             }            for(m=firstpass; m<=lastpass; m++){
             for(i=1; i<=nlstate;i++){              k2=anint[m][i]+(mint[m][i]/12.);
               kk1=0.;              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                 for(j=1; j<=nlstate;j++){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];                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];
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];                if (m<lastpass) {
             }                  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 (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)                }
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);                
           }                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                  dateintsum=dateintsum+k2;
         }                  k2cpt++;
       }                }
                  /*}*/
   /******/            }
           }
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {        } /* end i */
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);           
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        pstamp(ficresp);
           nhstepm = nhstepm/hstepm;        if  (cptcovn>0) {
                    fprintf(ficresp, "\n#********** Variable "); 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           oldm=oldms;savm=savms;          fprintf(ficresp, "**********\n#");
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            fprintf(ficlog, "\n#********** Variable "); 
           for (h=0; h<=nhstepm; h++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             if (h==(int) (calagedate+YEARM*cpt)) {          fprintf(ficlog, "**********\n#");
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);        }
             }        for(i=1; i<=nlstate;i++) 
             for(j=1; j<=nlstate+ndeath;j++) {          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
               kk1=0.;kk2=0;        fprintf(ficresp, "\n");
               for(i=1; i<=nlstate;i++) {                      
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];            for(i=iagemin; i <= iagemax+3; i++){
               }          if(i==iagemax+3){
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);            fprintf(ficlog,"Total");
             }          }else{
           }            if(first==1){
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              first=0;
         }              printf("See log file for details...\n");
       }            }
    }            fprintf(ficlog,"Age %d", i);
   }          }
            for(jk=1; jk <=nlstate ; jk++){
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               pp[jk] += freq[jk][m][i]; 
   if (popforecast==1) {          }
     free_ivector(popage,0,AGESUP);          for(jk=1; jk <=nlstate ; jk++){
     free_vector(popeffectif,0,AGESUP);            for(m=-1, pos=0; m <=0 ; m++)
     free_vector(popcount,0,AGESUP);              pos += freq[jk][m][i];
   }            if(pp[jk]>=1.e-10){
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);              if(first==1){
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   fclose(ficrespop);              }
 }              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             }else{
 /***********************************************/              if(first==1)
 /**************** Main Program *****************/                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
 /***********************************************/              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             }
 int main(int argc, char *argv[])          }
 {  
           for(jk=1; jk <=nlstate ; jk++){
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   double agedeb, agefin,hf;              pp[jk] += freq[jk][m][i];
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          }       
           for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
   double fret;            pos += pp[jk];
   double **xi,tmp,delta;            posprop += prop[jk][i];
           }
   double dum; /* Dummy variable */          for(jk=1; jk <=nlstate ; jk++){
   double ***p3mat;            if(pos>=1.e-5){
   int *indx;              if(first==1)
   char line[MAXLINE], linepar[MAXLINE];                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   char title[MAXLINE];              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];            }else{
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];              if(first==1)
                  printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }
   char filerest[FILENAMELENGTH];            if( i <= iagemax){
   char fileregp[FILENAMELENGTH];              if(pos>=1.e-5){
   char popfile[FILENAMELENGTH];                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];                /*probs[i][jk][j1]= pp[jk]/pos;*/
   int firstobs=1, lastobs=10;                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   int sdeb, sfin; /* Status at beginning and end */              }
   int c,  h , cpt,l;              else
   int ju,jl, mi;                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;            }
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          }
   int mobilav=0,popforecast=0;          
   int hstepm, nhstepm;          for(jk=-1; jk <=nlstate+ndeath; jk++)
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;            for(m=-1; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
   double bage, fage, age, agelim, agebase;              if(first==1)
   double ftolpl=FTOL;                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   double **prlim;                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   double *severity;              }
   double ***param; /* Matrix of parameters */          if(i <= iagemax)
   double  *p;            fprintf(ficresp,"\n");
   double **matcov; /* Matrix of covariance */          if(first==1)
   double ***delti3; /* Scale */            printf("Others in log...\n");
   double *delti; /* Scale */          fprintf(ficlog,"\n");
   double ***eij, ***vareij;        }
   double **varpl; /* Variances of prevalence limits by age */        /*}*/
   double *epj, vepp;    }
   double kk1, kk2;    dateintmean=dateintsum/k2cpt; 
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;   
      fclose(ficresp);
     free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   char version[80]="Imach version 0.8e, May 2002, INED-EUROREVES ";    free_vector(pp,1,nlstate);
   char *alph[]={"a","a","b","c","d","e"}, str[4];    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     /* End of Freq */
   }
   char z[1]="c", occ;  
 #include <sys/time.h>  /************ Prevalence ********************/
 #include <time.h>  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)
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  {  
      /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   /* long total_usecs;       in each health status at the date of interview (if between dateprev1 and dateprev2).
   struct timeval start_time, end_time;       We still use firstpass and lastpass as another selection.
      */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */   
   getcwd(pathcd, size);    int i, m, jk, j1, bool, z1,j;
   
   printf("\n%s",version);    double **prop;
   if(argc <=1){    double posprop; 
     printf("\nEnter the parameter file name: ");    double  y2; /* in fractional years */
     scanf("%s",pathtot);    int iagemin, iagemax;
   }    int first; /** to stop verbosity which is redirected to log file */
   else{  
     strcpy(pathtot,argv[1]);    iagemin= (int) agemin;
   }    iagemax= (int) agemax;
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    /*pp=vector(1,nlstate);*/
   /*cygwin_split_path(pathtot,path,optionfile);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   /* cutv(path,optionfile,pathtot,'\\');*/    j1=0;
     
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    /*j=cptcoveff;*/
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   chdir(path);    
   replace(pathc,path);    first=1;
     for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
 /*-------- arguments in the command line --------*/      /*for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;*/
   strcpy(fileres,"r");        
   strcat(fileres, optionfilefiname);        for (i=1; i<=nlstate; i++)  
   strcat(fileres,".txt");    /* Other files have txt extension */          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
   /*---------arguments file --------*/       
         for (i=1; i<=imx; i++) { /* Each individual */
   if((ficpar=fopen(optionfile,"r"))==NULL)    {          bool=1;
     printf("Problem with optionfile %s\n",optionfile);          if  (cptcovn>0) {
     goto end;            for (z1=1; z1<=cptcoveff; z1++) 
   }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
   strcpy(filereso,"o");          } 
   strcat(filereso,fileres);          if (bool==1) { 
   if((ficparo=fopen(filereso,"w"))==NULL) {            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     printf("Problem with Output resultfile: %s\n", filereso);goto end;              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
   }              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
   /* Reads comments: lines beginning with '#' */                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   while((c=getc(ficpar))=='#' && c!= EOF){                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); 
     ungetc(c,ficpar);                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     fgets(line, MAXLINE, ficpar);                  /*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]]);*/
     puts(line);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     fputs(line,ficparo);                  prop[s[m][i]][iagemax+3] += weight[i]; 
   }                } 
   ungetc(c,ficpar);              }
             } /* end selection of waves */
   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);          }
   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);        for(i=iagemin; i <= iagemax+3; i++){  
 while((c=getc(ficpar))=='#' && c!= EOF){          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
     ungetc(c,ficpar);            posprop += prop[jk][i]; 
     fgets(line, MAXLINE, ficpar);          } 
     puts(line);          
     fputs(line,ficparo);          for(jk=1; jk <=nlstate ; jk++){     
   }            if( i <=  iagemax){ 
   ungetc(c,ficpar);              if(posprop>=1.e-5){ 
                  probs[i][jk][j1]= prop[jk][i]/posprop;
                  } else{
   covar=matrix(0,NCOVMAX,1,n);                if(first==1){
   cptcovn=0;                  first=0;
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;                  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]);
                 }
   ncovmodel=2+cptcovn;              }
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */            } 
            }/* end jk */ 
   /* Read guess parameters */        }/* end i */ 
   /* Reads comments: lines beginning with '#' */      /*} *//* end i1 */
   while((c=getc(ficpar))=='#' && c!= EOF){    } /* end j1 */
     ungetc(c,ficpar);    
     fgets(line, MAXLINE, ficpar);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     puts(line);    /*free_vector(pp,1,nlstate);*/
     fputs(line,ficparo);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   }  }  /* End of prevalence */
   ungetc(c,ficpar);  
    /************* Waves Concatenation ***************/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
     for(i=1; i <=nlstate; i++)  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
     for(j=1; j <=nlstate+ndeath-1; j++){  {
       fscanf(ficpar,"%1d%1d",&i1,&j1);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       fprintf(ficparo,"%1d%1d",i1,j1);       Death is a valid wave (if date is known).
       printf("%1d%1d",i,j);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
       for(k=1; k<=ncovmodel;k++){       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
         fscanf(ficpar," %lf",&param[i][j][k]);       and mw[mi+1][i]. dh depends on stepm.
         printf(" %lf",param[i][j][k]);       */
         fprintf(ficparo," %lf",param[i][j][k]);  
       }    int i, mi, m;
       fscanf(ficpar,"\n");    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       printf("\n");       double sum=0., jmean=0.;*/
       fprintf(ficparo,"\n");    int first;
     }    int j, k=0,jk, ju, jl;
      double sum=0.;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    first=0;
     jmin=100000;
   p=param[1][1];    jmax=-1;
      jmean=0.;
   /* Reads comments: lines beginning with '#' */    for(i=1; i<=imx; i++){
   while((c=getc(ficpar))=='#' && c!= EOF){      mi=0;
     ungetc(c,ficpar);      m=firstpass;
     fgets(line, MAXLINE, ficpar);      while(s[m][i] <= nlstate){
     puts(line);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     fputs(line,ficparo);          mw[++mi][i]=m;
   }        if(m >=lastpass)
   ungetc(c,ficpar);          break;
         else
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          m++;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      }/* end while */
   for(i=1; i <=nlstate; i++){      if (s[m][i] > nlstate){
     for(j=1; j <=nlstate+ndeath-1; j++){        mi++;     /* Death is another wave */
       fscanf(ficpar,"%1d%1d",&i1,&j1);        /* if(mi==0)  never been interviewed correctly before death */
       printf("%1d%1d",i,j);           /* Only death is a correct wave */
       fprintf(ficparo,"%1d%1d",i1,j1);        mw[mi][i]=m;
       for(k=1; k<=ncovmodel;k++){      }
         fscanf(ficpar,"%le",&delti3[i][j][k]);  
         printf(" %le",delti3[i][j][k]);      wav[i]=mi;
         fprintf(ficparo," %le",delti3[i][j][k]);      if(mi==0){
       }        nbwarn++;
       fscanf(ficpar,"\n");        if(first==0){
       printf("\n");          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
       fprintf(ficparo,"\n");          first=1;
     }        }
   }        if(first==1){
   delti=delti3[1][1];          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
          }
   /* Reads comments: lines beginning with '#' */      } /* end mi==0 */
   while((c=getc(ficpar))=='#' && c!= EOF){    } /* End individuals */
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);    for(i=1; i<=imx; i++){
     puts(line);      for(mi=1; mi<wav[i];mi++){
     fputs(line,ficparo);        if (stepm <=0)
   }          dh[mi][i]=1;
   ungetc(c,ficpar);        else{
            if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
   matcov=matrix(1,npar,1,npar);            if (agedc[i] < 2*AGESUP) {
   for(i=1; i <=npar; i++){              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     fscanf(ficpar,"%s",&str);              if(j==0) j=1;  /* Survives at least one month after exam */
     printf("%s",str);              else if(j<0){
     fprintf(ficparo,"%s",str);                nberr++;
     for(j=1; j <=i; j++){                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]);
       fscanf(ficpar," %le",&matcov[i][j]);                j=1; /* Temporary Dangerous patch */
       printf(" %.5le",matcov[i][j]);                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
       fprintf(ficparo," %.5le",matcov[i][j]);                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     }                fprintf(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);
     fscanf(ficpar,"\n");              }
     printf("\n");              k=k+1;
     fprintf(ficparo,"\n");              if (j >= jmax){
   }                jmax=j;
   for(i=1; i <=npar; i++)                ijmax=i;
     for(j=i+1;j<=npar;j++)              }
       matcov[i][j]=matcov[j][i];              if (j <= jmin){
                    jmin=j;
   printf("\n");                ijmin=i;
               }
               sum=sum+j;
     /*-------- Rewriting paramater file ----------*/              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
      strcpy(rfileres,"r");    /* "Rparameterfile */              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/            }
      strcat(rfileres,".");    /* */          }
      strcat(rfileres,optionfilext);    /* Other files have txt extension */          else{
     if((ficres =fopen(rfileres,"w"))==NULL) {            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       printf("Problem writing new parameter file: %s\n", fileres);goto end;  /*        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]); */
     }  
     fprintf(ficres,"#%s\n",version);            k=k+1;
                if (j >= jmax) {
     /*-------- data file ----------*/              jmax=j;
     if((fic=fopen(datafile,"r"))==NULL)    {              ijmax=i;
       printf("Problem with datafile: %s\n", datafile);goto end;            }
     }            else if (j <= jmin){
               jmin=j;
     n= lastobs;              ijmin=i;
     severity = vector(1,maxwav);            }
     outcome=imatrix(1,maxwav+1,1,n);            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     num=ivector(1,n);            /*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]);*/
     moisnais=vector(1,n);            if(j<0){
     annais=vector(1,n);              nberr++;
     moisdc=vector(1,n);              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]);
     andc=vector(1,n);              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]);
     agedc=vector(1,n);            }
     cod=ivector(1,n);            sum=sum+j;
     weight=vector(1,n);          }
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */          jk= j/stepm;
     mint=matrix(1,maxwav,1,n);          jl= j -jk*stepm;
     anint=matrix(1,maxwav,1,n);          ju= j -(jk+1)*stepm;
     s=imatrix(1,maxwav+1,1,n);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
     adl=imatrix(1,maxwav+1,1,n);                if(jl==0){
     tab=ivector(1,NCOVMAX);              dh[mi][i]=jk;
     ncodemax=ivector(1,8);              bh[mi][i]=0;
             }else{ /* We want a negative bias in order to only have interpolation ie
     i=1;                    * to avoid the price of an extra matrix product in likelihood */
     while (fgets(line, MAXLINE, fic) != NULL)    {              dh[mi][i]=jk+1;
       if ((i >= firstobs) && (i <=lastobs)) {              bh[mi][i]=ju;
                    }
         for (j=maxwav;j>=1;j--){          }else{
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);            if(jl <= -ju){
           strcpy(line,stra);              dh[mi][i]=jk;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);              bh[mi][i]=jl;       /* bias is positive if real duration
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);                                   * is higher than the multiple of stepm and negative otherwise.
         }                                   */
                    }
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            else{
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);              dh[mi][i]=jk+1;
               bh[mi][i]=ju;
         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(dh[mi][i]==0){
               dh[mi][i]=1; /* At least one step */
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);              bh[mi][i]=ju; /* At least one step */
         for (j=ncovcol;j>=1;j--){              /*  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);*/
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);            }
         }          } /* end if mle */
         num[i]=atol(stra);        }
              } /* end wave */
         /*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;}*/    jmean=sum/k;
     printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
         i=i+1;    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("ii=%d", ij);  /*********** Tricode ****************************/
        scanf("%d",i);*/  void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
   imx=i-1; /* Number of individuals */  {
     /**< Uses cptcovn+2*cptcovprod as the number of covariates */
   /* for (i=1; i<=imx; i++){    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    /* Boring subroutine which should only output nbcode[Tvar[j]][k]
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    /* nbcode[Tvar[j]][1]= 
     }*/    */
    /*  for (i=1; i<=imx; i++){  
      if (s[4][i]==9)  s[4][i]=-1;    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
      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]));}*/    int modmaxcovj=0; /* Modality max of covariates j */
      int cptcode=0; /* Modality max of covariates j */
      int modmincovj=0; /* Modality min of covariates j */
   /* Calculation of the number of parameter from char model*/  
   Tvar=ivector(1,15);  
   Tprod=ivector(1,15);    cptcoveff=0; 
   Tvaraff=ivector(1,15);   
   Tvard=imatrix(1,15,1,2);    for (k=-1; k < maxncov; k++) Ndum[k]=0;
   Tage=ivector(1,15);          for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
      
   if (strlen(model) >1){    /* Loop on covariates without age and products */
     j=0, j1=0, k1=1, k2=1;    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
     j=nbocc(model,'+');      for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
     j1=nbocc(model,'*');                                 modality of this covariate Vj*/ 
     cptcovn=j+1;        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
     cptcovprod=j1;                                      * If product of Vn*Vm, still boolean *:
                                          * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
     strcpy(modelsav,model);                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
       printf("Error. Non available option model=%s ",model);                                        modality of the nth covariate of individual i. */
       goto end;        if (ij > modmaxcovj)
     }          modmaxcovj=ij; 
            else if (ij < modmincovj) 
     for(i=(j+1); i>=1;i--){          modmincovj=ij; 
       cutv(stra,strb,modelsav,'+');        if ((ij < -1) && (ij > NCOVMAX)){
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          exit(1);
       /*scanf("%d",i);*/        }else
       if (strchr(strb,'*')) {        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
         cutv(strd,strc,strb,'*');        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
         if (strcmp(strc,"age")==0) {        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
           cptcovprod--;        /* getting the maximum value of the modality of the covariate
           cutv(strb,stre,strd,'V');           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
           Tvar[i]=atoi(stre);           female is 1, then modmaxcovj=1.*/
           cptcovage++;      }
             Tage[cptcovage]=i;      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
             /*printf("stre=%s ", stre);*/      cptcode=modmaxcovj;
         }      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
         else if (strcmp(strd,"age")==0) {     /*for (i=0; i<=cptcode; i++) {*/
           cptcovprod--;      for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
           cutv(strb,stre,strc,'V');        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
           Tvar[i]=atoi(stre);        if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
           cptcovage++;          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
           Tage[cptcovage]=i;        }
         }        /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
         else {           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
           cutv(strb,stre,strc,'V');      } /* Ndum[-1] number of undefined modalities */
           Tvar[i]=ncovcol+k1;  
           cutv(strb,strc,strd,'V');      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
           Tprod[k1]=i;      /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
           Tvard[k1][1]=atoi(strc);      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
           Tvard[k1][2]=atoi(stre);         modmincovj=3; modmaxcovj = 7;
           Tvar[cptcovn+k2]=Tvard[k1][1];         There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
           Tvar[cptcovn+k2+1]=Tvard[k1][2];         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
           for (k=1; k<=lastobs;k++)         variables V1_1 and V1_2.
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];         nbcode[Tvar[j]][ij]=k;
           k1++;         nbcode[Tvar[j]][1]=0;
           k2=k2+2;         nbcode[Tvar[j]][2]=1;
         }         nbcode[Tvar[j]][3]=2;
       }      */
       else {      ij=1; /* ij is similar to i but can jumps over null modalities */
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/      for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
        /*  scanf("%d",i);*/        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
       cutv(strd,strc,strb,'V');          /*recode from 0 */
       Tvar[i]=atoi(strc);          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
       }            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
       strcpy(modelsav,stra);                                         k is a modality. If we have model=V1+V1*sex 
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
         scanf("%d",i);*/            ij++;
     }          }
 }          if (ij > ncodemax[j]) break; 
          }  /* end of loop on */
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);      } /* end of loop on modality */ 
   printf("cptcovprod=%d ", cptcovprod);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
   scanf("%d ",i);*/    
     fclose(fic);   for (k=-1; k< maxncov; k++) Ndum[k]=0; 
     
     /*  if(mle==1){*/    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
     if (weightopt != 1) { /* Maximisation without weights*/     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
       for(i=1;i<=n;i++) weight[i]=1.0;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
     }     Ndum[ij]++; 
     /*-calculation of age at interview from date of interview and age at death -*/   } 
     agev=matrix(1,maxwav,1,imx);  
    ij=1;
     for (i=1; i<=imx; i++) {   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
       for(m=2; (m<= maxwav); m++) {     /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){     if((Ndum[i]!=0) && (i<=ncovcol)){
          anint[m][i]=9999;       /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
          s[m][i]=-1;       Tvaraff[ij]=i; /*For printing (unclear) */
        }       ij++;
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;     }else
       }         Tvaraff[ij]=0;
     }   }
    ij--;
     for (i=1; i<=imx; i++)  {   cptcoveff=ij; /*Number of total covariates*/
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);  
       for(m=1; (m<= maxwav); m++){  }
         if(s[m][i] >0){  
           if (s[m][i] >= nlstate+1) {  
             if(agedc[i]>0)  /*********** Health Expectancies ****************/
               if(moisdc[i]!=99 && andc[i]!=9999)  
                 agev[m][i]=agedc[i];  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/  
            else {  {
               if (andc[i]!=9999){    /* Health expectancies, no variances */
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    int i, j, nhstepm, hstepm, h, nstepm;
               agev[m][i]=-1;    int nhstepma, nstepma; /* Decreasing with age */
               }    double age, agelim, hf;
             }    double ***p3mat;
           }    double eip;
           else if(s[m][i] !=9){ /* Should no more exist */  
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    pstamp(ficreseij);
             if(mint[m][i]==99 || anint[m][i]==9999)    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
               agev[m][i]=1;    fprintf(ficreseij,"# Age");
             else if(agev[m][i] <agemin){    for(i=1; i<=nlstate;i++){
               agemin=agev[m][i];      for(j=1; j<=nlstate;j++){
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/        fprintf(ficreseij," e%1d%1d ",i,j);
             }      }
             else if(agev[m][i] >agemax){      fprintf(ficreseij," e%1d. ",i);
               agemax=agev[m][i];    }
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    fprintf(ficreseij,"\n");
             }  
             /*agev[m][i]=anint[m][i]-annais[i];*/    
             /*   agev[m][i] = age[i]+2*m;*/    if(estepm < stepm){
           }      printf ("Problem %d lower than %d\n",estepm, stepm);
           else { /* =9 */    }
             agev[m][i]=1;    else  hstepm=estepm;   
             s[m][i]=-1;    /* We compute the life expectancy from trapezoids spaced every estepm months
           }     * This is mainly to measure the difference between two models: for example
         }     * if stepm=24 months pijx are given only every 2 years and by summing them
         else /*= 0 Unknown */     * we are calculating an estimate of the Life Expectancy assuming a linear 
           agev[m][i]=1;     * progression in between and thus overestimating or underestimating according
       }     * to the curvature of the survival function. If, for the same date, we 
         * estimate the model with stepm=1 month, we can keep estepm to 24 months
     }     * to compare the new estimate of Life expectancy with the same linear 
     for (i=1; i<=imx; i++)  {     * hypothesis. A more precise result, taking into account a more precise
       for(m=1; (m<= maxwav); m++){     * curvature will be obtained if estepm is as small as stepm. */
         if (s[m][i] > (nlstate+ndeath)) {  
           printf("Error: Wrong value in nlstate or ndeath\n");      /* For example we decided to compute the life expectancy with the smallest unit */
           goto end;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         }       nhstepm is the number of hstepm from age to agelim 
       }       nstepm is the number of stepm from age to agelin. 
     }       Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like estepm months */
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
     free_vector(severity,1,maxwav);       means that if the survival funtion is printed only each two years of age and if
     free_imatrix(outcome,1,maxwav+1,1,n);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     free_vector(moisnais,1,n);       results. So we changed our mind and took the option of the best precision.
     free_vector(annais,1,n);    */
     /* free_matrix(mint,1,maxwav,1,n);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
        free_matrix(anint,1,maxwav,1,n);*/  
     free_vector(moisdc,1,n);    agelim=AGESUP;
     free_vector(andc,1,n);    /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepm matrices, stored
             in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
     wav=ivector(1,imx);      
     dh=imatrix(1,lastpass-firstpass+1,1,imx);  /* nhstepm age range expressed in number of stepm */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
        /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* Concatenates waves */    /* if (stepm >= YEARM) hstepm=1;*/
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   
       Tcode=ivector(1,100);    for (age=bage; age<=fage; age ++){ 
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       ncodemax[1]=1;      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      /* if (stepm >= YEARM) hstepm=1;*/
            nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
    codtab=imatrix(1,100,1,10);  
    h=0;      /* If stepm=6 months */
    m=pow(2,cptcoveff);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
           in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
    for(k=1;k<=cptcoveff; k++){      
      for(i=1; i <=(m/pow(2,k));i++){      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
        for(j=1; j <= ncodemax[k]; j++){      
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
            h++;      
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;      printf("%d|",(int)age);fflush(stdout);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
          }      
        }      /* Computing expectancies */
      }      for(i=1; i<=nlstate;i++)
    }        for(j=1; j<=nlstate;j++)
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
       codtab[1][2]=1;codtab[2][2]=2; */            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
    /* for(i=1; i <=m ;i++){            
       for(k=1; k <=cptcovn; k++){            /* 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]);*/
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);  
       }          }
       printf("\n");  
       }      fprintf(ficreseij,"%3.0f",age );
       scanf("%d",i);*/      for(i=1; i<=nlstate;i++){
            eip=0;
    /* Calculates basic frequencies. Computes observed prevalence at single age        for(j=1; j<=nlstate;j++){
        and prints on file fileres'p'. */          eip +=eij[i][j][(int)age];
           fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
            }
            fprintf(ficreseij,"%9.4f", eip );
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      }
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficreseij,"\n");
     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 */    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
          printf("\n");
     /* For Powell, parameters are in a vector p[] starting at p[1]    fprintf(ficlog,"\n");
        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) */  }
   
     if(mle==1){  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[] )
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);  
     }  {
        /* Covariances of health expectancies eij and of total life expectancies according
     /*--------- results files --------------*/     to initial status i, ei. .
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);    */
      int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
     int nhstepma, nstepma; /* Decreasing with age */
    jk=1;    double age, agelim, hf;
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    double ***p3matp, ***p3matm, ***varhe;
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");    double **dnewm,**doldm;
    for(i=1,jk=1; i <=nlstate; i++){    double *xp, *xm;
      for(k=1; k <=(nlstate+ndeath); k++){    double **gp, **gm;
        if (k != i)    double ***gradg, ***trgradg;
          {    int theta;
            printf("%d%d ",i,k);  
            fprintf(ficres,"%1d%1d ",i,k);    double eip, vip;
            for(j=1; j <=ncovmodel; j++){  
              printf("%f ",p[jk]);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
              fprintf(ficres,"%f ",p[jk]);    xp=vector(1,npar);
              jk++;    xm=vector(1,npar);
            }    dnewm=matrix(1,nlstate*nlstate,1,npar);
            printf("\n");    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
            fprintf(ficres,"\n");    
          }    pstamp(ficresstdeij);
      }    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
    }    fprintf(ficresstdeij,"# Age");
  if(mle==1){    for(i=1; i<=nlstate;i++){
     /* Computing hessian and covariance matrix */      for(j=1; j<=nlstate;j++)
     ftolhess=ftol; /* Usually correct */        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
     hesscov(matcov, p, npar, delti, ftolhess, func);      fprintf(ficresstdeij," e%1d. ",i);
  }    }
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");    fprintf(ficresstdeij,"\n");
     printf("# Scales (for hessian or gradient estimation)\n");  
      for(i=1,jk=1; i <=nlstate; i++){    pstamp(ficrescveij);
       for(j=1; j <=nlstate+ndeath; j++){    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
         if (j!=i) {    fprintf(ficrescveij,"# Age");
           fprintf(ficres,"%1d%1d",i,j);    for(i=1; i<=nlstate;i++)
           printf("%1d%1d",i,j);      for(j=1; j<=nlstate;j++){
           for(k=1; k<=ncovmodel;k++){        cptj= (j-1)*nlstate+i;
             printf(" %.5e",delti[jk]);        for(i2=1; i2<=nlstate;i2++)
             fprintf(ficres," %.5e",delti[jk]);          for(j2=1; j2<=nlstate;j2++){
             jk++;            cptj2= (j2-1)*nlstate+i2;
           }            if(cptj2 <= cptj)
           printf("\n");              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           fprintf(ficres,"\n");          }
         }      }
       }    fprintf(ficrescveij,"\n");
      }    
        if(estepm < stepm){
     k=1;      printf ("Problem %d lower than %d\n",estepm, stepm);
     fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");    }
     printf("# 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");    else  hstepm=estepm;   
     for(i=1;i<=npar;i++){    /* We compute the life expectancy from trapezoids spaced every estepm months
       /*  if (k>nlstate) k=1;     * This is mainly to measure the difference between two models: for example
       i1=(i-1)/(ncovmodel*nlstate)+1;     * if stepm=24 months pijx are given only every 2 years and by summing them
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);     * we are calculating an estimate of the Life Expectancy assuming a linear 
       printf("%s%d%d",alph[k],i1,tab[i]);*/     * progression in between and thus overestimating or underestimating according
       fprintf(ficres,"%3d",i);     * to the curvature of the survival function. If, for the same date, we 
       printf("%3d",i);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       for(j=1; j<=i;j++){     * to compare the new estimate of Life expectancy with the same linear 
         fprintf(ficres," %.5e",matcov[i][j]);     * hypothesis. A more precise result, taking into account a more precise
         printf(" %.5e",matcov[i][j]);     * curvature will be obtained if estepm is as small as stepm. */
       }  
       fprintf(ficres,"\n");    /* For example we decided to compute the life expectancy with the smallest unit */
       printf("\n");    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       k++;       nhstepm is the number of hstepm from age to agelim 
     }       nstepm is the number of stepm from age to agelin. 
           Look at hpijx to understand the reason of that which relies in memory size
     while((c=getc(ficpar))=='#' && c!= EOF){       and note for a fixed period like estepm months */
       ungetc(c,ficpar);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fgets(line, MAXLINE, ficpar);       survival function given by stepm (the optimization length). Unfortunately it
       puts(line);       means that if the survival funtion is printed only each two years of age and if
       fputs(line,ficparo);       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.
     ungetc(c,ficpar);    */
     estepm=0;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     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 stepm=6 months */
     if (fage <= 2) {    /* nhstepm age range expressed in number of stepm */
       bage = ageminpar;    agelim=AGESUP;
       fage = agemaxpar;    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
        /* if (stepm >= YEARM) hstepm=1;*/
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     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);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     while((c=getc(ficpar))=='#' && c!= EOF){    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     ungetc(c,ficpar);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     fgets(line, MAXLINE, ficpar);    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     puts(line);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
     fputs(line,ficparo);  
   }    for (age=bage; age<=fage; age ++){ 
   ungetc(c,ficpar);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
        /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);      /* if (stepm >= YEARM) hstepm=1;*/
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
            /* If stepm=6 months */
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     ungetc(c,ficpar);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     fgets(line, MAXLINE, ficpar);      
     puts(line);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     fputs(line,ficparo);  
   }      /* Computing  Variances of health expectancies */
   ungetc(c,ficpar);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
           decrease memory allocation */
       for(theta=1; theta <=npar; theta++){
    dateprev1=anprev1+mprev1/12.+jprev1/365.;        for(i=1; i<=npar; i++){ 
    dateprev2=anprev2+mprev2/12.+jprev2/365.;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
   fscanf(ficpar,"pop_based=%d\n",&popbased);        }
   fprintf(ficparo,"pop_based=%d\n",popbased);          hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   fprintf(ficres,"pop_based=%d\n",popbased);          hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
      
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<= nlstate; j++){
     ungetc(c,ficpar);          for(i=1; i<=nlstate; i++){
     fgets(line, MAXLINE, ficpar);            for(h=0; h<=nhstepm-1; h++){
     puts(line);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
     fputs(line,ficparo);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   }            }
   ungetc(c,ficpar);          }
         }
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);       
 fprintf(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(ij=1; ij<= nlstate*nlstate; ij++)
 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);          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
           }
 while((c=getc(ficpar))=='#' && c!= EOF){      }/* End theta */
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      
     puts(line);      for(h=0; h<=nhstepm-1; h++)
     fputs(line,ficparo);        for(j=1; j<=nlstate*nlstate;j++)
   }          for(theta=1; theta <=npar; theta++)
   ungetc(c,ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
       
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);  
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);       for(ij=1;ij<=nlstate*nlstate;ij++)
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);        for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
        printf("%d|",(int)age);fflush(stdout);
 /*------------ gnuplot -------------*/       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);       for(h=0;h<=nhstepm-1;h++){
          for(k=0;k<=nhstepm-1;k++){
 /*------------ free_vector  -------------*/          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
  chdir(path);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
            for(ij=1;ij<=nlstate*nlstate;ij++)
  free_ivector(wav,1,imx);            for(ji=1;ji<=nlstate*nlstate;ji++)
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          }
  free_ivector(num,1,n);      }
  free_vector(agedc,1,n);  
  /*free_matrix(covar,1,NCOVMAX,1,n);*/      /* Computing expectancies */
  fclose(ficparo);      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
  fclose(ficres);      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
 /*--------- index.htm --------*/          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);            
             /* 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]);*/
    
   /*--------------- Prevalence limit --------------*/          }
    
   strcpy(filerespl,"pl");      fprintf(ficresstdeij,"%3.0f",age );
   strcat(filerespl,fileres);      for(i=1; i<=nlstate;i++){
   if((ficrespl=fopen(filerespl,"w"))==NULL) {        eip=0.;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        vip=0.;
   }        for(j=1; j<=nlstate;j++){
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);          eip += eij[i][j][(int)age];
   fprintf(ficrespl,"#Prevalence limit\n");          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
   fprintf(ficrespl,"#Age ");            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
   fprintf(ficrespl,"\n");        }
          fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
   prlim=matrix(1,nlstate,1,nlstate);      }
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresstdeij,"\n");
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficrescveij,"%3.0f",age );
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(i=1; i<=nlstate;i++)
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        for(j=1; j<=nlstate;j++){
   k=0;          cptj= (j-1)*nlstate+i;
   agebase=ageminpar;          for(i2=1; i2<=nlstate;i2++)
   agelim=agemaxpar;            for(j2=1; j2<=nlstate;j2++){
   ftolpl=1.e-10;              cptj2= (j2-1)*nlstate+i2;
   i1=cptcoveff;              if(cptj2 <= cptj)
   if (cptcovn < 1){i1=1;}                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
   for(cptcov=1;cptcov<=i1;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      fprintf(ficrescveij,"\n");
         k=k+1;     
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    }
         fprintf(ficrespl,"\n#******");    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         for(j=1;j<=cptcoveff;j++)    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
         fprintf(ficrespl,"******\n");    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
            free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for (age=agebase; age<=agelim; age++){    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    printf("\n");
           fprintf(ficrespl,"%.0f",age );    fprintf(ficlog,"\n");
           for(i=1; i<=nlstate;i++)  
           fprintf(ficrespl," %.5f", prlim[i][i]);    free_vector(xm,1,npar);
           fprintf(ficrespl,"\n");    free_vector(xp,1,npar);
         }    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
       }    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     }    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   fclose(ficrespl);  }
   
   /*------------- h Pij x at various ages ------------*/  /************ Variance ******************/
    void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  {
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    /* Variance of health expectancies */
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   }    /* double **newm;*/
   printf("Computing pij: result on file '%s' \n", filerespij);    double **dnewm,**doldm;
      double **dnewmp,**doldmp;
   stepsize=(int) (stepm+YEARM-1)/YEARM;    int i, j, nhstepm, hstepm, h, nstepm ;
   /*if (stepm<=24) stepsize=2;*/    int k;
     double *xp;
   agelim=AGESUP;    double **gp, **gm;  /* for var eij */
   hstepm=stepsize*YEARM; /* Every year of age */    double ***gradg, ***trgradg; /*for var eij */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    double **gradgp, **trgradgp; /* for var p point j */
      double *gpp, *gmp; /* for var p point j */
   k=0;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   for(cptcov=1;cptcov<=i1;cptcov++){    double ***p3mat;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double age,agelim, hf;
       k=k+1;    double ***mobaverage;
         fprintf(ficrespij,"\n#****** ");    int theta;
         for(j=1;j<=cptcoveff;j++)    char digit[4];
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    char digitp[25];
         fprintf(ficrespij,"******\n");  
            char fileresprobmorprev[FILENAMELENGTH];
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    if(popbased==1){
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      if(mobilav!=0)
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        strcpy(digitp,"-populbased-mobilav-");
           oldm=oldms;savm=savms;      else strcpy(digitp,"-populbased-nomobil-");
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      }
           fprintf(ficrespij,"# Age");    else 
           for(i=1; i<=nlstate;i++)      strcpy(digitp,"-stablbased-");
             for(j=1; j<=nlstate+ndeath;j++)  
               fprintf(ficrespij," %1d-%1d",i,j);    if (mobilav!=0) {
           fprintf(ficrespij,"\n");      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
            for (h=0; h<=nhstepm; h++){      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
             for(i=1; i<=nlstate;i++)        printf(" Error in movingaverage mobilav=%d\n",mobilav);
               for(j=1; j<=nlstate+ndeath;j++)      }
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    }
             fprintf(ficrespij,"\n");  
              }    strcpy(fileresprobmorprev,"prmorprev"); 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    sprintf(digit,"%-d",ij);
           fprintf(ficrespij,"\n");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
         }    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     }    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
   }    strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
   fclose(ficrespij);    }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
   /*---------- Forecasting ------------------*/    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   if((stepm == 1) && (strcmp(model,".")==0)){    pstamp(ficresprobmorprev);
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);    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);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   }    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   else{      fprintf(ficresprobmorprev," p.%-d SE",j);
     erreur=108;      for(i=1; i<=nlstate;i++)
     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(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   }    }  
      fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
   /*---------- Health expectancies and variances ------------*/    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
   strcpy(filerest,"t");    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   strcat(filerest,fileres);  /*   } */
   if((ficrest=fopen(filerest,"w"))==NULL) {    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    pstamp(ficresvij);
   }    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    if(popbased==1)
       fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
     else
   strcpy(filerese,"e");      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   strcat(filerese,fileres);    fprintf(ficresvij,"# Age");
   if((ficreseij=fopen(filerese,"w"))==NULL) {    for(i=1; i<=nlstate;i++)
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);      for(j=1; j<=nlstate;j++)
   }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    fprintf(ficresvij,"\n");
   
  strcpy(fileresv,"v");    xp=vector(1,npar);
   strcat(fileresv,fileres);    dnewm=matrix(1,nlstate,1,npar);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    doldm=matrix(1,nlstate,1,nlstate);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
   }    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);  
   calagedate=-1;    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
   k=0;    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   for(cptcov=1;cptcov<=i1;cptcov++){    
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    if(estepm < stepm){
       k=k+1;      printf ("Problem %d lower than %d\n",estepm, stepm);
       fprintf(ficrest,"\n#****** ");    }
       for(j=1;j<=cptcoveff;j++)    else  hstepm=estepm;   
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    /* For example we decided to compute the life expectancy with the smallest unit */
       fprintf(ficrest,"******\n");    /* 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 
       fprintf(ficreseij,"\n#****** ");       nstepm is the number of stepm from age to agelin. 
       for(j=1;j<=cptcoveff;j++)       Look at function hpijx to understand why (it is linked to memory size questions) */
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fprintf(ficreseij,"******\n");       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
       fprintf(ficresvij,"\n#****** ");       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       for(j=1;j<=cptcoveff;j++)       results. So we changed our mind and took the option of the best precision.
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    */
       fprintf(ficresvij,"******\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       oldm=oldms;savm=savms;      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);        nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
        p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       oldm=oldms;savm=savms;      gp=matrix(0,nhstepm,1,nlstate);
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);      gm=matrix(0,nhstepm,1,nlstate);
      
   
        for(theta=1; theta <=npar; theta++){
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       fprintf(ficrest,"\n");        }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       epj=vector(1,nlstate+1);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       for(age=bage; age <=fage ;age++){  
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        if (popbased==1) {
         if (popbased==1) {          if(mobilav ==0){
           for(i=1; i<=nlstate;i++)            for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][k];              prlim[i][i]=probs[(int)age][i][ij];
         }          }else{ /* mobilav */ 
                    for(i=1; i<=nlstate;i++)
         fprintf(ficrest," %4.0f",age);              prlim[i][i]=mobaverage[(int)age][i][ij];
         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]);*/        for(j=1; j<= nlstate; j++){
           }          for(h=0; h<=nhstepm; h++){
           epj[nlstate+1] +=epj[j];            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
         }              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         for(i=1, vepp=0.;i <=nlstate;i++)        }
           for(j=1;j <=nlstate;j++)        /* This for computing probability of death (h=1 means
             vepp += vareij[i][j][(int)age];           computed over hstepm matrices product = hstepm*stepm months) 
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));           as a weighted average of prlim.
         for(j=1;j <=nlstate;j++){        */
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         }          for(i=1,gpp[j]=0.; i<= nlstate; i++)
         fprintf(ficrest,"\n");            gpp[j] += prlim[i][i]*p3mat[i][j][1];
       }        }    
     }        /* end probability of death */
   }  
 free_matrix(mint,1,maxwav,1,n);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     free_vector(weight,1,n);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   fclose(ficreseij);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   fclose(ficresvij);   
   fclose(ficrest);        if (popbased==1) {
   fclose(ficpar);          if(mobilav ==0){
   free_vector(epj,1,nlstate+1);            for(i=1; i<=nlstate;i++)
                prlim[i][i]=probs[(int)age][i][ij];
   /*------- Variance limit prevalence------*/            }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
   strcpy(fileresvpl,"vpl");              prlim[i][i]=mobaverage[(int)age][i][ij];
   strcat(fileresvpl,fileres);          }
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {        }
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);  
     exit(0);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
   }          for(h=0; h<=nhstepm; h++){
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   k=0;          }
   for(cptcov=1;cptcov<=i1;cptcov++){        }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        /* This for computing probability of death (h=1 means
       k=k+1;           computed over hstepm matrices product = hstepm*stepm months) 
       fprintf(ficresvpl,"\n#****** ");           as a weighted average of prlim.
       for(j=1;j<=cptcoveff;j++)        */
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       fprintf(ficresvpl,"******\n");          for(i=1,gmp[j]=0.; i<= nlstate; i++)
                 gmp[j] += prlim[i][i]*p3mat[i][j][1];
       varpl=matrix(1,nlstate,(int) bage, (int) fage);        }    
       oldm=oldms;savm=savms;        /* end probability of death */
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);  
     }        for(j=1; j<= nlstate; j++) /* vareij */
  }          for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
   fclose(ficresvpl);          }
   
   /*---------- End : free ----------------*/        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
          }
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      } /* End theta */
    
        trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);      for(h=0; h<=nhstepm; h++) /* veij */
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(j=1; j<=nlstate;j++)
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          for(theta=1; theta <=npar; theta++)
              trgradg[h][j][theta]=gradg[h][theta][j];
   free_matrix(matcov,1,npar,1,npar);  
   free_vector(delti,1,npar);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
   free_matrix(agev,1,maxwav,1,imx);        for(theta=1; theta <=npar; theta++)
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          trgradgp[j][theta]=gradgp[theta][j];
     
   if(erreur >0)  
     printf("End of Imach with error or warning %d\n",erreur);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   else   printf("End of Imach\n");      for(i=1;i<=nlstate;i++)
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        for(j=1;j<=nlstate;j++)
            vareij[i][j][(int)age] =0.;
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/  
   /*printf("Total time was %d uSec.\n", total_usecs);*/      for(h=0;h<=nhstepm;h++){
   /*------ End -----------*/        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]);
  end:          for(i=1;i<=nlstate;i++)
 #ifdef windows            for(j=1;j<=nlstate;j++)
   /* chdir(pathcd);*/              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
 #endif        }
  /*system("wgnuplot graph.plt");*/      }
  /*system("../gp37mgw/wgnuplot graph.plt");*/    
  /*system("cd ../gp37mgw");*/      /* pptj */
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
  strcpy(plotcmd,GNUPLOTPROGRAM);      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
  strcat(plotcmd," ");      for(j=nlstate+1;j<=nlstate+ndeath;j++)
  strcat(plotcmd,optionfilegnuplot);        for(i=nlstate+1;i<=nlstate+ndeath;i++)
  system(plotcmd);          varppt[j][i]=doldmp[j][i];
       /* end ppptj */
 #ifdef windows      /*  x centered again */
   while (z[0] != 'q') {      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     /* chdir(path); */      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");   
     scanf("%s",z);      if (popbased==1) {
     if (z[0] == 'c') system("./imach");        if(mobilav ==0){
     else if (z[0] == 'e') system(optionfilehtm);          for(i=1; i<=nlstate;i++)
     else if (z[0] == 'g') system(plotcmd);            prlim[i][i]=probs[(int)age][i][ij];
     else if (z[0] == 'q') exit(0);        }else{ /* mobilav */ 
   }          for(i=1; i<=nlstate;i++)
 #endif            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 ******************/
   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*************/
   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);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               /* printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
    /* endread:*/
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   syscompilerinfo()
    {
      /* #include "syscompilerinfo.h"*/
   #include <gnu/libc-version.h>
   #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
   #endif
   
   // 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 \n"); /* 32-bit */
   #elif UINTPTR_MAX == 0xffffffffffffffff
     printf("64-bit \n");/* 64-bit */
   #else
    printf("wtf-bit \n"); /* wtf */
   #endif
   
   struct utsname sysInfo;
   
      if (uname(&sysInfo) != -1) {
         puts(sysInfo.sysname);
         puts(sysInfo.nodename);
         puts(sysInfo.release);
         puts(sysInfo.version);
         puts(sysInfo.machine);
      }
      else
         perror("uname() error");
      printf("GNU C version %d\n", __GNUC_VERSION__);
     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("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname='%s'\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     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.1.44  
changed lines
  Added in v.1.167


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