Diff for /imach/src/imach.c between versions 1.30 and 1.160

version 1.30, 2002/03/08 16:17:18 version 1.160, 2014/09/02 09:24:05
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.160  2014/09/02 09:24:05  brouard
      *** empty log message ***
   This program computes Healthy Life Expectancies from  
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    Revision 1.159  2014/09/01 10:34:10  brouard
   first survey ("cross") where individuals from different ages are    Summary: WIN32
   interviewed on their health status or degree of disability (in the    Author: Brouard
   case of a health survey which is our main interest) -2- at least a  
   second wave of interviews ("longitudinal") which measure each change    Revision 1.158  2014/08/27 17:11:51  brouard
   (if any) in individual health status.  Health expectancies are    *** empty log message ***
   computed from the time spent in each health state according to a  
   model. More health states you consider, more time is necessary to reach the    Revision 1.157  2014/08/27 16:26:55  brouard
   Maximum Likelihood of the parameters involved in the model.  The    Summary: Preparing windows Visual studio version
   simplest model is the multinomial logistic model where pij is the    Author: Brouard
   probabibility to be observed in state j at the second wave  
   conditional to be observed in state i at the first wave. Therefore    In order to compile on Visual studio, time.h is now correct and time_t
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    and tm struct should be used. difftime should be used but sometimes I
   'age' is age and 'sex' is a covariate. If you want to have a more    just make the differences in raw time format (time(&now).
   complex model than "constant and age", you should modify the program    Trying to suppress #ifdef LINUX
   where the markup *Covariates have to be included here again* invites    Add xdg-open for __linux in order to open default browser.
   you to do it.  More covariates you add, slower the  
   convergence.    Revision 1.156  2014/08/25 20:10:10  brouard
     *** empty log message ***
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.155  2014/08/25 18:32:34  brouard
   identical for each individual. Also, if a individual missed an    Summary: New compile, minor changes
   intermediate interview, the information is lost, but taken into    Author: Brouard
   account using an interpolation or extrapolation.    
     Revision 1.154  2014/06/20 17:32:08  brouard
   hPijx is the probability to be observed in state i at age x+h    Summary: Outputs now all graphs of convergence to period prevalence
   conditional to the observed state i at age x. The delay 'h' can be  
   split into an exact number (nh*stepm) of unobserved intermediate    Revision 1.153  2014/06/20 16:45:46  brouard
   states. This elementary transition (by month or quarter trimester,    Summary: If 3 live state, convergence to period prevalence on same graph
   semester or year) is model as a multinomial logistic.  The hPx    Author: Brouard
   matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply    Revision 1.152  2014/06/18 17:54:09  brouard
   hPijx.    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.151  2014/06/18 16:43:30  brouard
   of the life expectancies. It also computes the prevalence limits.    *** empty log message ***
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.150  2014/06/18 16:42:35  brouard
            Institut national d'études démographiques, Paris.    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
   This software have been partly granted by Euro-REVES, a concerted action    Author: brouard
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.149  2014/06/18 15:51:14  brouard
   software can be distributed freely for non commercial use. Latest version    Summary: Some fixes in parameter files errors
   can be accessed at http://euroreves.ined.fr/imach .    Author: Nicolas Brouard
   **********************************************************************/  
      Revision 1.148  2014/06/17 17:38:48  brouard
 #include <math.h>    Summary: Nothing new
 #include <stdio.h>    Author: Brouard
 #include <stdlib.h>  
 #include <unistd.h>    Just a new packaging for OS/X version 0.98nS
   
 #define MAXLINE 256    Revision 1.147  2014/06/16 10:33:11  brouard
 #define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"    *** empty log message ***
 #define FILENAMELENGTH 80  
 /*#define DEBUG*/    Revision 1.146  2014/06/16 10:20:28  brouard
 #define windows    Summary: Merge
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Author: Brouard
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     Merge, before building revised version.
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.145  2014/06/10 21:23:15  brouard
     Summary: Debugging with valgrind
 #define NINTERVMAX 8    Author: Nicolas Brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Lot of changes in order to output the results with some covariates
 #define NCOVMAX 8 /* Maximum number of covariates */    After the Edimburgh REVES conference 2014, it seems mandatory to
 #define MAXN 20000    improve the code.
 #define YEARM 12. /* Number of months per year */    No more memory valgrind error but a lot has to be done in order to
 #define AGESUP 130    continue the work of splitting the code into subroutines.
 #define AGEBASE 40    Also, decodemodel has been improved. Tricode is still not
     optimal. nbcode should be improved. Documentation has been added in
     the source code.
 int erreur; /* Error number */  
 int nvar;    Revision 1.143  2014/01/26 09:45:38  brouard
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int ndeath=1; /* Number of dead states */    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.142  2014/01/26 03:57:36  brouard
     Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.141  2014/01/26 02:42:01  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.140  2011/09/02 10:37:54  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Summary: times.h is ok with mingw32 now.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    Revision 1.139  2010/06/14 07:50:17  brouard
 FILE *ficgp,*ficresprob,*ficpop;    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 FILE *ficreseij;    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.138  2010/04/30 18:19:40  brouard
   char fileresv[FILENAMELENGTH];    *** empty log message ***
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.137  2010/04/29 18:11:38  brouard
     (Module): Checking covariates for more complex models
 #define NR_END 1    than V1+V2. A lot of change to be done. Unstable.
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.136  2010/04/26 20:30:53  brouard
     (Module): merging some libgsl code. Fixing computation
 #define NRANSI    of likelione (using inter/intrapolation if mle = 0) in order to
 #define ITMAX 200    get same likelihood as if mle=1.
     Some cleaning of code and comments added.
 #define TOL 2.0e-4  
     Revision 1.135  2009/10/29 15:33:14  brouard
 #define CGOLD 0.3819660    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.134  2009/10/29 13:18:53  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.133  2009/07/06 10:21:25  brouard
 #define TINY 1.0e-20    just nforces
   
 static double maxarg1,maxarg2;    Revision 1.132  2009/07/06 08:22:05  brouard
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Many tings
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.131  2009/06/20 16:22:47  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Some dimensions resccaled
 #define rint(a) floor(a+0.5)  
     Revision 1.130  2009/05/26 06:44:34  brouard
 static double sqrarg;    (Module): Max Covariate is now set to 20 instead of 8. A
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    lot of cleaning with variables initialized to 0. Trying to make
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   
 int imx;    Revision 1.129  2007/08/31 13:49:27  lievre
 int stepm;    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.128  2006/06/30 13:02:05  brouard
 int m,nb;    (Module): Clarifications on computing e.j
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Revision 1.127  2006/04/28 18:11:50  brouard
 double **pmmij, ***probs, ***mobaverage;    (Module): Yes the sum of survivors was wrong since
 double dateintmean=0;    imach-114 because nhstepm was no more computed in the age
     loop. Now we define nhstepma in the age loop.
 double *weight;    (Module): In order to speed up (in case of numerous covariates) we
 int **s; /* Status */    compute health expectancies (without variances) in a first step
 double *agedc, **covar, idx;    and then all the health expectancies with variances or standard
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    deviation (needs data from the Hessian matrices) which slows the
     computation.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    In the future we should be able to stop the program is only health
 double ftolhess; /* Tolerance for computing hessian */    expectancies and graph are needed without standard deviations.
   
 /**************** split *************************/    Revision 1.126  2006/04/28 17:23:28  brouard
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    (Module): Yes the sum of survivors was wrong since
 {    imach-114 because nhstepm was no more computed in the age
    char *s;                             /* pointer */    loop. Now we define nhstepma in the age loop.
    int  l1, l2;                         /* length counters */    Version 0.98h
   
    l1 = strlen( path );                 /* length of path */    Revision 1.125  2006/04/04 15:20:31  lievre
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Errors in calculation of health expectancies. Age was not initialized.
 #ifdef windows    Forecasting file added.
    s = strrchr( path, '\\' );           /* find last / */  
 #else    Revision 1.124  2006/03/22 17:13:53  lievre
    s = strrchr( path, '/' );            /* find last / */    Parameters are printed with %lf instead of %f (more numbers after the comma).
 #endif    The log-likelihood is printed in the log file
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.123  2006/03/20 10:52:43  brouard
       extern char       *getwd( );    * imach.c (Module): <title> changed, corresponds to .htm file
     name. <head> headers where missing.
       if ( getwd( dirc ) == NULL ) {  
 #else    * imach.c (Module): Weights can have a decimal point as for
       extern char       *getcwd( );    English (a comma might work with a correct LC_NUMERIC environment,
     otherwise the weight is truncated).
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Modification of warning when the covariates values are not 0 or
 #endif    1.
          return( GLOCK_ERROR_GETCWD );    Version 0.98g
       }  
       strcpy( name, path );             /* we've got it */    Revision 1.122  2006/03/20 09:45:41  brouard
    } else {                             /* strip direcotry from path */    (Module): Weights can have a decimal point as for
       s++;                              /* after this, the filename */    English (a comma might work with a correct LC_NUMERIC environment,
       l2 = strlen( s );                 /* length of filename */    otherwise the weight is truncated).
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Modification of warning when the covariates values are not 0 or
       strcpy( name, s );                /* save file name */    1.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Version 0.98g
       dirc[l1-l2] = 0;                  /* add zero */  
    }    Revision 1.121  2006/03/16 17:45:01  lievre
    l1 = strlen( dirc );                 /* length of directory */    * imach.c (Module): Comments concerning covariates added
 #ifdef windows  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    * imach.c (Module): refinements in the computation of lli if
 #else    status=-2 in order to have more reliable computation if stepm is
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    not 1 month. Version 0.98f
 #endif  
    s = strrchr( name, '.' );            /* find last / */    Revision 1.120  2006/03/16 15:10:38  lievre
    s++;    (Module): refinements in the computation of lli if
    strcpy(ext,s);                       /* save extension */    status=-2 in order to have more reliable computation if stepm is
    l1= strlen( name);    not 1 month. Version 0.98f
    l2= strlen( s)+1;  
    strncpy( finame, name, l1-l2);    Revision 1.119  2006/03/15 17:42:26  brouard
    finame[l1-l2]= 0;    (Module): Bug if status = -2, the loglikelihood was
    return( 0 );                         /* we're done */    computed as likelihood omitting the logarithm. Version O.98e
 }  
     Revision 1.118  2006/03/14 18:20:07  brouard
     (Module): varevsij Comments added explaining the second
 /******************************************/    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 void replace(char *s, char*t)    (Module): Function pstamp added
 {    (Module): Version 0.98d
   int i;  
   int lg=20;    Revision 1.117  2006/03/14 17:16:22  brouard
   i=0;    (Module): varevsij Comments added explaining the second
   lg=strlen(t);    table of variances if popbased=1 .
   for(i=0; i<= lg; i++) {    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (s[i] = t[i]);    (Module): Function pstamp added
     if (t[i]== '\\') s[i]='/';    (Module): Version 0.98d
   }  
 }    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
 int nbocc(char *s, char occ)    varian-covariance of ej. is needed (Saito).
 {  
   int i,j=0;    Revision 1.115  2006/02/27 12:17:45  brouard
   int lg=20;    (Module): One freematrix added in mlikeli! 0.98c
   i=0;  
   lg=strlen(s);    Revision 1.114  2006/02/26 12:57:58  brouard
   for(i=0; i<= lg; i++) {    (Module): Some improvements in processing parameter
   if  (s[i] == occ ) j++;    filename with strsep.
   }  
   return j;    Revision 1.113  2006/02/24 14:20:24  brouard
 }    (Module): Memory leaks checks with valgrind and:
     datafile was not closed, some imatrix were not freed and on matrix
 void cutv(char *u,char *v, char*t, char occ)    allocation too.
 {  
   int i,lg,j,p=0;    Revision 1.112  2006/01/30 09:55:26  brouard
   i=0;    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    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
   lg=strlen(t);    can be a simple dot '.'.
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);    Revision 1.110  2006/01/25 00:51:50  brouard
   }    (Module): Lots of cleaning and bugs added (Gompertz)
      u[p]='\0';  
     Revision 1.109  2006/01/24 19:37:15  brouard
    for(j=0; j<= lg; j++) {    (Module): Comments (lines starting with a #) are allowed in data.
     if (j>=(p+1))(v[j-p-1] = t[j]);  
   }    Revision 1.108  2006/01/19 18:05:42  lievre
 }    Gnuplot problem appeared...
     To be fixed
 /********************** nrerror ********************/  
     Revision 1.107  2006/01/19 16:20:37  brouard
 void nrerror(char error_text[])    Test existence of gnuplot in imach path
 {  
   fprintf(stderr,"ERREUR ...\n");    Revision 1.106  2006/01/19 13:24:36  brouard
   fprintf(stderr,"%s\n",error_text);    Some cleaning and links added in html output
   exit(1);  
 }    Revision 1.105  2006/01/05 20:23:19  lievre
 /*********************** vector *******************/    *** empty log message ***
 double *vector(int nl, int nh)  
 {    Revision 1.104  2005/09/30 16:11:43  lievre
   double *v;    (Module): sump fixed, loop imx fixed, and simplifications.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Module): If the status is missing at the last wave but we know
   if (!v) nrerror("allocation failure in vector");    that the person is alive, then we can code his/her status as -2
   return v-nl+NR_END;    (instead of missing=-1 in earlier versions) and his/her
 }    contributions to the likelihood is 1 - Prob of dying from last
     health status (= 1-p13= p11+p12 in the easiest case of somebody in
 /************************ free vector ******************/    the healthy state at last known wave). Version is 0.98
 void free_vector(double*v, int nl, int nh)  
 {    Revision 1.103  2005/09/30 15:54:49  lievre
   free((FREE_ARG)(v+nl-NR_END));    (Module): sump fixed, loop imx fixed, and simplifications.
 }  
     Revision 1.102  2004/09/15 17:31:30  brouard
 /************************ivector *******************************/    Add the possibility to read data file including tab characters.
 int *ivector(long nl,long nh)  
 {    Revision 1.101  2004/09/15 10:38:38  brouard
   int *v;    Fix on curr_time
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Revision 1.100  2004/07/12 18:29:06  brouard
   return v-nl+NR_END;    Add version for Mac OS X. Just define UNIX in Makefile
 }  
     Revision 1.99  2004/06/05 08:57:40  brouard
 /******************free ivector **************************/    *** empty log message ***
 void free_ivector(int *v, long nl, long nh)  
 {    Revision 1.98  2004/05/16 15:05:56  brouard
   free((FREE_ARG)(v+nl-NR_END));    New version 0.97 . First attempt to estimate force of mortality
 }    directly from the data i.e. without the need of knowing the health
     state at each age, but using a Gompertz model: log u =a + b*age .
 /******************* imatrix *******************************/    This is the basic analysis of mortality and should be done before any
 int **imatrix(long nrl, long nrh, long ncl, long nch)    other analysis, in order to test if the mortality estimated from the
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    cross-longitudinal survey is different from the mortality estimated
 {    from other sources like vital statistic data.
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;  
   int **m;    The same imach parameter file can be used but the option for mle should be -3.
    
   /* allocate pointers to rows */    Agnès, who wrote this part of the code, tried to keep most of the
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    former routines in order to include the new code within the former code.
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    The output is very simple: only an estimate of the intercept and of
   m -= nrl;    the slope with 95% confident intervals.
    
      Current limitations:
   /* allocate rows and set pointers to them */    A) Even if you enter covariates, i.e. with the
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    B) There is no computation of Life Expectancy nor Life Table.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.97  2004/02/20 13:25:42  lievre
      Version 0.96d. Population forecasting command line is (temporarily)
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    suppressed.
    
   /* return pointer to array of pointers to rows */    Revision 1.96  2003/07/15 15:38:55  brouard
   return m;    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 }    rewritten within the same printf. Workaround: many printfs.
   
 /****************** free_imatrix *************************/    Revision 1.95  2003/07/08 07:54:34  brouard
 void free_imatrix(m,nrl,nrh,ncl,nch)    * imach.c (Repository):
       int **m;    (Repository): Using imachwizard code to output a more meaningful covariance
       long nch,ncl,nrh,nrl;    matrix (cov(a12,c31) instead of numbers.
      /* free an int matrix allocated by imatrix() */  
 {    Revision 1.94  2003/06/27 13:00:02  brouard
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    Just cleaning
   free((FREE_ARG) (m+nrl-NR_END));  
 }    Revision 1.93  2003/06/25 16:33:55  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
 /******************* matrix *******************************/    exist so I changed back to asctime which exists.
 double **matrix(long nrl, long nrh, long ncl, long nch)    (Module): Version 0.96b
 {  
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    Revision 1.92  2003/06/25 16:30:45  brouard
   double **m;    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    Revision 1.91  2003/06/25 15:30:29  brouard
   m += NR_END;    * imach.c (Repository): Duplicated warning errors corrected.
   m -= nrl;    (Repository): Elapsed time after each iteration is now output. It
     helps to forecast when convergence will be reached. Elapsed time
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    is stamped in powell.  We created a new html file for the graphs
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    concerning matrix of covariance. It has extension -cov.htm.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    mle=-1 a template is output in file "or"mypar.txt with the design
   return m;    of the covariance matrix to be input.
 }  
     Revision 1.89  2003/06/24 12:30:52  brouard
 /*************************free matrix ************************/    (Module): Some bugs corrected for windows. Also, when
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    mle=-1 a template is output in file "or"mypar.txt with the design
 {    of the covariance matrix to be input.
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));    Revision 1.88  2003/06/23 17:54:56  brouard
 }    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
   
 /******************* ma3x *******************************/    Revision 1.87  2003/06/18 12:26:01  brouard
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    Version 0.96
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    Revision 1.86  2003/06/17 20:04:08  brouard
   double ***m;    (Module): Change position of html and gnuplot routines and added
     routine fileappend.
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    Revision 1.85  2003/06/17 13:12:43  brouard
   m += NR_END;    * imach.c (Repository): Check when date of death was earlier that
   m -= nrl;    current date of interview. It may happen when the death was just
     prior to the death. In this case, dh was negative and likelihood
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    was wrong (infinity). We still send an "Error" but patch by
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    assuming that the date of death was just one stepm after the
   m[nrl] += NR_END;    interview.
   m[nrl] -= ncl;    (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    memory allocation. But we also truncated to 8 characters (left
     truncation)
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    (Repository): No more line truncation errors.
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  
   m[nrl][ncl] += NR_END;    Revision 1.84  2003/06/13 21:44:43  brouard
   m[nrl][ncl] -= nll;    * imach.c (Repository): Replace "freqsummary" at a correct
   for (j=ncl+1; j<=nch; j++)    place. It differs from routine "prevalence" which may be called
     m[nrl][j]=m[nrl][j-1]+nlay;    many times. Probs is memory consuming and must be used with
      parcimony.
   for (i=nrl+1; i<=nrh; i++) {    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)    Revision 1.83  2003/06/10 13:39:11  lievre
       m[i][j]=m[i][j-1]+nlay;    *** empty log message ***
   }  
   return m;    Revision 1.82  2003/06/05 15:57:20  brouard
 }    Add log in  imach.c and  fullversion number is now printed.
   
 /*************************free ma3x ************************/  */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  /*
 {     Interpolated Markov Chain
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Short summary of the programme:
   free((FREE_ARG)(m+nrl-NR_END));    
 }    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /***************** f1dim *************************/    first survey ("cross") where individuals from different ages are
 extern int ncom;    interviewed on their health status or degree of disability (in the
 extern double *pcom,*xicom;    case of a health survey which is our main interest) -2- at least a
 extern double (*nrfunc)(double []);    second wave of interviews ("longitudinal") which measure each change
      (if any) in individual health status.  Health expectancies are
 double f1dim(double x)    computed from the time spent in each health state according to a
 {    model. More health states you consider, more time is necessary to reach the
   int j;    Maximum Likelihood of the parameters involved in the model.  The
   double f;    simplest model is the multinomial logistic model where pij is the
   double *xt;    probability to be observed in state j at the second wave
      conditional to be observed in state i at the first wave. Therefore
   xt=vector(1,ncom);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    'age' is age and 'sex' is a covariate. If you want to have a more
   f=(*nrfunc)(xt);    complex model than "constant and age", you should modify the program
   free_vector(xt,1,ncom);    where the markup *Covariates have to be included here again* invites
   return f;    you to do it.  More covariates you add, slower the
 }    convergence.
   
 /*****************brent *************************/    The advantage of this computer programme, compared to a simple
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    multinomial logistic model, is clear when the delay between waves is not
 {    identical for each individual. Also, if a individual missed an
   int iter;    intermediate interview, the information is lost, but taken into
   double a,b,d,etemp;    account using an interpolation or extrapolation.  
   double fu,fv,fw,fx;  
   double ftemp;    hPijx is the probability to be observed in state i at age x+h
   double p,q,r,tol1,tol2,u,v,w,x,xm;    conditional to the observed state i at age x. The delay 'h' can be
   double e=0.0;    split into an exact number (nh*stepm) of unobserved intermediate
      states. This elementary transition (by month, quarter,
   a=(ax < cx ? ax : cx);    semester or year) is modelled as a multinomial logistic.  The hPx
   b=(ax > cx ? ax : cx);    matrix is simply the matrix product of nh*stepm elementary matrices
   x=w=v=bx;    and the contribution of each individual to the likelihood is simply
   fw=fv=fx=(*f)(x);    hPijx.
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);    Also this programme outputs the covariance matrix of the parameters but also
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    of the life expectancies. It also computes the period (stable) prevalence. 
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    
     printf(".");fflush(stdout);    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 #ifdef DEBUG             Institut national d'études démographiques, Paris.
     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);    This software have been partly granted by Euro-REVES, a concerted action
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    from the European Union.
 #endif    It is copyrighted identically to a GNU software product, ie programme and
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    software can be distributed freely for non commercial use. Latest version
       *xmin=x;    can be accessed at http://euroreves.ined.fr/imach .
       return fx;  
     }    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
     ftemp=fu;    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     if (fabs(e) > tol1) {    
       r=(x-w)*(fx-fv);    **********************************************************************/
       q=(x-v)*(fx-fw);  /*
       p=(x-v)*q-(x-w)*r;    main
       q=2.0*(q-r);    read parameterfile
       if (q > 0.0) p = -p;    read datafile
       q=fabs(q);    concatwav
       etemp=e;    freqsummary
       e=d;    if (mle >= 1)
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))      mlikeli
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    print results files
       else {    if mle==1 
         d=p/q;       computes hessian
         u=x+d;    read end of parameter file: agemin, agemax, bage, fage, estepm
         if (u-a < tol2 || b-u < tol2)        begin-prev-date,...
           d=SIGN(tol1,xm-x);    open gnuplot file
       }    open html file
     } else {    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
       d=CGOLD*(e=(x >= xm ? a-x : b-x));     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
     }                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));      freexexit2 possible for memory heap.
     fu=(*f)(u);  
     if (fu <= fx) {    h Pij x                         | pij_nom  ficrestpij
       if (u >= x) a=x; else b=x;     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
       SHFT(v,w,x,u)         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
         SHFT(fv,fw,fx,fu)         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
         } else {  
           if (u < x) a=u; else b=u;         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
           if (fu <= fw || w == x) {         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
             v=w;    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
             w=u;     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
             fv=fw;     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
             fw=fu;  
           } else if (fu <= fv || v == x || v == w) {    forecasting if prevfcast==1 prevforecast call prevalence()
             v=u;    health expectancies
             fv=fu;    Variance-covariance of DFLE
           }    prevalence()
         }     movingaverage()
   }    varevsij() 
   nrerror("Too many iterations in brent");    if popbased==1 varevsij(,popbased)
   *xmin=x;    total life expectancies
   return fx;    Variance of period (stable) prevalence
 }   end
   */
 /****************** mnbrak ***********************/  
   
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))   
 {  #include <math.h>
   double ulim,u,r,q, dum;  #include <stdio.h>
   double fu;  #include <stdlib.h>
    #include <string.h>
   *fa=(*func)(*ax);  
   *fb=(*func)(*bx);  #ifdef _WIN32
   if (*fb > *fa) {  #include <io.h>
     SHFT(dum,*ax,*bx,dum)  #else
       SHFT(dum,*fb,*fa,dum)  #include <unistd.h>
       }  #endif
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);  #include <limits.h>
   while (*fb > *fc) {  #include <sys/types.h>
     r=(*bx-*ax)*(*fb-*fc);  #include <sys/stat.h>
     q=(*bx-*cx)*(*fb-*fa);  #include <errno.h>
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  /* extern int errno; */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);  /* #ifdef LINUX */
     if ((*bx-u)*(u-*cx) > 0.0) {  /* #include <time.h> */
       fu=(*func)(u);  /* #include "timeval.h" */
     } else if ((*cx-u)*(u-ulim) > 0.0) {  /* #else */
       fu=(*func)(u);  /* #include <sys/time.h> */
       if (fu < *fc) {  /* #endif */
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  
           SHFT(*fb,*fc,fu,(*func)(u))  #include <time.h>
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  #ifdef GSL
       u=ulim;  #include <gsl/gsl_errno.h>
       fu=(*func)(u);  #include <gsl/gsl_multimin.h>
     } else {  #endif
       u=(*cx)+GOLD*(*cx-*bx);  
       fu=(*func)(u);  /* #include <libintl.h> */
     }  /* #define _(String) gettext (String) */
     SHFT(*ax,*bx,*cx,u)  
       SHFT(*fa,*fb,*fc,fu)  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
       }  
 }  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 /*************** linmin ************************/  #define FILENAMELENGTH 132
   
 int ncom;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 double *pcom,*xicom;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 double (*nrfunc)(double []);  
    #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
 {  
   double brent(double ax, double bx, double cx,  #define NINTERVMAX 8
                double (*f)(double), double tol, double *xmin);  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
   double f1dim(double x);  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
               double *fc, double (*func)(double));  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
   int j;  #define MAXN 20000
   double xx,xmin,bx,ax;  #define YEARM 12. /**< Number of months per year */
   double fx,fb,fa;  #define AGESUP 130
    #define AGEBASE 40
   ncom=n;  #define AGEGOMP 10. /**< Minimal age for Gompertz adjustment */
   pcom=vector(1,n);  #ifdef _WIN32
   xicom=vector(1,n);  #define DIRSEPARATOR '\\'
   nrfunc=func;  #define CHARSEPARATOR "\\"
   for (j=1;j<=n;j++) {  #define ODIRSEPARATOR '/'
     pcom[j]=p[j];  #else
     xicom[j]=xi[j];  #define DIRSEPARATOR '/'
   }  #define CHARSEPARATOR "/"
   ax=0.0;  #define ODIRSEPARATOR '\\'
   xx=1.0;  #endif
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  /* $Id$ */
 #ifdef DEBUG  /* $State$ */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
 #endif  char version[]="Imach version 0.98nX, August 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
   for (j=1;j<=n;j++) {  char fullversion[]="$Revision$ $Date$"; 
     xi[j] *= xmin;  char strstart[80];
     p[j] += xi[j];  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   }  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   free_vector(xicom,1,n);  int nvar=0, nforce=0; /* Number of variables, number of forces */
   free_vector(pcom,1,n);  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
 }  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) */
 /*************** powell ************************/  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
             double (*func)(double []))  int cptcovprodnoage=0; /**< Number of covariate products without age */   
 {  int cptcoveff=0; /* Total number of covariates to vary for printing results */
   void linmin(double p[], double xi[], int n, double *fret,  int cptcov=0; /* Working variable */
               double (*func)(double []));  int npar=NPARMAX;
   int i,ibig,j;  int nlstate=2; /* Number of live states */
   double del,t,*pt,*ptt,*xit;  int ndeath=1; /* Number of dead states */
   double fp,fptt;  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   double *xits;  int popbased=0;
   pt=vector(1,n);  
   ptt=vector(1,n);  int *wav; /* Number of waves for this individuual 0 is possible */
   xit=vector(1,n);  int maxwav=0; /* Maxim number of waves */
   xits=vector(1,n);  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
   *fret=(*func)(p);  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
   for (j=1;j<=n;j++) pt[j]=p[j];  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
   for (*iter=1;;++(*iter)) {                     to the likelihood and the sum of weights (done by funcone)*/
     fp=(*fret);  int mle=1, weightopt=0;
     ibig=0;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
     del=0.0;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
     for (i=1;i<=n;i++)             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       printf(" %d %.12f",i, p[i]);  double jmean=1; /* Mean space between 2 waves */
     printf("\n");  double **matprod2(); /* test */
     for (i=1;i<=n;i++) {  double **oldm, **newm, **savm; /* Working pointers to matrices */
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       fptt=(*fret);  /*FILE *fic ; */ /* Used in readdata only */
 #ifdef DEBUG  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
       printf("fret=%lf \n",*fret);  FILE *ficlog, *ficrespow;
 #endif  int globpr=0; /* Global variable for printing or not */
       printf("%d",i);fflush(stdout);  double fretone; /* Only one call to likelihood */
       linmin(p,xit,n,fret,func);  long ipmx=0; /* Number of contributions */
       if (fabs(fptt-(*fret)) > del) {  double sw; /* Sum of weights */
         del=fabs(fptt-(*fret));  char filerespow[FILENAMELENGTH];
         ibig=i;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       }  FILE *ficresilk;
 #ifdef DEBUG  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       printf("%d %.12e",i,(*fret));  FILE *ficresprobmorprev;
       for (j=1;j<=n;j++) {  FILE *fichtm, *fichtmcov; /* Html File */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  FILE *ficreseij;
         printf(" x(%d)=%.12e",j,xit[j]);  char filerese[FILENAMELENGTH];
       }  FILE *ficresstdeij;
       for(j=1;j<=n;j++)  char fileresstde[FILENAMELENGTH];
         printf(" p=%.12e",p[j]);  FILE *ficrescveij;
       printf("\n");  char filerescve[FILENAMELENGTH];
 #endif  FILE  *ficresvij;
     }  char fileresv[FILENAMELENGTH];
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  FILE  *ficresvpl;
 #ifdef DEBUG  char fileresvpl[FILENAMELENGTH];
       int k[2],l;  char title[MAXLINE];
       k[0]=1;  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       k[1]=-1;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       printf("Max: %.12e",(*func)(p));  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
       for (j=1;j<=n;j++)  char command[FILENAMELENGTH];
         printf(" %.12e",p[j]);  int  outcmd=0;
       printf("\n");  
       for(l=0;l<=1;l++) {  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  char filelog[FILENAMELENGTH]; /* Log file */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  char filerest[FILENAMELENGTH];
         }  char fileregp[FILENAMELENGTH];
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  char popfile[FILENAMELENGTH];
       }  
 #endif  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
   
   /* struct timeval start_time, end_time, curr_time, last_time, forecast_time; */
       free_vector(xit,1,n);  /* struct timezone tzp; */
       free_vector(xits,1,n);  /* extern int gettimeofday(); */
       free_vector(ptt,1,n);  struct tm tml, *gmtime(), *localtime();
       free_vector(pt,1,n);  
       return;  extern time_t time();
     }  
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  struct tm start_time, end_time, curr_time, last_time, forecast_time;
     for (j=1;j<=n;j++) {  time_t  rstart_time, rend_time, rcurr_time, rlast_time, rforecast_time; /* raw time */
       ptt[j]=2.0*p[j]-pt[j];  struct tm tm;
       xit[j]=p[j]-pt[j];  
       pt[j]=p[j];  char strcurr[80], strfor[80];
     }  
     fptt=(*func)(ptt);  char *endptr;
     if (fptt < fp) {  long lval;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  double dval;
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);  #define NR_END 1
         for (j=1;j<=n;j++) {  #define FREE_ARG char*
           xi[j][ibig]=xi[j][n];  #define FTOL 1.0e-10
           xi[j][n]=xit[j];  
         }  #define NRANSI 
 #ifdef DEBUG  #define ITMAX 200 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  
         for(j=1;j<=n;j++)  #define TOL 2.0e-4 
           printf(" %.12e",xit[j]);  
         printf("\n");  #define CGOLD 0.3819660 
 #endif  #define ZEPS 1.0e-10 
       }  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     }  
   }  #define GOLD 1.618034 
 }  #define GLIMIT 100.0 
   #define TINY 1.0e-20 
 /**** Prevalence limit ****************/  
   static double maxarg1,maxarg2;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    
      matrix by transitions matrix until convergence is reached */  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   #define rint(a) floor(a+0.5)
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  static double sqrarg;
   double **matprod2();  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   double **out, cov[NCOVMAX], **pmij();  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   double **newm;  int agegomp= AGEGOMP;
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   int imx; 
   for (ii=1;ii<=nlstate+ndeath;ii++)  int stepm=1;
     for (j=1;j<=nlstate+ndeath;j++){  /* Stepm, step in month: minimum step interpolation*/
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }  int estepm;
   /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
    cov[1]=1.;  
    int m,nb;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  long *num;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     newm=savm;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     /* Covariates have to be included here again */  double **pmmij, ***probs;
      cov[2]=agefin;  double *ageexmed,*agecens;
    double dateintmean=0;
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  double *weight;
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/  int **s; /* Status */
       }  double *agedc;
       for (k=1; k<=cptcovage;k++)  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];                    * covar=matrix(0,NCOVMAX,1,n); 
       for (k=1; k<=cptcovprod;k++)                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  double  idx; 
   int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  int *Ndum; /** Freq of modality (tricode */
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/  int **codtab; /**< codtab=imatrix(1,100,1,10); */
   int **Tvard, *Tprod, cptcovprod, *Tvaraff;
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  double *lsurv, *lpop, *tpop;
   
     savm=oldm;  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
     oldm=newm;  double ftolhess; /**< Tolerance for computing hessian */
     maxmax=0.;  
     for(j=1;j<=nlstate;j++){  /**************** split *************************/
       min=1.;  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
       max=0.;  {
       for(i=1; i<=nlstate; i++) {    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
         sumnew=0;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    */ 
         prlim[i][j]= newm[i][j]/(1-sumnew);    char  *ss;                            /* pointer */
         max=FMAX(max,prlim[i][j]);    int   l1, l2;                         /* length counters */
         min=FMIN(min,prlim[i][j]);  
       }    l1 = strlen(path );                   /* length of path */
       maxmin=max-min;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       maxmax=FMAX(maxmax,maxmin);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     }    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     if(maxmax < ftolpl){      strcpy( name, path );               /* we got the fullname name because no directory */
       return prlim;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   }      /* get current working directory */
 }      /*    extern  char* getcwd ( char *buf , int len);*/
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
 /*************** transition probabilities ***************/        return( GLOCK_ERROR_GETCWD );
       }
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )      /* got dirc from getcwd*/
 {      printf(" DIRC = %s \n",dirc);
   double s1, s2;    } else {                              /* strip direcotry from path */
   /*double t34;*/      ss++;                               /* after this, the filename */
   int i,j,j1, nc, ii, jj;      l2 = strlen( ss );                  /* length of filename */
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     for(i=1; i<= nlstate; i++){      strcpy( name, ss );         /* save file name */
     for(j=1; j<i;j++){      strncpy( dirc, path, l1 - l2 );     /* now the directory */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      dirc[l1-l2] = 0;                    /* add zero */
         /*s2 += param[i][j][nc]*cov[nc];*/      printf(" DIRC2 = %s \n",dirc);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    }
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    /* We add a separator at the end of dirc if not exists */
       }    l1 = strlen( dirc );                  /* length of directory */
       ps[i][j]=s2;    if( dirc[l1-1] != DIRSEPARATOR ){
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/      dirc[l1] =  DIRSEPARATOR;
     }      dirc[l1+1] = 0; 
     for(j=i+1; j<=nlstate+ndeath;j++){      printf(" DIRC3 = %s \n",dirc);
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    }
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    ss = strrchr( name, '.' );            /* find last / */
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    if (ss >0){
       }      ss++;
       ps[i][j]=s2;      strcpy(ext,ss);                     /* save extension */
     }      l1= strlen( name);
   }      l2= strlen(ss)+1;
     /*ps[3][2]=1;*/      strncpy( finame, name, l1-l2);
       finame[l1-l2]= 0;
   for(i=1; i<= nlstate; i++){    }
      s1=0;  
     for(j=1; j<i; j++)    return( 0 );                          /* we're done */
       s1+=exp(ps[i][j]);  }
     for(j=i+1; j<=nlstate+ndeath; j++)  
       s1+=exp(ps[i][j]);  
     ps[i][i]=1./(s1+1.);  /******************************************/
     for(j=1; j<i; j++)  
       ps[i][j]= exp(ps[i][j])*ps[i][i];  void replace_back_to_slash(char *s, char*t)
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    int i;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    int lg=0;
   } /* end i */    i=0;
     lg=strlen(t);
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    for(i=0; i<= lg; i++) {
     for(jj=1; jj<= nlstate+ndeath; jj++){      (s[i] = t[i]);
       ps[ii][jj]=0;      if (t[i]== '\\') s[i]='/';
       ps[ii][ii]=1;    }
     }  }
   }  
   char *trimbb(char *out, char *in)
   { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    char *s;
     for(jj=1; jj<= nlstate+ndeath; jj++){    s=out;
      printf("%lf ",ps[ii][jj]);    while (*in != '\0'){
    }      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
     printf("\n ");        in++;
     }      }
     printf("\n ");printf("%lf ",cov[2]);*/      *out++ = *in++;
 /*    }
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    *out='\0';
   goto end;*/    return s;
     return ps;  }
 }  
   char *cutl(char *blocc, char *alocc, char *in, char occ)
 /**************** Product of 2 matrices ******************/  {
     /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
 {       gives blocc="abcdef2ghi" and alocc="j".
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times       If occ is not found blocc is null and alocc is equal to in. Returns blocc
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    */
   /* in, b, out are matrice of pointers which should have been initialized    char *s, *t;
      before: only the contents of out is modified. The function returns    t=in;s=in;
      a pointer to pointers identical to out */    while ((*in != occ) && (*in != '\0')){
   long i, j, k;      *alocc++ = *in++;
   for(i=nrl; i<= nrh; i++)    }
     for(k=ncolol; k<=ncoloh; k++)    if( *in == occ){
       for(j=ncl,out[i][k]=0.; j<=nch; j++)      *(alocc)='\0';
         out[i][k] +=in[i][j]*b[j][k];      s=++in;
     }
   return out;   
 }    if (s == t) {/* occ not found */
       *(alocc-(in-s))='\0';
       in=s;
 /************* Higher Matrix Product ***************/    }
     while ( *in != '\0'){
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )      *blocc++ = *in++;
 {    }
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  
      duration (i.e. until    *blocc='\0';
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    return t;
      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).  char *cutv(char *blocc, char *alocc, char *in, char occ)
      Model is determined by parameters x and covariates have to be  {
      included manually here.    /* 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".
        If occ is not found blocc is null and alocc is equal to in. Returns alocc
   int i, j, d, h, k;    */
   double **out, cov[NCOVMAX];    char *s, *t;
   double **newm;    t=in;s=in;
     while (*in != '\0'){
   /* Hstepm could be zero and should return the unit matrix */      while( *in == occ){
   for (i=1;i<=nlstate+ndeath;i++)        *blocc++ = *in++;
     for (j=1;j<=nlstate+ndeath;j++){        s=in;
       oldm[i][j]=(i==j ? 1.0 : 0.0);      }
       po[i][j][0]=(i==j ? 1.0 : 0.0);      *blocc++ = *in++;
     }    }
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    if (s == t) /* occ not found */
   for(h=1; h <=nhstepm; h++){      *(blocc-(in-s))='\0';
     for(d=1; d <=hstepm; d++){    else
       newm=savm;      *(blocc-(in-s)-1)='\0';
       /* Covariates have to be included here again */    in=s;
       cov[1]=1.;    while ( *in != '\0'){
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      *alocc++ = *in++;
       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];    *alocc='\0';
       for (k=1; k<=cptcovprod;k++)    return s;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  }
   
   int nbocc(char *s, char occ)
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  {
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    int i,j=0;
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    int lg=20;
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    i=0;
       savm=oldm;    lg=strlen(s);
       oldm=newm;    for(i=0; i<= lg; i++) {
     }    if  (s[i] == occ ) j++;
     for(i=1; i<=nlstate+ndeath; i++)    }
       for(j=1;j<=nlstate+ndeath;j++) {    return 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]);  
          */  /* void cutv(char *u,char *v, char*t, char occ) */
       }  /* { */
   } /* end h */  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
   return po;  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
 }  /*      gives u="abcdef2ghi" and v="j" *\/ */
   /*   int i,lg,j,p=0; */
   /*   i=0; */
 /*************** log-likelihood *************/  /*   lg=strlen(t); */
 double func( double *x)  /*   for(j=0; j<=lg-1; j++) { */
 {  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   int i, ii, j, k, mi, d, kk;  /*   } */
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;  /*   for(j=0; j<p; j++) { */
   double sw; /* Sum of weights */  /*     (u[j] = t[j]); */
   double lli; /* Individual log likelihood */  /*   } */
   long ipmx;  /*      u[p]='\0'; */
   /*extern weight */  
   /* We are differentiating ll according to initial status */  /*    for(j=0; j<= lg; j++) { */
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
   /*for(i=1;i<imx;i++)  /*   } */
     printf(" %d\n",s[4][i]);  /* } */
   */  
   cov[1]=1.;  #ifdef _WIN32
   char * strsep(char **pp, const char *delim)
   for(k=1; k<=nlstate; k++) ll[k]=0.;  {
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    char *p, *q;
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];           
     for(mi=1; mi<= wav[i]-1; mi++){    if ((p = *pp) == NULL)
       for (ii=1;ii<=nlstate+ndeath;ii++)      return 0;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    if ((q = strpbrk (p, delim)) != NULL)
       for(d=0; d<dh[mi][i]; d++){    {
         newm=savm;      *pp = q + 1;
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      *q = '\0';
         for (kk=1; kk<=cptcovage;kk++) {    }
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    else
         }      *pp = 0;
            return p;
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  }
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  #endif
         savm=oldm;  
         oldm=newm;  /********************** nrerror ********************/
          
          void nrerror(char error_text[])
       } /* end mult */  {
          fprintf(stderr,"ERREUR ...\n");
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);    fprintf(stderr,"%s\n",error_text);
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    exit(EXIT_FAILURE);
       ipmx +=1;  }
       sw += weight[i];  /*********************** vector *******************/
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  double *vector(int nl, int nh)
     } /* end of wave */  {
   } /* end of individual */    double *v;
     v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    if (!v) nrerror("allocation failure in vector");
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */    return v-nl+NR_END;
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  }
   return -l;  
 }  /************************ free vector ******************/
   void free_vector(double*v, int nl, int nh)
   {
 /*********** Maximum Likelihood Estimation ***************/    free((FREE_ARG)(v+nl-NR_END));
   }
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  
 {  /************************ivector *******************************/
   int i,j, iter;  int *ivector(long nl,long nh)
   double **xi,*delti;  {
   double fret;    int *v;
   xi=matrix(1,npar,1,npar);    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   for (i=1;i<=npar;i++)    if (!v) nrerror("allocation failure in ivector");
     for (j=1;j<=npar;j++)    return v-nl+NR_END;
       xi[i][j]=(i==j ? 1.0 : 0.0);  }
   printf("Powell\n");  
   powell(p,xi,npar,ftol,&iter,&fret,func);  /******************free ivector **************************/
   void free_ivector(int *v, long nl, long nh)
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  {
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    free((FREE_ARG)(v+nl-NR_END));
   }
 }  
   /************************lvector *******************************/
 /**** Computes Hessian and covariance matrix ***/  long *lvector(long nl,long nh)
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  {
 {    long *v;
   double  **a,**y,*x,pd;    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   double **hess;    if (!v) nrerror("allocation failure in ivector");
   int i, j,jk;    return v-nl+NR_END;
   int *indx;  }
   
   double hessii(double p[], double delta, int theta, double delti[]);  /******************free lvector **************************/
   double hessij(double p[], double delti[], int i, int j);  void free_lvector(long *v, long nl, long nh)
   void lubksb(double **a, int npar, int *indx, double b[]) ;  {
   void ludcmp(double **a, int npar, int *indx, double *d) ;    free((FREE_ARG)(v+nl-NR_END));
   }
   hess=matrix(1,npar,1,npar);  
   /******************* imatrix *******************************/
   printf("\nCalculation of the hessian matrix. Wait...\n");  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   for (i=1;i<=npar;i++){       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     printf("%d",i);fflush(stdout);  { 
     hess[i][i]=hessii(p,ftolhess,i,delti);    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     /*printf(" %f ",p[i]);*/    int **m; 
     /*printf(" %lf ",hess[i][i]);*/    
   }    /* allocate pointers to rows */ 
      m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   for (i=1;i<=npar;i++) {    if (!m) nrerror("allocation failure 1 in matrix()"); 
     for (j=1;j<=npar;j++)  {    m += NR_END; 
       if (j>i) {    m -= nrl; 
         printf(".%d%d",i,j);fflush(stdout);    
         hess[i][j]=hessij(p,delti,i,j);    
         hess[j][i]=hess[i][j];        /* allocate rows and set pointers to them */ 
         /*printf(" %lf ",hess[i][j]);*/    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     }    m[nrl] += NR_END; 
   }    m[nrl] -= ncl; 
   printf("\n");    
     for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    
      /* return pointer to array of pointers to rows */ 
   a=matrix(1,npar,1,npar);    return m; 
   y=matrix(1,npar,1,npar);  } 
   x=vector(1,npar);  
   indx=ivector(1,npar);  /****************** free_imatrix *************************/
   for (i=1;i<=npar;i++)  void free_imatrix(m,nrl,nrh,ncl,nch)
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];        int **m;
   ludcmp(a,npar,indx,&pd);        long nch,ncl,nrh,nrl; 
        /* free an int matrix allocated by imatrix() */ 
   for (j=1;j<=npar;j++) {  { 
     for (i=1;i<=npar;i++) x[i]=0;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     x[j]=1;    free((FREE_ARG) (m+nrl-NR_END)); 
     lubksb(a,npar,indx,x);  } 
     for (i=1;i<=npar;i++){  
       matcov[i][j]=x[i];  /******************* matrix *******************************/
     }  double **matrix(long nrl, long nrh, long ncl, long nch)
   }  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   printf("\n#Hessian matrix#\n");    double **m;
   for (i=1;i<=npar;i++) {  
     for (j=1;j<=npar;j++) {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       printf("%.3e ",hess[i][j]);    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
     printf("\n");    m -= nrl;
   }  
     m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   /* Recompute Inverse */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   for (i=1;i<=npar;i++)    m[nrl] += NR_END;
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    m[nrl] -= ncl;
   ludcmp(a,npar,indx,&pd);  
     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   /*  printf("\n#Hessian matrix recomputed#\n");    return m;
     /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
   for (j=1;j<=npar;j++) {  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
     for (i=1;i<=npar;i++) x[i]=0;  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
     x[j]=1;     */
     lubksb(a,npar,indx,x);  }
     for (i=1;i<=npar;i++){  
       y[i][j]=x[i];  /*************************free matrix ************************/
       printf("%.3e ",y[i][j]);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     }  {
     printf("\n");    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   }    free((FREE_ARG)(m+nrl-NR_END));
   */  }
   
   free_matrix(a,1,npar,1,npar);  /******************* ma3x *******************************/
   free_matrix(y,1,npar,1,npar);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   free_vector(x,1,npar);  {
   free_ivector(indx,1,npar);    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
   free_matrix(hess,1,npar,1,npar);    double ***m;
   
     m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
 }    if (!m) nrerror("allocation failure 1 in matrix()");
     m += NR_END;
 /*************** hessian matrix ****************/    m -= nrl;
 double hessii( double x[], double delta, int theta, double delti[])  
 {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   int i;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   int l=1, lmax=20;    m[nrl] += NR_END;
   double k1,k2;    m[nrl] -= ncl;
   double p2[NPARMAX+1];  
   double res;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;  
   double fx;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   int k=0,kmax=10;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   double l1;    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
   fx=func(x);    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;
   for(l=0 ; l <=lmax; l++){    
     l1=pow(10,l);    for (i=nrl+1; i<=nrh; i++) {
     delts=delt;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     for(k=1 ; k <kmax; k=k+1){      for (j=ncl+1; j<=nch; j++) 
       delt = delta*(l1*k);        m[i][j]=m[i][j-1]+nlay;
       p2[theta]=x[theta] +delt;    }
       k1=func(p2)-fx;    return m; 
       p2[theta]=x[theta]-delt;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
       k2=func(p2)-fx;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
       /*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 ma3x ************************/
       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_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
 #endif  {
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         k=kmax;    free((FREE_ARG)(m+nrl-NR_END));
       }  }
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  
         k=kmax; l=lmax*10.;  /*************** function subdirf ***********/
       }  char *subdirf(char fileres[])
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  {
         delts=delt;    /* Caution optionfilefiname is hidden */
       }    strcpy(tmpout,optionfilefiname);
     }    strcat(tmpout,"/"); /* Add to the right */
   }    strcat(tmpout,fileres);
   delti[theta]=delts;    return tmpout;
   return res;  }
    
 }  /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
 double hessij( double x[], double delti[], int thetai,int thetaj)  {
 {    
   int i;    /* Caution optionfilefiname is hidden */
   int l=1, l1, lmax=20;    strcpy(tmpout,optionfilefiname);
   double k1,k2,k3,k4,res,fx;    strcat(tmpout,"/");
   double p2[NPARMAX+1];    strcat(tmpout,preop);
   int k;    strcat(tmpout,fileres);
     return tmpout;
   fx=func(x);  }
   for (k=1; k<=2; k++) {  
     for (i=1;i<=npar;i++) p2[i]=x[i];  /*************** function subdirf3 ***********/
     p2[thetai]=x[thetai]+delti[thetai]/k;  char *subdirf3(char fileres[], char *preop, char *preop2)
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  {
     k1=func(p2)-fx;    
      /* Caution optionfilefiname is hidden */
     p2[thetai]=x[thetai]+delti[thetai]/k;    strcpy(tmpout,optionfilefiname);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    strcat(tmpout,"/");
     k2=func(p2)-fx;    strcat(tmpout,preop);
      strcat(tmpout,preop2);
     p2[thetai]=x[thetai]-delti[thetai]/k;    strcat(tmpout,fileres);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    return tmpout;
     k3=func(p2)-fx;  }
    
     p2[thetai]=x[thetai]-delti[thetai]/k;  /***************** f1dim *************************/
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  extern int ncom; 
     k4=func(p2)-fx;  extern double *pcom,*xicom;
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  extern double (*nrfunc)(double []); 
 #ifdef DEBUG   
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);  double f1dim(double x) 
 #endif  { 
   }    int j; 
   return res;    double f;
 }    double *xt; 
    
 /************** Inverse of matrix **************/    xt=vector(1,ncom); 
 void ludcmp(double **a, int n, int *indx, double *d)    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
 {    f=(*nrfunc)(xt); 
   int i,imax,j,k;    free_vector(xt,1,ncom); 
   double big,dum,sum,temp;    return f; 
   double *vv;  } 
    
   vv=vector(1,n);  /*****************brent *************************/
   *d=1.0;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   for (i=1;i<=n;i++) {  { 
     big=0.0;    int iter; 
     for (j=1;j<=n;j++)    double a,b,d,etemp;
       if ((temp=fabs(a[i][j])) > big) big=temp;    double fu=0,fv,fw,fx;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    double ftemp;
     vv[i]=1.0/big;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
   }    double e=0.0; 
   for (j=1;j<=n;j++) {   
     for (i=1;i<j;i++) {    a=(ax < cx ? ax : cx); 
       sum=a[i][j];    b=(ax > cx ? ax : cx); 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    x=w=v=bx; 
       a[i][j]=sum;    fw=fv=fx=(*f)(x); 
     }    for (iter=1;iter<=ITMAX;iter++) { 
     big=0.0;      xm=0.5*(a+b); 
     for (i=j;i<=n;i++) {      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       sum=a[i][j];      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       for (k=1;k<j;k++)      printf(".");fflush(stdout);
         sum -= a[i][k]*a[k][j];      fprintf(ficlog,".");fflush(ficlog);
       a[i][j]=sum;  #ifdef DEBUG
       if ( (dum=vv[i]*fabs(sum)) >= big) {      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);
         big=dum;      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);
         imax=i;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
       }  #endif
     }      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     if (j != imax) {        *xmin=x; 
       for (k=1;k<=n;k++) {        return fx; 
         dum=a[imax][k];      } 
         a[imax][k]=a[j][k];      ftemp=fu;
         a[j][k]=dum;      if (fabs(e) > tol1) { 
       }        r=(x-w)*(fx-fv); 
       *d = -(*d);        q=(x-v)*(fx-fw); 
       vv[imax]=vv[j];        p=(x-v)*q-(x-w)*r; 
     }        q=2.0*(q-r); 
     indx[j]=imax;        if (q > 0.0) p = -p; 
     if (a[j][j] == 0.0) a[j][j]=TINY;        q=fabs(q); 
     if (j != n) {        etemp=e; 
       dum=1.0/(a[j][j]);        e=d; 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     }          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   }        else { 
   free_vector(vv,1,n);  /* Doesn't work */          d=p/q; 
 ;          u=x+d; 
 }          if (u-a < tol2 || b-u < tol2) 
             d=SIGN(tol1,xm-x); 
 void lubksb(double **a, int n, int *indx, double b[])        } 
 {      } else { 
   int i,ii=0,ip,j;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   double sum;      } 
        u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
   for (i=1;i<=n;i++) {      fu=(*f)(u); 
     ip=indx[i];      if (fu <= fx) { 
     sum=b[ip];        if (u >= x) a=x; else b=x; 
     b[ip]=b[i];        SHFT(v,w,x,u) 
     if (ii)          SHFT(fv,fw,fx,fu) 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];          } else { 
     else if (sum) ii=i;            if (u < x) a=u; else b=u; 
     b[i]=sum;            if (fu <= fw || w == x) { 
   }              v=w; 
   for (i=n;i>=1;i--) {              w=u; 
     sum=b[i];              fv=fw; 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];              fw=fu; 
     b[i]=sum/a[i][i];            } else if (fu <= fv || v == x || v == w) { 
   }              v=u; 
 }              fv=fu; 
             } 
 /************ Frequencies ********************/          } 
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)    } 
 {  /* Some frequencies */    nrerror("Too many iterations in brent"); 
      *xmin=x; 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;    return fx; 
   double ***freq; /* Frequencies */  } 
   double *pp;  
   double pos, k2, dateintsum=0,k2cpt=0;  /****************** mnbrak ***********************/
   FILE *ficresp;  
   char fileresp[FILENAMELENGTH];  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
                double (*func)(double)) 
   pp=vector(1,nlstate);  { 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    double ulim,u,r,q, dum;
   strcpy(fileresp,"p");    double fu; 
   strcat(fileresp,fileres);   
   if((ficresp=fopen(fileresp,"w"))==NULL) {    *fa=(*func)(*ax); 
     printf("Problem with prevalence resultfile: %s\n", fileresp);    *fb=(*func)(*bx); 
     exit(0);    if (*fb > *fa) { 
   }      SHFT(dum,*ax,*bx,dum) 
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        SHFT(dum,*fb,*fa,dum) 
   j1=0;        } 
     *cx=(*bx)+GOLD*(*bx-*ax); 
   j=cptcoveff;    *fc=(*func)(*cx); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
   for(k1=1; k1<=j;k1++){      q=(*bx-*cx)*(*fb-*fa); 
    for(i1=1; i1<=ncodemax[k1];i1++){      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
        j1++;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      ulim=(*bx)+GLIMIT*(*cx-*bx); 
          scanf("%d", i);*/      if ((*bx-u)*(u-*cx) > 0.0) { 
         for (i=-1; i<=nlstate+ndeath; i++)          fu=(*func)(u); 
          for (jk=-1; jk<=nlstate+ndeath; jk++)        } else if ((*cx-u)*(u-ulim) > 0.0) { 
            for(m=agemin; m <= agemax+3; m++)        fu=(*func)(u); 
              freq[i][jk][m]=0;        if (fu < *fc) { 
           SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
         dateintsum=0;            SHFT(*fb,*fc,fu,(*func)(u)) 
         k2cpt=0;            } 
        for (i=1; i<=imx; i++) {      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
          bool=1;        u=ulim; 
          if  (cptcovn>0) {        fu=(*func)(u); 
            for (z1=1; z1<=cptcoveff; z1++)      } else { 
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        u=(*cx)+GOLD*(*cx-*bx); 
                bool=0;        fu=(*func)(u); 
          }      } 
          if (bool==1) {      SHFT(*ax,*bx,*cx,u) 
            for(m=firstpass; m<=lastpass; m++){        SHFT(*fa,*fb,*fc,fu) 
              k2=anint[m][i]+(mint[m][i]/12.);        } 
              if ((k2>=dateprev1) && (k2<=dateprev2)) {  } 
                if(agev[m][i]==0) agev[m][i]=agemax+1;  
                if(agev[m][i]==1) agev[m][i]=agemax+2;  /*************** linmin ************************/
                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];  int ncom; 
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {  double *pcom,*xicom;
                  dateintsum=dateintsum+k2;  double (*nrfunc)(double []); 
                  k2cpt++;   
                }  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   { 
              }    double brent(double ax, double bx, double cx, 
            }                 double (*f)(double), double tol, double *xmin); 
          }    double f1dim(double x); 
        }    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
                        double *fc, double (*func)(double)); 
        fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    int j; 
     double xx,xmin,bx,ax; 
         if  (cptcovn>0) {    double fx,fb,fa;
          fprintf(ficresp, "\n#********** Variable ");   
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);    ncom=n; 
        fprintf(ficresp, "**********\n#");    pcom=vector(1,n); 
         }    xicom=vector(1,n); 
        for(i=1; i<=nlstate;i++)    nrfunc=func; 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    for (j=1;j<=n;j++) { 
        fprintf(ficresp, "\n");      pcom[j]=p[j]; 
              xicom[j]=xi[j]; 
   for(i=(int)agemin; i <= (int)agemax+3; i++){    } 
     if(i==(int)agemax+3)    ax=0.0; 
       printf("Total");    xx=1.0; 
     else    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       printf("Age %d", i);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     for(jk=1; jk <=nlstate ; jk++){  #ifdef DEBUG
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
         pp[jk] += freq[jk][m][i];    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     }  #endif
     for(jk=1; jk <=nlstate ; jk++){    for (j=1;j<=n;j++) { 
       for(m=-1, pos=0; m <=0 ; m++)      xi[j] *= xmin; 
         pos += freq[jk][m][i];      p[j] += xi[j]; 
       if(pp[jk]>=1.e-10)    } 
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);    free_vector(xicom,1,n); 
       else    free_vector(pcom,1,n); 
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  } 
     }  
   char *asc_diff_time(long time_sec, char ascdiff[])
      for(jk=1; jk <=nlstate ; jk++){  {
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    long sec_left, days, hours, minutes;
         pp[jk] += freq[jk][m][i];    days = (time_sec) / (60*60*24);
      }    sec_left = (time_sec) % (60*60*24);
     hours = (sec_left) / (60*60) ;
     for(jk=1,pos=0; jk <=nlstate ; jk++)    sec_left = (sec_left) %(60*60);
       pos += pp[jk];    minutes = (sec_left) /60;
     for(jk=1; jk <=nlstate ; jk++){    sec_left = (sec_left) % (60);
       if(pos>=1.e-5)    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    return ascdiff;
       else  }
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  
       if( i <= (int) agemax){  /*************** powell ************************/
         if(pos>=1.e-5){  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);              double (*func)(double [])) 
           probs[i][jk][j1]= pp[jk]/pos;  { 
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/    void linmin(double p[], double xi[], int n, double *fret, 
         }                double (*func)(double [])); 
       else    int i,ibig,j; 
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    double del,t,*pt,*ptt,*xit;
       }    double fp,fptt;
     }    double *xits;
     for(jk=-1; jk <=nlstate+ndeath; jk++)    int niterf, itmp;
       for(m=-1; m <=nlstate+ndeath; m++)  
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    pt=vector(1,n); 
     if(i <= (int) agemax)    ptt=vector(1,n); 
       fprintf(ficresp,"\n");    xit=vector(1,n); 
     printf("\n");    xits=vector(1,n); 
     }    *fret=(*func)(p); 
     }    for (j=1;j<=n;j++) pt[j]=p[j]; 
  }      rcurr_time = time(NULL);  
   dateintmean=dateintsum/k2cpt;    for (*iter=1;;++(*iter)) { 
        fp=(*fret); 
   fclose(ficresp);      ibig=0; 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      del=0.0; 
   free_vector(pp,1,nlstate);      rlast_time=rcurr_time;
       /* (void) gettimeofday(&curr_time,&tzp); */
   /* End of Freq */      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);
 /************ Prevalence ********************/      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret,rcurr_time-rlast_time, rcurr_time-rstart_time); fflush(ficlog);
 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)  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tm_sec-start_time.tm_sec); */
 {  /* Some frequencies */     for (i=1;i<=n;i++) {
          printf(" %d %.12f",i, p[i]);
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;        fprintf(ficlog," %d %.12lf",i, p[i]);
   double ***freq; /* Frequencies */        fprintf(ficrespow," %.12lf", p[i]);
   double *pp;      }
   double pos, k2;      printf("\n");
       fprintf(ficlog,"\n");
   pp=vector(1,nlstate);      fprintf(ficrespow,"\n");fflush(ficrespow);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      if(*iter <=3){
          tml = *localtime(&rcurr_time);
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        strcpy(strcurr,asctime(&tml));
   j1=0;  /*       asctime_r(&tm,strcurr); */
          rforecast_time=rcurr_time; 
   j=cptcoveff;        itmp = strlen(strcurr);
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
            strcurr[itmp-1]='\0';
  for(k1=1; k1<=j;k1++){        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
     for(i1=1; i1<=ncodemax[k1];i1++){        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
       j1++;        for(niterf=10;niterf<=30;niterf+=10){
            rforecast_time=rcurr_time+(niterf-*iter)*(rcurr_time-rlast_time);
       for (i=-1; i<=nlstate+ndeath; i++)            forecast_time = *localtime(&rforecast_time);
         for (jk=-1; jk<=nlstate+ndeath; jk++)    /*      asctime_r(&tmf,strfor); */
           for(m=agemin; m <= agemax+3; m++)          strcpy(strfor,asctime(&forecast_time));
             freq[i][jk][m]=0;          itmp = strlen(strfor);
                if(strfor[itmp-1]=='\n')
       for (i=1; i<=imx; i++) {          strfor[itmp-1]='\0';
         bool=1;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
         if  (cptcovn>0) {          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
           for (z1=1; z1<=cptcoveff; z1++)        }
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      }
               bool=0;      for (i=1;i<=n;i++) { 
         }        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         if (bool==1) {        fptt=(*fret); 
           for(m=firstpass; m<=lastpass; m++){  #ifdef DEBUG
             k2=anint[m][i]+(mint[m][i]/12.);        printf("fret=%lf \n",*fret);
             if ((k2>=dateprev1) && (k2<=dateprev2)) {        fprintf(ficlog,"fret=%lf \n",*fret);
               if(agev[m][i]==0) agev[m][i]=agemax+1;  #endif
               if(agev[m][i]==1) agev[m][i]=agemax+2;        printf("%d",i);fflush(stdout);
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];        fprintf(ficlog,"%d",i);fflush(ficlog);
               /* freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];  */        linmin(p,xit,n,fret,func); 
             }        if (fabs(fptt-(*fret)) > del) { 
           }          del=fabs(fptt-(*fret)); 
         }          ibig=i; 
       }        } 
         for(i=(int)agemin; i <= (int)agemax+3; i++){  #ifdef DEBUG
           for(jk=1; jk <=nlstate ; jk++){        printf("%d %.12e",i,(*fret));
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        fprintf(ficlog,"%d %.12e",i,(*fret));
               pp[jk] += freq[jk][m][i];        for (j=1;j<=n;j++) {
           }          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           for(jk=1; jk <=nlstate ; jk++){          printf(" x(%d)=%.12e",j,xit[j]);
             for(m=-1, pos=0; m <=0 ; m++)          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
             pos += freq[jk][m][i];        }
         }        for(j=1;j<=n;j++) {
                  printf(" p=%.12e",p[j]);
          for(jk=1; jk <=nlstate ; jk++){          fprintf(ficlog," p=%.12e",p[j]);
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        }
              pp[jk] += freq[jk][m][i];        printf("\n");
          }        fprintf(ficlog,"\n");
            #endif
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
          for(jk=1; jk <=nlstate ; jk++){            #ifdef DEBUG
            if( i <= (int) agemax){        int k[2],l;
              if(pos>=1.e-5){        k[0]=1;
                probs[i][jk][j1]= pp[jk]/pos;        k[1]=-1;
              }        printf("Max: %.12e",(*func)(p));
            }        fprintf(ficlog,"Max: %.12e",(*func)(p));
          }        for (j=1;j<=n;j++) {
                    printf(" %.12e",p[j]);
         }          fprintf(ficlog," %.12e",p[j]);
     }        }
   }        printf("\n");
          fprintf(ficlog,"\n");
          for(l=0;l<=1;l++) {
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          for (j=1;j<=n;j++) {
   free_vector(pp,1,nlstate);            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
              printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
 }  /* End of Freq */            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
           }
 /************* Waves Concatenation ***************/          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
           fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)        }
 {  #endif
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.  
      Death is a valid wave (if date is known).  
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        free_vector(xit,1,n); 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        free_vector(xits,1,n); 
      and mw[mi+1][i]. dh depends on stepm.        free_vector(ptt,1,n); 
      */        free_vector(pt,1,n); 
         return; 
   int i, mi, m;      } 
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
      double sum=0., jmean=0.;*/      for (j=1;j<=n;j++) { 
         ptt[j]=2.0*p[j]-pt[j]; 
   int j, k=0,jk, ju, jl;        xit[j]=p[j]-pt[j]; 
   double sum=0.;        pt[j]=p[j]; 
   jmin=1e+5;      } 
   jmax=-1;      fptt=(*func)(ptt); 
   jmean=0.;      if (fptt < fp) { 
   for(i=1; i<=imx; i++){        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     mi=0;        if (t < 0.0) { 
     m=firstpass;          linmin(p,xit,n,fret,func); 
     while(s[m][i] <= nlstate){          for (j=1;j<=n;j++) { 
       if(s[m][i]>=1)            xi[j][ibig]=xi[j][n]; 
         mw[++mi][i]=m;            xi[j][n]=xit[j]; 
       if(m >=lastpass)          }
         break;  #ifdef DEBUG
       else          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         m++;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     }/* end while */          for(j=1;j<=n;j++){
     if (s[m][i] > nlstate){            printf(" %.12e",xit[j]);
       mi++;     /* Death is another wave */            fprintf(ficlog," %.12e",xit[j]);
       /* if(mi==0)  never been interviewed correctly before death */          }
          /* Only death is a correct wave */          printf("\n");
       mw[mi][i]=m;          fprintf(ficlog,"\n");
     }  #endif
         }
     wav[i]=mi;      } 
     if(mi==0)    } 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  } 
   }  
   /**** Prevalence limit (stable or period prevalence)  ****************/
   for(i=1; i<=imx; i++){  
     for(mi=1; mi<wav[i];mi++){  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       if (stepm <=0)  {
         dh[mi][i]=1;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       else{       matrix by transitions matrix until convergence is reached */
         if (s[mw[mi+1][i]][i] > nlstate) {  
           if (agedc[i] < 2*AGESUP) {    int i, ii,j,k;
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);    double min, max, maxmin, maxmax,sumnew=0.;
           if(j==0) j=1;  /* Survives at least one month after exam */    /* double **matprod2(); */ /* test */
           k=k+1;    double **out, cov[NCOVMAX+1], **pmij();
           if (j >= jmax) jmax=j;    double **newm;
           if (j <= jmin) jmin=j;    double agefin, delaymax=50 ; /* Max number of years to converge */
           sum=sum+j;  
           /*if (j<0) printf("j=%d num=%d \n",j,i); */    for (ii=1;ii<=nlstate+ndeath;ii++)
           }      for (j=1;j<=nlstate+ndeath;j++){
         }        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         else{      }
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  
           k=k+1;     cov[1]=1.;
           if (j >= jmax) jmax=j;   
           else if (j <= jmin)jmin=j;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           sum=sum+j;      newm=savm;
         }      /* Covariates have to be included here again */
         jk= j/stepm;      cov[2]=agefin;
         jl= j -jk*stepm;      
         ju= j -(jk+1)*stepm;      for (k=1; k<=cptcovn;k++) {
         if(jl <= -ju)        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           dh[mi][i]=jk;        /*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]]);*/
         else      }
           dh[mi][i]=jk+1;      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
         if(dh[mi][i]==0)      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
           dh[mi][i]=1; /* At least one step */      /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
       }      
     }      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   }      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   jmean=sum/k;      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
  }      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
 /*********** Tricode ****************************/      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
 void tricode(int *Tvar, int **nbcode, int imx)      
 {      savm=oldm;
   int Ndum[20],ij=1, k, j, i;      oldm=newm;
   int cptcode=0;      maxmax=0.;
   cptcoveff=0;      for(j=1;j<=nlstate;j++){
          min=1.;
   for (k=0; k<19; k++) Ndum[k]=0;        max=0.;
   for (k=1; k<=7; k++) ncodemax[k]=0;        for(i=1; i<=nlstate; i++) {
           sumnew=0;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     for (i=1; i<=imx; i++) {          prlim[i][j]= newm[i][j]/(1-sumnew);
       ij=(int)(covar[Tvar[j]][i]);          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
       Ndum[ij]++;          max=FMAX(max,prlim[i][j]);
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          min=FMIN(min,prlim[i][j]);
       if (ij > cptcode) cptcode=ij;        }
     }        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
     for (i=0; i<=cptcode; i++) {      }
       if(Ndum[i]!=0) ncodemax[j]++;      if(maxmax < ftolpl){
     }        return prlim;
     ij=1;      }
     }
   }
     for (i=1; i<=ncodemax[j]; i++) {  
       for (k=0; k<=19; k++) {  /*************** transition probabilities ***************/ 
         if (Ndum[k] != 0) {  
           nbcode[Tvar[j]][ij]=k;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
           ij++;  {
         }    /* According to parameters values stored in x and the covariate's values stored in cov,
         if (ij > ncodemax[j]) break;       computes the probability to be observed in state j being in state i by appying the
       }         model to the ncovmodel covariates (including constant and age).
     }       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
   }         and, according on how parameters are entered, the position of the coefficient xij(nc) of the
        ncth covariate in the global vector x is given by the formula:
  for (k=0; k<19; k++) Ndum[k]=0;       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
        j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
  for (i=1; i<=ncovmodel-2; i++) {       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
       ij=Tvar[i];       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
       Ndum[ij]++;       Outputs ps[i][j] the probability to be observed in j being in j according to
     }       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     */
  ij=1;    double s1, lnpijopii;
  for (i=1; i<=10; i++) {    /*double t34;*/
    if((Ndum[i]!=0) && (i<=ncov)){    int i,j,j1, nc, ii, jj;
      Tvaraff[ij]=i;  
      ij++;      for(i=1; i<= nlstate; i++){
    }        for(j=1; j<i;j++){
  }          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
              /*lnpijopii += param[i][j][nc]*cov[nc];*/
     cptcoveff=ij-1;            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
 }  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
           }
 /*********** Health Expectancies ****************/          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)        }
 {        for(j=i+1; j<=nlstate+ndeath;j++){
   /* Health expectancies */          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   int i, j, nhstepm, hstepm, h;            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
   double age, agelim,hf;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
   double ***p3mat;  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
            }
   fprintf(ficreseij,"# Health expectancies\n");          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   fprintf(ficreseij,"# Age");        }
   for(i=1; i<=nlstate;i++)      }
     for(j=1; j<=nlstate;j++)      
       fprintf(ficreseij," %1d-%1d",i,j);      for(i=1; i<= nlstate; i++){
   fprintf(ficreseij,"\n");        s1=0;
         for(j=1; j<i; j++){
   hstepm=1*YEARM; /*  Every j years of age (in month) */          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }
   agelim=AGESUP;        for(j=i+1; j<=nlstate+ndeath; j++){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
     /* nhstepm age range expressed in number of stepm */          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);        }
     /* Typically if 20 years = 20*12/6=40 stepm */        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
     /*if (stepm >= YEARM) hstepm=1;*/        ps[i][i]=1./(s1+1.);
 hstepm=1;        /* Computing other pijs */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */        for(j=1; j<i; j++)
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          ps[i][j]= exp(ps[i][j])*ps[i][i];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        for(j=i+1; j<=nlstate+ndeath; j++)
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          ps[i][j]= exp(ps[i][j])*ps[i][i];
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);          /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
 hf=stepm/YEARM;      } /* end i */
 /*printf("stepm=%d nhstepm=%d hstepm=%d age=%lf ",stepm, nhstepm, hstepm, age);*/      
     for(i=1; i<=nlstate;i++)      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       for(j=1; j<=nlstate;j++)        for(jj=1; jj<= nlstate+ndeath; jj++){
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){          ps[ii][jj]=0;
           eij[i][j][(int)age] +=hf*(p3mat[i][j][h]+p3mat[i][j][h+1])/2.0;          ps[ii][ii]=1;
         }        }
          }
     /* hf=1;      
        if (stepm >= YEARM) hf=stepm/YEARM;*/      
 hf=stepm/YEARM;      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
        /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
     fprintf(ficreseij,"%3.0f",age );      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
     for(i=1; i<=nlstate;i++)      /*   } */
       for(j=1; j<=nlstate;j++){      /*   printf("\n "); */
         fprintf(ficreseij," %9.4f", eij[i][j][(int)age]);      /* } */
       }      /* printf("\n ");printf("%lf ",cov[2]);*/
     fprintf(ficreseij,"\n");      /*
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(i=1; i<= npar; i++) printf("%f ",x[i]);
   }        goto end;*/
 }      return ps;
   }
 /************ Variance ******************/  
 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)  /**************** Product of 2 matrices ******************/
 {  
   /* Variance of health expectancies */  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  {
   double **newm;    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
   double **dnewm,**doldm;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   int i, j, nhstepm, hstepm, h;    /* in, b, out are matrice of pointers which should have been initialized 
   int k, cptcode;       before: only the contents of out is modified. The function returns
   double *xp;       a pointer to pointers identical to out */
   double **gp, **gm;    int i, j, k;
   double ***gradg, ***trgradg;    for(i=nrl; i<= nrh; i++)
   double ***p3mat;      for(k=ncolol; k<=ncoloh; k++){
   double age,agelim;        out[i][k]=0.;
   int theta;        for(j=ncl; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
    fprintf(ficresvij,"# Covariances of life expectancies\n");      }
   fprintf(ficresvij,"# Age");    return out;
   for(i=1; i<=nlstate;i++)  }
     for(j=1; j<=nlstate;j++)  
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);  
   fprintf(ficresvij,"\n");  /************* Higher Matrix Product ***************/
   
   xp=vector(1,npar);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   dnewm=matrix(1,nlstate,1,npar);  {
   doldm=matrix(1,nlstate,1,nlstate);    /* Computes the transition matrix starting at age 'age' over 
         'nhstepm*hstepm*stepm' months (i.e. until
   hstepm=1*YEARM; /* Every year of age */       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */       nhstepm*hstepm matrices. 
   agelim = AGESUP;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */       (typically every 2 years instead of every month which is too big 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */       for the memory).
     if (stepm >= YEARM) hstepm=1;       Model is determined by parameters x and covariates have to be 
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */       included manually here. 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);       */
     gp=matrix(0,nhstepm,1,nlstate);  
     gm=matrix(0,nhstepm,1,nlstate);    int i, j, d, h, k;
     double **out, cov[NCOVMAX+1];
     for(theta=1; theta <=npar; theta++){    double **newm;
       for(i=1; i<=npar; i++){ /* Computes gradient */  
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    /* Hstepm could be zero and should return the unit matrix */
       }    for (i=1;i<=nlstate+ndeath;i++)
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        for (j=1;j<=nlstate+ndeath;j++){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        oldm[i][j]=(i==j ? 1.0 : 0.0);
         po[i][j][0]=(i==j ? 1.0 : 0.0);
       if (popbased==1) {      }
         for(i=1; i<=nlstate;i++)    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           prlim[i][i]=probs[(int)age][i][ij];    for(h=1; h <=nhstepm; h++){
       }      for(d=1; d <=hstepm; d++){
          newm=savm;
       for(j=1; j<= nlstate; j++){        /* Covariates have to be included here again */
         for(h=0; h<=nhstepm; h++){        cov[1]=1.;
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        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];
       for(i=1; i<=npar; i++) /* Computes gradient */        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
          /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
       if (popbased==1) {        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         for(i=1; i<=nlstate;i++)        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           prlim[i][i]=probs[(int)age][i][ij];                     pmij(pmmij,cov,ncovmodel,x,nlstate));
       }        savm=oldm;
         oldm=newm;
       for(j=1; j<= nlstate; j++){      }
         for(h=0; h<=nhstepm; h++){      for(i=1; i<=nlstate+ndeath; i++)
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        for(j=1;j<=nlstate+ndeath;j++) {
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          po[i][j][h]=newm[i][j];
         }          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
       }        }
       /*printf("h=%d ",h);*/
       for(j=1; j<= nlstate; j++)    } /* end h */
         for(h=0; h<=nhstepm; h++){  /*     printf("\n H=%d \n",h); */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    return po;
         }  }
     } /* End theta */  
   
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);  /*************** log-likelihood *************/
   double func( double *x)
     for(h=0; h<=nhstepm; h++)  {
       for(j=1; j<=nlstate;j++)    int i, ii, j, k, mi, d, kk;
         for(theta=1; theta <=npar; theta++)    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
           trgradg[h][j][theta]=gradg[h][theta][j];    double **out;
     double sw; /* Sum of weights */
     for(i=1;i<=nlstate;i++)    double lli; /* Individual log likelihood */
       for(j=1;j<=nlstate;j++)    int s1, s2;
         vareij[i][j][(int)age] =0.;    double bbh, survp;
     for(h=0;h<=nhstepm;h++){    long ipmx;
       for(k=0;k<=nhstepm;k++){    /*extern weight */
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    /* We are differentiating ll according to initial status */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
         for(i=1;i<=nlstate;i++)    /*for(i=1;i<imx;i++) 
           for(j=1;j<=nlstate;j++)      printf(" %d\n",s[4][i]);
             vareij[i][j][(int)age] += doldm[i][j];    */
       }    cov[1]=1.;
     }  
     h=1;    for(k=1; k<=nlstate; k++) ll[k]=0.;
     if (stepm >= YEARM) h=stepm/YEARM;  
     fprintf(ficresvij,"%.0f ",age );    if(mle==1){
     for(i=1; i<=nlstate;i++)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(j=1; j<=nlstate;j++){        /* Computes the values of the ncovmodel covariates of the model
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
       }           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
     fprintf(ficresvij,"\n");           to be observed in j being in i according to the model.
     free_matrix(gp,0,nhstepm,1,nlstate);         */
     free_matrix(gm,0,nhstepm,1,nlstate);        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);          cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
   } /* End age */           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
             has been calculated etc */
   free_vector(xp,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
   free_matrix(doldm,1,nlstate,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
   free_matrix(dnewm,1,nlstate,1,nlstate);            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);
             }
 /************ Variance of prevlim ******************/          for(d=0; d<dh[mi][i]; d++){
 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)            newm=savm;
 {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* Variance of prevalence limit */            for (kk=1; kk<=cptcovage;kk++) {
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
   double **newm;            }
   double **dnewm,**doldm;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   int i, j, nhstepm, hstepm;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   int k, cptcode;            savm=oldm;
   double *xp;            oldm=newm;
   double *gp, *gm;          } /* end mult */
   double **gradg, **trgradg;        
   double age,agelim;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   int theta;          /* 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 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");           * (in months) between two waves is not a multiple of stepm, we rounded to 
   fprintf(ficresvpl,"# Age");           * the nearest (and in case of equal distance, to the lowest) interval but now
   for(i=1; i<=nlstate;i++)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       fprintf(ficresvpl," %1d-%1d",i,i);           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
   fprintf(ficresvpl,"\n");           * probability in order to take into account the bias as a fraction of the way
            * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   xp=vector(1,npar);           * -stepm/2 to stepm/2 .
   dnewm=matrix(1,nlstate,1,npar);           * For stepm=1 the results are the same as for previous versions of Imach.
   doldm=matrix(1,nlstate,1,nlstate);           * For stepm > 1 the results are less biased than in previous versions. 
             */
   hstepm=1*YEARM; /* Every year of age */          s1=s[mw[mi][i]][i];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          s2=s[mw[mi+1][i]][i];
   agelim = AGESUP;          bbh=(double)bh[mi][i]/(double)stepm; 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          /* bias bh is positive if real duration
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */           * is higher than the multiple of stepm and negative otherwise.
     if (stepm >= YEARM) hstepm=1;           */
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     gradg=matrix(1,npar,1,nlstate);          if( s2 > nlstate){ 
     gp=vector(1,nlstate);            /* i.e. if s2 is a death state and if the date of death is known 
     gm=vector(1,nlstate);               then the contribution to the likelihood is the probability to 
                die between last step unit time and current  step unit time, 
     for(theta=1; theta <=npar; theta++){               which is also equal to probability to die before dh 
       for(i=1; i<=npar; i++){ /* Computes gradient */               minus probability to die before dh-stepm . 
         xp[i] = x[i] + (i==theta ?delti[theta]:0);               In version up to 0.92 likelihood was computed
       }          as if date of death was unknown. Death was treated as any other
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          health state: the date of the interview describes the actual state
       for(i=1;i<=nlstate;i++)          and not the date of a change in health state. The former idea was
         gp[i] = prlim[i][i];          to consider that at each interview the state was recorded
              (healthy, disable or death) and IMaCh was corrected; but when we
       for(i=1; i<=npar; i++) /* Computes gradient */          introduced the exact date of death then we should have modified
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          the contribution of an exact death to the likelihood. This new
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          contribution is smaller and very dependent of the step unit
       for(i=1;i<=nlstate;i++)          stepm. It is no more the probability to die between last interview
         gm[i] = prlim[i][i];          and month of death but the probability to survive from last
           interview up to one month before death multiplied by the
       for(i=1;i<=nlstate;i++)          probability to die within a month. Thanks to Chris
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          Jackson for correcting this bug.  Former versions increased
     } /* End theta */          mortality artificially. The bad side is that we add another loop
           which slows down the processing. The difference can be up to 10%
     trgradg =matrix(1,nlstate,1,npar);          lower mortality.
             */
     for(j=1; j<=nlstate;j++)            lli=log(out[s1][s2] - savm[s1][s2]);
       for(theta=1; theta <=npar; theta++)  
         trgradg[j][theta]=gradg[theta][j];  
           } else if  (s2==-2) {
     for(i=1;i<=nlstate;i++)            for (j=1,survp=0. ; j<=nlstate; j++) 
       varpl[i][(int)age] =0.;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);            /*survp += out[s1][j]; */
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);            lli= log(survp);
     for(i=1;i<=nlstate;i++)          }
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          
           else if  (s2==-4) { 
     fprintf(ficresvpl,"%.0f ",age );            for (j=3,survp=0. ; j<=nlstate; j++)  
     for(i=1; i<=nlstate;i++)              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));            lli= log(survp); 
     fprintf(ficresvpl,"\n");          } 
     free_vector(gp,1,nlstate);  
     free_vector(gm,1,nlstate);          else if  (s2==-5) { 
     free_matrix(gradg,1,npar,1,nlstate);            for (j=1,survp=0. ; j<=2; j++)  
     free_matrix(trgradg,1,nlstate,1,npar);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   } /* End age */            lli= log(survp); 
           } 
   free_vector(xp,1,npar);          
   free_matrix(doldm,1,nlstate,1,npar);          else{
   free_matrix(dnewm,1,nlstate,1,nlstate);            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
             /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
 }          } 
           /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
 /************ Variance of one-step probabilities  ******************/          /*if(lli ==000.0)*/
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)          /*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;
   int i, j;          sw += weight[i];
   int k=0, cptcode;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **dnewm,**doldm;        } /* end of wave */
   double *xp;      } /* end of individual */
   double *gp, *gm;    }  else if(mle==2){
   double **gradg, **trgradg;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double age,agelim, cov[NCOVMAX];        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int theta;        for(mi=1; mi<= wav[i]-1; mi++){
   char fileresprob[FILENAMELENGTH];          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
   strcpy(fileresprob,"prob");              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   strcat(fileresprob,fileres);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {            }
     printf("Problem with resultfile: %s\n", fileresprob);          for(d=0; d<=dh[mi][i]; d++){
   }            newm=savm;
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   xp=vector(1,npar);            }
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
              savm=oldm;
   cov[1]=1;            oldm=newm;
   for (age=bage; age<=fage; age ++){          } /* end mult */
     cov[2]=age;        
     gradg=matrix(1,npar,1,9);          s1=s[mw[mi][i]][i];
     trgradg=matrix(1,9,1,npar);          s2=s[mw[mi+1][i]][i];
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          bbh=(double)bh[mi][i]/(double)stepm; 
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
              ipmx +=1;
     for(theta=1; theta <=npar; theta++){          sw += weight[i];
       for(i=1; i<=npar; i++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        } /* end of wave */
            } /* end of individual */
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    }  else if(mle==3){  /* exponential inter-extrapolation */
          for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       k=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(i=1; i<= (nlstate+ndeath); i++){        for(mi=1; mi<= wav[i]-1; mi++){
         for(j=1; j<=(nlstate+ndeath);j++){          for (ii=1;ii<=nlstate+ndeath;ii++)
            k=k+1;            for (j=1;j<=nlstate+ndeath;j++){
           gp[k]=pmmij[i][j];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
           for(d=0; d<dh[mi][i]; d++){
       for(i=1; i<=npar; i++)            newm=savm;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       pmij(pmmij,cov,ncovmodel,xp,nlstate);            }
       k=0;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       for(i=1; i<=(nlstate+ndeath); i++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(j=1; j<=(nlstate+ndeath);j++){            savm=oldm;
           k=k+1;            oldm=newm;
           gm[k]=pmmij[i][j];          } /* end mult */
         }        
       }          s1=s[mw[mi][i]][i];
                s2=s[mw[mi+1][i]][i];
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)          bbh=(double)bh[mi][i]/(double)stepm; 
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];            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;
           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++)        } /* end of wave */
       trgradg[j][theta]=gradg[theta][j];      } /* end of individual */
      }else if (mle==4){  /* ml=4 no inter-extrapolation */
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
      pmij(pmmij,cov,ncovmodel,x,nlstate);          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
      k=0;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      for(i=1; i<=(nlstate+ndeath); i++){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
        for(j=1; j<=(nlstate+ndeath);j++){            }
          k=k+1;          for(d=0; d<dh[mi][i]; d++){
          gm[k]=pmmij[i][j];            newm=savm;
         }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      }            for (kk=1; kk<=cptcovage;kk++) {
                    cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      /*printf("\n%d ",(int)age);            }
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){          
                    out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));            savm=oldm;
      }*/            oldm=newm;
           } /* end mult */
   fprintf(ficresprob,"\n%d ",(int)age);        
           s1=s[mw[mi][i]][i];
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){          s2=s[mw[mi+1][i]][i];
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);          if( s2 > nlstate){ 
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);            lli=log(out[s1][s2] - savm[s1][s2]);
   }          }else{
             lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          }
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));          ipmx +=1;
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          sw += weight[i];
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 }  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
  free_vector(xp,1,npar);        } /* end of wave */
 fclose(ficresprob);      } /* end of individual */
     }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
 }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 /******************* Printing html file ***********/        for(mi=1; mi<= wav[i]-1; mi++){
 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 optionfile[],char optionfilehtm[],char rfileres[] ){          for (ii=1;ii<=nlstate+ndeath;ii++)
   int jj1, k1, i1, cpt;            for (j=1;j<=nlstate+ndeath;j++){
   FILE *fichtm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /*char optionfilehtm[FILENAMELENGTH];*/              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
   strcpy(optionfilehtm,optionfile);          for(d=0; d<dh[mi][i]; d++){
   strcat(optionfilehtm,".htm");            newm=savm;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     printf("Problem with %s \n",optionfilehtm), exit(0);            for (kk=1; kk<=cptcovage;kk++) {
   }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.71 </font> <hr size=\"2\" color=\"#EC5E5E\">          
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 Total number of observations=%d <br>            savm=oldm;
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>            oldm=newm;
 <hr  size=\"2\" color=\"#EC5E5E\">          } /* end mult */
 <li>Outputs files<br><br>\n        
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n          s1=s[mw[mi][i]][i];
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>          s2=s[mw[mi+1][i]][i];
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>          ipmx +=1;
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>          sw += weight[i];
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>          /*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]);*/
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>        } /* end of wave */
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>      } /* end of individual */
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>    } /* End of if */
         - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
      l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
 fprintf(fichtm," <li>Graphs</li><p>");    return -l;
   }
  m=cptcoveff;  
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  /*************** log-likelihood *************/
   double funcone( double *x)
  jj1=0;  {
  for(k1=1; k1<=m;k1++){    /* Same as likeli but slower because of a lot of printf and if */
    for(i1=1; i1<=ncodemax[k1];i1++){    int i, ii, j, k, mi, d, kk;
        jj1++;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
        if (cptcovn > 0) {    double **out;
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    double lli; /* Individual log likelihood */
          for (cpt=1; cpt<=cptcoveff;cpt++)    double llt;
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);    int s1, s2;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    double bbh, survp;
        }    /*extern weight */
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>    /* We are differentiating ll according to initial status */
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
        for(cpt=1; cpt<nlstate;cpt++){    /*for(i=1;i<imx;i++) 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>      printf(" %d\n",s[4][i]);
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    */
        }    cov[1]=1.;
     for(cpt=1; cpt<=nlstate;cpt++) {  
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    for(k=1; k<=nlstate; k++) ll[k]=0.;
 interval) in state (%d): v%s%d%d.gif <br>  
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      for(cpt=1; cpt<=nlstate;cpt++) {      for(mi=1; mi<= wav[i]-1; mi++){
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>        for (ii=1;ii<=nlstate+ndeath;ii++)
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          for (j=1;j<=nlstate+ndeath;j++){
      }            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      fprintf(fichtm,"\n<br>- Total life expectancy by age and            savm[ii][j]=(ii==j ? 1.0 : 0.0);
 health expectancies in states (1) and (2): e%s%d.gif<br>          }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        for(d=0; d<dh[mi][i]; d++){
 fprintf(fichtm,"\n</body>");          newm=savm;
    }          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
    }          for (kk=1; kk<=cptcovage;kk++) {
 fclose(fichtm);            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 }          }
           /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
 /******************* Gnuplot file **************/          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double agemin, double agemaxpar, double fage , char pathc[], double p[]){                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
           savm=oldm;
   strcpy(optionfilegnuplot,optionfilefiname);          oldm=newm;
   strcat(optionfilegnuplot,".plt");        } /* end mult */
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {        
     printf("Problem with file %s",optionfilegnuplot);        s1=s[mw[mi][i]][i];
   }        s2=s[mw[mi+1][i]][i];
         bbh=(double)bh[mi][i]/(double)stepm; 
 #ifdef windows        /* bias is positive if real duration
     fprintf(ficgp,"cd \"%s\" \n",pathc);         * is higher than the multiple of stepm and negative otherwise.
 #endif         */
 m=pow(2,cptcoveff);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
            lli=log(out[s1][s2] - savm[s1][s2]);
  /* 1eme*/        } else if  (s2==-2) {
   for (cpt=1; cpt<= nlstate ; cpt ++) {          for (j=1,survp=0. ; j<=nlstate; j++) 
    for (k1=1; k1<= m ; k1 ++) {            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           lli= log(survp);
 #ifdef windows        }else if (mle==1){
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 #endif        } else if(mle==2){
 #ifdef unix          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);        } else if(mle==3){  /* exponential inter-extrapolation */
 #endif          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
         } else if (mle==4){  /* mle=4 no inter-extrapolation */
 for (i=1; i<= nlstate ; i ++) {          lli=log(out[s1][s2]); /* Original formula */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        } else{  /* mle=0 back to 1 */
   else fprintf(ficgp," \%%*lf (\%%*lf)");          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 }          /*lli=log(out[s1][s2]); */ /* Original formula */
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);        } /* End of if */
     for (i=1; i<= nlstate ; i ++) {        ipmx +=1;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        sw += weight[i];
   else fprintf(ficgp," \%%*lf (\%%*lf)");        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 }        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        if(globpr){
      for (i=1; i<= nlstate ; i ++) {          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");   %11.6f %11.6f %11.6f ", \
   else fprintf(ficgp," \%%*lf (\%%*lf)");                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
 }                    2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
 #ifdef unix            llt +=ll[k]*gipmx/gsw;
 fprintf(ficgp,"\nset ter gif small size 400,300");            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
 #endif          }
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);          fprintf(ficresilk," %10.6f\n", -llt);
    }        }
   }      } /* end of wave */
   /*2 eme*/    } /* end of individual */
     for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   for (k1=1; k1<= m ; k1 ++) {    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
        if(globpr==0){ /* First time we count the contributions and weights */
     for (i=1; i<= nlstate+1 ; i ++) {      gipmx=ipmx;
       k=2*i;      gsw=sw;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    }
       for (j=1; j<= nlstate+1 ; j ++) {    return -l;
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }    
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");  /*************** function likelione ***********/
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);  {
       for (j=1; j<= nlstate+1 ; j ++) {    /* This routine should help understanding what is done with 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");       the selection of individuals/waves and
         else fprintf(ficgp," \%%*lf (\%%*lf)");       to check the exact contribution to the likelihood.
 }         Plotting could be done.
       fprintf(ficgp,"\" t\"\" w l 0,");     */
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    int k;
       for (j=1; j<= nlstate+1 ; j ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    if(*globpri !=0){ /* Just counts and sums, no printings */
   else fprintf(ficgp," \%%*lf (\%%*lf)");      strcpy(fileresilk,"ilk"); 
 }        strcat(fileresilk,fileres);
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
       else fprintf(ficgp,"\" t\"\" w l 0,");        printf("Problem with resultfile: %s\n", fileresilk);
     }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);      }
   }      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
        fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
   /*3eme*/      /*  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++) 
   for (k1=1; k1<= m ; k1 ++) {        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
     for (cpt=1; cpt<= nlstate ; cpt ++) {      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       k=2+nlstate*(cpt-1);    }
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);  
       for (i=1; i< nlstate ; i ++) {    *fretone=(*funcone)(p);
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);    if(*globpri !=0){
       }      fclose(ficresilk);
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
     }      fflush(fichtm); 
     }    } 
      return;
   /* CV preval stat */  }
     for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {  
       k=3;  /*********** Maximum Likelihood Estimation ***************/
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemaxpar,fileres,k1,k+cpt+1,k+1);  
   void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
       for (i=1; i< nlstate ; i ++)  {
         fprintf(ficgp,"+$%d",k+i+1);    int i,j, iter;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    double **xi;
          double fret;
       l=3+(nlstate+ndeath)*cpt;    double fretone; /* Only one call to likelihood */
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    /*  char filerespow[FILENAMELENGTH];*/
       for (i=1; i< nlstate ; i ++) {    xi=matrix(1,npar,1,npar);
         l=3+(nlstate+ndeath)*cpt;    for (i=1;i<=npar;i++)
         fprintf(ficgp,"+$%d",l+i+1);      for (j=1;j<=npar;j++)
       }        xi[i][j]=(i==j ? 1.0 : 0.0);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      printf("Powell\n");  fprintf(ficlog,"Powell\n");
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    strcpy(filerespow,"pow"); 
     }    strcat(filerespow,fileres);
   }      if((ficrespow=fopen(filerespow,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", filerespow);
   /* proba elementaires */      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
    for(i=1,jk=1; i <=nlstate; i++){    }
     for(k=1; k <=(nlstate+ndeath); k++){    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       if (k != i) {    for (i=1;i<=nlstate;i++)
         for(j=1; j <=ncovmodel; j++){      for(j=1;j<=nlstate+ndeath;j++)
                if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    fprintf(ficrespow,"\n");
           jk++;  
           fprintf(ficgp,"\n");    powell(p,xi,npar,ftol,&iter,&fret,func);
         }  
       }    free_matrix(xi,1,npar,1,npar);
     }    fclose(ficrespow);
     }    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     for(jk=1; jk <=m; jk++) {    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemaxpar);  
    i=1;  }
    for(k2=1; k2<=nlstate; k2++) {  
      k3=i;  /**** Computes Hessian and covariance matrix ***/
      for(k=1; k<=(nlstate+ndeath); k++) {  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
        if (k != k2){  {
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    double  **a,**y,*x,pd;
 ij=1;    double **hess;
         for(j=3; j <=ncovmodel; j++) {    int i, j,jk;
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    int *indx;
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);  
             ij++;    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);
           else    void lubksb(double **a, int npar, int *indx, double b[]) ;
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    void ludcmp(double **a, int npar, int *indx, double *d) ;
         }    double gompertz(double p[]);
           fprintf(ficgp,")/(1");    hess=matrix(1,npar,1,npar);
          
         for(k1=1; k1 <=nlstate; k1++){      printf("\nCalculation of the hessian matrix. Wait...\n");
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
 ij=1;    for (i=1;i<=npar;i++){
           for(j=3; j <=ncovmodel; j++){      printf("%d",i);fflush(stdout);
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {      fprintf(ficlog,"%d",i);fflush(ficlog);
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);     
             ij++;       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
           }      
           else      /*  printf(" %f ",p[i]);
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
           }    }
           fprintf(ficgp,")");    
         }    for (i=1;i<=npar;i++) {
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);      for (j=1;j<=npar;j++)  {
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        if (j>i) { 
         i=i+ncovmodel;          printf(".%d%d",i,j);fflush(stdout);
        }          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
      }          hess[i][j]=hessij(p,delti,i,j,func,npar);
    }          
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);          hess[j][i]=hess[i][j];    
    }          /*printf(" %lf ",hess[i][j]);*/
            }
   fclose(ficgp);      }
 }  /* end gnuplot */    }
     printf("\n");
     fprintf(ficlog,"\n");
 /*************** Moving average **************/  
 void movingaverage(double agedeb, double fage,double agemin, double ***mobaverage){    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
     fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   int i, cpt, cptcod;    
     for (agedeb=agemin; agedeb<=fage; agedeb++)    a=matrix(1,npar,1,npar);
       for (i=1; i<=nlstate;i++)    y=matrix(1,npar,1,npar);
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    x=vector(1,npar);
           mobaverage[(int)agedeb][i][cptcod]=0.;    indx=ivector(1,npar);
        for (i=1;i<=npar;i++)
     for (agedeb=agemin+4; agedeb<=fage; agedeb++){      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
       for (i=1; i<=nlstate;i++){    ludcmp(a,npar,indx,&pd);
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){  
           for (cpt=0;cpt<=4;cpt++){    for (j=1;j<=npar;j++) {
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];      for (i=1;i<=npar;i++) x[i]=0;
           }      x[j]=1;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      lubksb(a,npar,indx,x);
         }      for (i=1;i<=npar;i++){ 
       }        matcov[i][j]=x[i];
     }      }
        }
 }  
     printf("\n#Hessian matrix#\n");
     fprintf(ficlog,"\n#Hessian matrix#\n");
 /************** Forecasting ******************/    for (i=1;i<=npar;i++) { 
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double agemin, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){      for (j=1;j<=npar;j++) { 
          printf("%.3e ",hess[i][j]);
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;        fprintf(ficlog,"%.3e ",hess[i][j]);
   int *popage;      }
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;      printf("\n");
   double *popeffectif,*popcount;      fprintf(ficlog,"\n");
   double ***p3mat;    }
   char fileresf[FILENAMELENGTH];  
     /* Recompute Inverse */
  agelim=AGESUP;    for (i=1;i<=npar;i++)
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     ludcmp(a,npar,indx,&pd);
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  
      /*  printf("\n#Hessian matrix recomputed#\n");
    
   strcpy(fileresf,"f");    for (j=1;j<=npar;j++) {
   strcat(fileresf,fileres);      for (i=1;i<=npar;i++) x[i]=0;
   if((ficresf=fopen(fileresf,"w"))==NULL) {      x[j]=1;
     printf("Problem with forecast resultfile: %s\n", fileresf);      lubksb(a,npar,indx,x);
   }      for (i=1;i<=npar;i++){ 
   printf("Computing forecasting: result on file '%s' \n", fileresf);        y[i][j]=x[i];
         printf("%.3e ",y[i][j]);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        fprintf(ficlog,"%.3e ",y[i][j]);
       }
   if (mobilav==1) {      printf("\n");
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      fprintf(ficlog,"\n");
     movingaverage(agedeb, fage, agemin, mobaverage);    }
   }    */
   
   stepsize=(int) (stepm+YEARM-1)/YEARM;    free_matrix(a,1,npar,1,npar);
   if (stepm<=12) stepsize=1;    free_matrix(y,1,npar,1,npar);
      free_vector(x,1,npar);
   agelim=AGESUP;    free_ivector(indx,1,npar);
      free_matrix(hess,1,npar,1,npar);
   hstepm=1;  
   hstepm=hstepm/stepm;  
   yp1=modf(dateintmean,&yp);  }
   anprojmean=yp;  
   yp2=modf((yp1*12),&yp);  /*************** hessian matrix ****************/
   mprojmean=yp;  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   yp1=modf((yp2*30.5),&yp);  {
   jprojmean=yp;    int i;
   if(jprojmean==0) jprojmean=1;    int l=1, lmax=20;
   if(mprojmean==0) jprojmean=1;    double k1,k2;
      double p2[MAXPARM+1]; /* identical to x */
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);    double res;
      double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   for(cptcov=1;cptcov<=i2;cptcov++){    double fx;
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    int k=0,kmax=10;
       k=k+1;    double l1;
       fprintf(ficresf,"\n#******");  
       for(j=1;j<=cptcoveff;j++) {    fx=func(x);
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for (i=1;i<=npar;i++) p2[i]=x[i];
       }    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
       fprintf(ficresf,"******\n");      l1=pow(10,l);
       fprintf(ficresf,"# StartingAge FinalAge");      delts=delt;
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);      for(k=1 ; k <kmax; k=k+1){
              delt = delta*(l1*k);
              p2[theta]=x[theta] +delt;
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
         fprintf(ficresf,"\n");        p2[theta]=x[theta]-delt;
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);          k2=func(p2)-fx;
         /*res= (k1-2.0*fx+k2)/delt/delt; */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);        
           nhstepm = nhstepm/hstepm;  #ifdef DEBUGHESS
                  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);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        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);
           oldm=oldms;savm=savms;  #endif
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
                if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
           for (h=0; h<=nhstepm; h++){          k=kmax;
             if (h==(int) (calagedate+YEARM*cpt)) {        }
               fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
             }          k=kmax; l=lmax*10.;
             for(j=1; j<=nlstate+ndeath;j++) {        }
               kk1=0.;kk2=0;        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
               for(i=1; i<=nlstate;i++) {                        delts=delt;
                 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];    delti[theta]=delts;
                 }    return res; 
                    
               }  }
               if (h==(int)(calagedate+12*cpt)){  
                 fprintf(ficresf," %.3f", kk1);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
                          {
               }    int i;
             }    int l=1, l1, lmax=20;
           }    double k1,k2,k3,k4,res,fx;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double p2[MAXPARM+1];
         }    int k;
       }  
     }    fx=func(x);
   }    for (k=1; k<=2; k++) {
              for (i=1;i<=npar;i++) p2[i]=x[i];
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      p2[thetai]=x[thetai]+delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   fclose(ficresf);      k1=func(p2)-fx;
 }    
 /************** Forecasting ******************/      p2[thetai]=x[thetai]+delti[thetai]/k;
 populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double agemin, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
        k2=func(p2)-fx;
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    
   int *popage;      p2[thetai]=x[thetai]-delti[thetai]/k;
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   double *popeffectif,*popcount;      k3=func(p2)-fx;
   double ***p3mat,***tabpop,***tabpopprev;    
   char filerespop[FILENAMELENGTH];      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      k4=func(p2)-fx;
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   agelim=AGESUP;  #ifdef DEBUG
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
        fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);  #endif
      }
      return res;
   strcpy(filerespop,"pop");  }
   strcat(filerespop,fileres);  
   if((ficrespop=fopen(filerespop,"w"))==NULL) {  /************** Inverse of matrix **************/
     printf("Problem with forecast resultfile: %s\n", filerespop);  void ludcmp(double **a, int n, int *indx, double *d) 
   }  { 
   printf("Computing forecasting: result on file '%s' \n", filerespop);    int i,imax,j,k; 
     double big,dum,sum,temp; 
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    double *vv; 
    
   if (mobilav==1) {    vv=vector(1,n); 
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    *d=1.0; 
     movingaverage(agedeb, fage, agemin, mobaverage);    for (i=1;i<=n;i++) { 
   }      big=0.0; 
       for (j=1;j<=n;j++) 
   stepsize=(int) (stepm+YEARM-1)/YEARM;        if ((temp=fabs(a[i][j])) > big) big=temp; 
   if (stepm<=12) stepsize=1;      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
        vv[i]=1.0/big; 
   agelim=AGESUP;    } 
      for (j=1;j<=n;j++) { 
   hstepm=1;      for (i=1;i<j;i++) { 
   hstepm=hstepm/stepm;        sum=a[i][j]; 
          for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
   if (popforecast==1) {        a[i][j]=sum; 
     if((ficpop=fopen(popfile,"r"))==NULL) {      } 
       printf("Problem with population file : %s\n",popfile);exit(0);      big=0.0; 
     }      for (i=j;i<=n;i++) { 
     popage=ivector(0,AGESUP);        sum=a[i][j]; 
     popeffectif=vector(0,AGESUP);        for (k=1;k<j;k++) 
     popcount=vector(0,AGESUP);          sum -= a[i][k]*a[k][j]; 
            a[i][j]=sum; 
     i=1;          if ( (dum=vv[i]*fabs(sum)) >= big) { 
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;          big=dum; 
              imax=i; 
     imx=i;        } 
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];      } 
   }      if (j != imax) { 
         for (k=1;k<=n;k++) { 
   for(cptcov=1;cptcov<=i2;cptcov++){          dum=a[imax][k]; 
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){          a[imax][k]=a[j][k]; 
       k=k+1;          a[j][k]=dum; 
       fprintf(ficrespop,"\n#******");        } 
       for(j=1;j<=cptcoveff;j++) {        *d = -(*d); 
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        vv[imax]=vv[j]; 
       }      } 
       fprintf(ficrespop,"******\n");      indx[j]=imax; 
       fprintf(ficrespop,"# Age");      if (a[j][j] == 0.0) a[j][j]=TINY; 
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);      if (j != n) { 
       if (popforecast==1)  fprintf(ficrespop," [Population]");        dum=1.0/(a[j][j]); 
              for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       for (cpt=0; cpt<=0;cpt++) {      } 
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);      } 
            free_vector(vv,1,n);  /* Doesn't work */
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){  ;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  } 
           nhstepm = nhstepm/hstepm;  
            void lubksb(double **a, int n, int *indx, double b[]) 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  { 
           oldm=oldms;savm=savms;    int i,ii=0,ip,j; 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      double sum; 
           
           for (h=0; h<=nhstepm; h++){    for (i=1;i<=n;i++) { 
             if (h==(int) (calagedate+YEARM*cpt)) {      ip=indx[i]; 
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);      sum=b[ip]; 
             }      b[ip]=b[i]; 
             for(j=1; j<=nlstate+ndeath;j++) {      if (ii) 
               kk1=0.;kk2=0;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
               for(i=1; i<=nlstate;i++) {                    else if (sum) ii=i; 
                 if (mobilav==1)      b[i]=sum; 
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    } 
                 else {    for (i=n;i>=1;i--) { 
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      sum=b[i]; 
                 }      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
               }      b[i]=sum/a[i][i]; 
               if (h==(int)(calagedate+12*cpt)){    } 
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;  } 
                   /*fprintf(ficrespop," %.3f", kk1);  
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/  void pstamp(FILE *fichier)
               }  {
             }    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
             for(i=1; i<=nlstate;i++){  }
               kk1=0.;  
                 for(j=1; j<=nlstate;j++){  /************ Frequencies ********************/
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];  void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
                 }  {  /* Some frequencies */
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];    
             }    int i, m, jk, k1,i1, j1, bool, z1,j;
     int first;
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    double ***freq; /* Frequencies */
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);    double *pp, **prop;
           }    double pos,posprop, k2, dateintsum=0,k2cpt=0;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    char fileresp[FILENAMELENGTH];
         }    
       }    pp=vector(1,nlstate);
      prop=matrix(1,nlstate,iagemin,iagemax+3);
   /******/    strcpy(fileresp,"p");
     strcat(fileresp,fileres);
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {    if((ficresp=fopen(fileresp,"w"))==NULL) {
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);        printf("Problem with prevalence resultfile: %s\n", fileresp);
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      exit(0);
           nhstepm = nhstepm/hstepm;    }
              freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    j1=0;
           oldm=oldms;savm=savms;    
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      j=cptcoveff;
           for (h=0; h<=nhstepm; h++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
             if (h==(int) (calagedate+YEARM*cpt)) {  
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);    first=1;
             }  
             for(j=1; j<=nlstate+ndeath;j++) {    /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
               kk1=0.;kk2=0;    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
               for(i=1; i<=nlstate;i++) {                  /*    j1++;
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];      */
               }    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
             }          scanf("%d", i);*/
           }        for (i=-5; i<=nlstate+ndeath; i++)  
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
         }            for(m=iagemin; m <= iagemax+3; m++)
       }              freq[i][jk][m]=0;
    }        
   }        for (i=1; i<=nlstate; i++)  
            for(m=iagemin; m <= iagemax+3; m++)
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            prop[i][m]=0;
         
   if (popforecast==1) {        dateintsum=0;
     free_ivector(popage,0,AGESUP);        k2cpt=0;
     free_vector(popeffectif,0,AGESUP);        for (i=1; i<=imx; i++) {
     free_vector(popcount,0,AGESUP);          bool=1;
   }          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            for (z1=1; z1<=cptcoveff; z1++)       
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
   fclose(ficrespop);                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
 }                bool=0;
                 /* printf("bool=%d i=%d, z1=%d, Tvaraff[%d]=%d, covar[Tvarff][%d]=%2f, codtab[%d][%d]=%d, nbcode[Tvaraff][codtab[%d][%d]=%d, j1=%d\n", 
 /***********************************************/                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
 /**************** Main Program *****************/                  j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
 /***********************************************/                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
               } 
 int main(int argc, char *argv[])          }
 {   
           if (bool==1){
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;            for(m=firstpass; m<=lastpass; m++){
   double agedeb, agefin,hf;              k2=anint[m][i]+(mint[m][i]/12.);
   double agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
   double fret;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   double **xi,tmp,delta;                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                 if (m<lastpass) {
   double dum; /* Dummy variable */                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
   double ***p3mat;                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
   int *indx;                }
   char line[MAXLINE], linepar[MAXLINE];                
   char title[MAXLINE];                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];                  dateintsum=dateintsum+k2;
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];                  k2cpt++;
                  }
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];                /*}*/
             }
   char filerest[FILENAMELENGTH];          }
   char fileregp[FILENAMELENGTH];        } /* end i */
   char popfile[FILENAMELENGTH];         
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
   int firstobs=1, lastobs=10;        pstamp(ficresp);
   int sdeb, sfin; /* Status at beginning and end */        if  (cptcovn>0) {
   int c,  h , cpt,l;          fprintf(ficresp, "\n#********** Variable "); 
   int ju,jl, mi;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;          fprintf(ficresp, "**********\n#");
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          fprintf(ficlog, "\n#********** Variable "); 
   int mobilav=0,popforecast=0;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   int hstepm, nhstepm;          fprintf(ficlog, "**********\n#");
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1;        }
         for(i=1; i<=nlstate;i++) 
   double bage, fage, age, agelim, agebase;          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   double ftolpl=FTOL;        fprintf(ficresp, "\n");
   double **prlim;        
   double *severity;        for(i=iagemin; i <= iagemax+3; i++){
   double ***param; /* Matrix of parameters */          if(i==iagemax+3){
   double  *p;            fprintf(ficlog,"Total");
   double **matcov; /* Matrix of covariance */          }else{
   double ***delti3; /* Scale */            if(first==1){
   double *delti; /* Scale */              first=0;
   double ***eij, ***vareij;              printf("See log file for details...\n");
   double **varpl; /* Variances of prevalence limits by age */            }
   double *epj, vepp;            fprintf(ficlog,"Age %d", i);
   double kk1, kk2;          }
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;          for(jk=1; jk <=nlstate ; jk++){
              for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               pp[jk] += freq[jk][m][i]; 
   char version[80]="Imach version 0.71, February 2002, INED-EUROREVES ";          }
   char *alph[]={"a","a","b","c","d","e"}, str[4];          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pos=0; m <=0 ; m++)
               pos += freq[jk][m][i];
   char z[1]="c", occ;            if(pp[jk]>=1.e-10){
 #include <sys/time.h>              if(first==1){
 #include <time.h>                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];              }
                fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   /* long total_usecs;            }else{
   struct timeval start_time, end_time;              if(first==1)
                  printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             }
           }
   printf("\n%s",version);  
   if(argc <=1){          for(jk=1; jk <=nlstate ; jk++){
     printf("\nEnter the parameter file name: ");            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     scanf("%s",pathtot);              pp[jk] += freq[jk][m][i];
   }          }       
   else{          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
     strcpy(pathtot,argv[1]);            pos += pp[jk];
   }            posprop += prop[jk][i];
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/          }
   /*cygwin_split_path(pathtot,path,optionfile);          for(jk=1; jk <=nlstate ; jk++){
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/            if(pos>=1.e-5){
   /* cutv(path,optionfile,pathtot,'\\');*/              if(first==1)
                 printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);            }else{
   chdir(path);              if(first==1)
   replace(pathc,path);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 /*-------- arguments in the command line --------*/            }
             if( i <= iagemax){
   strcpy(fileres,"r");              if(pos>=1.e-5){
   strcat(fileres, optionfilefiname);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   strcat(fileres,".txt");    /* Other files have txt extension */                /*probs[i][jk][j1]= pp[jk]/pos;*/
                 /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   /*---------arguments file --------*/              }
               else
   if((ficpar=fopen(optionfile,"r"))==NULL)    {                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     printf("Problem with optionfile %s\n",optionfile);            }
     goto end;          }
   }          
           for(jk=-1; jk <=nlstate+ndeath; jk++)
   strcpy(filereso,"o");            for(m=-1; m <=nlstate+ndeath; m++)
   strcat(filereso,fileres);              if(freq[jk][m][i] !=0 ) {
   if((ficparo=fopen(filereso,"w"))==NULL) {              if(first==1)
     printf("Problem with Output resultfile: %s\n", filereso);goto end;                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   }                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
   /* Reads comments: lines beginning with '#' */          if(i <= iagemax)
   while((c=getc(ficpar))=='#' && c!= EOF){            fprintf(ficresp,"\n");
     ungetc(c,ficpar);          if(first==1)
     fgets(line, MAXLINE, ficpar);            printf("Others in log...\n");
     puts(line);          fprintf(ficlog,"\n");
     fputs(line,ficparo);        }
   }        /*}*/
   ungetc(c,ficpar);    }
     dateintmean=dateintsum/k2cpt; 
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);   
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);    fclose(ficresp);
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 while((c=getc(ficpar))=='#' && c!= EOF){    free_vector(pp,1,nlstate);
     ungetc(c,ficpar);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     fgets(line, MAXLINE, ficpar);    /* End of Freq */
     puts(line);  }
     fputs(line,ficparo);  
   }  /************ Prevalence ********************/
   ungetc(c,ficpar);  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)
    {  
        /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   covar=matrix(0,NCOVMAX,1,n);       in each health status at the date of interview (if between dateprev1 and dateprev2).
   cptcovn=0;       We still use firstpass and lastpass as another selection.
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    */
    
   ncovmodel=2+cptcovn;    int i, m, jk, k1, i1, j1, bool, z1,j;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    double ***freq; /* Frequencies */
      double *pp, **prop;
   /* Read guess parameters */    double pos,posprop; 
   /* Reads comments: lines beginning with '#' */    double  y2; /* in fractional years */
   while((c=getc(ficpar))=='#' && c!= EOF){    int iagemin, iagemax;
     ungetc(c,ficpar);    int first; /** to stop verbosity which is redirected to log file */
     fgets(line, MAXLINE, ficpar);  
     puts(line);    iagemin= (int) agemin;
     fputs(line,ficparo);    iagemax= (int) agemax;
   }    /*pp=vector(1,nlstate);*/
   ungetc(c,ficpar);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
      /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    j1=0;
     for(i=1; i <=nlstate; i++)    
     for(j=1; j <=nlstate+ndeath-1; j++){    /*j=cptcoveff;*/
       fscanf(ficpar,"%1d%1d",&i1,&j1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       fprintf(ficparo,"%1d%1d",i1,j1);    
       printf("%1d%1d",i,j);    first=1;
       for(k=1; k<=ncovmodel;k++){    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
         fscanf(ficpar," %lf",&param[i][j][k]);      /*for(i1=1; i1<=ncodemax[k1];i1++){
         printf(" %lf",param[i][j][k]);        j1++;*/
         fprintf(ficparo," %lf",param[i][j][k]);        
       }        for (i=1; i<=nlstate; i++)  
       fscanf(ficpar,"\n");          for(m=iagemin; m <= iagemax+3; m++)
       printf("\n");            prop[i][m]=0.0;
       fprintf(ficparo,"\n");       
     }        for (i=1; i<=imx; i++) { /* Each individual */
            bool=1;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;          if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
   p=param[1][1];              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                  bool=0;
   /* Reads comments: lines beginning with '#' */          } 
   while((c=getc(ficpar))=='#' && c!= EOF){          if (bool==1) { 
     ungetc(c,ficpar);            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     fgets(line, MAXLINE, ficpar);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     puts(line);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     fputs(line,ficparo);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
   }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
   ungetc(c,ficpar);                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
                 if (s[m][i]>0 && s[m][i]<=nlstate) { 
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);                  /*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]]);*/
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   for(i=1; i <=nlstate; i++){                  prop[s[m][i]][iagemax+3] += weight[i]; 
     for(j=1; j <=nlstate+ndeath-1; j++){                } 
       fscanf(ficpar,"%1d%1d",&i1,&j1);              }
       printf("%1d%1d",i,j);            } /* end selection of waves */
       fprintf(ficparo,"%1d%1d",i1,j1);          }
       for(k=1; k<=ncovmodel;k++){        }
         fscanf(ficpar,"%le",&delti3[i][j][k]);        for(i=iagemin; i <= iagemax+3; i++){  
         printf(" %le",delti3[i][j][k]);          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
         fprintf(ficparo," %le",delti3[i][j][k]);            posprop += prop[jk][i]; 
       }          } 
       fscanf(ficpar,"\n");          
       printf("\n");          for(jk=1; jk <=nlstate ; jk++){     
       fprintf(ficparo,"\n");            if( i <=  iagemax){ 
     }              if(posprop>=1.e-5){ 
   }                probs[i][jk][j1]= prop[jk][i]/posprop;
   delti=delti3[1][1];              } else{
                  if(first==1){
   /* Reads comments: lines beginning with '#' */                  first=0;
   while((c=getc(ficpar))=='#' && c!= EOF){                  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]);
     ungetc(c,ficpar);                }
     fgets(line, MAXLINE, ficpar);              }
     puts(line);            } 
     fputs(line,ficparo);          }/* end jk */ 
   }        }/* end i */ 
   ungetc(c,ficpar);      /*} *//* end i1 */
      } /* end j1 */
   matcov=matrix(1,npar,1,npar);    
   for(i=1; i <=npar; i++){    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     fscanf(ficpar,"%s",&str);    /*free_vector(pp,1,nlstate);*/
     printf("%s",str);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     fprintf(ficparo,"%s",str);  }  /* End of prevalence */
     for(j=1; j <=i; j++){  
       fscanf(ficpar," %le",&matcov[i][j]);  /************* Waves Concatenation ***************/
       printf(" %.5le",matcov[i][j]);  
       fprintf(ficparo," %.5le",matcov[i][j]);  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)
     }  {
     fscanf(ficpar,"\n");    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
     printf("\n");       Death is a valid wave (if date is known).
     fprintf(ficparo,"\n");       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
   }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
   for(i=1; i <=npar; i++)       and mw[mi+1][i]. dh depends on stepm.
     for(j=i+1;j<=npar;j++)       */
       matcov[i][j]=matcov[j][i];  
        int i, mi, m;
   printf("\n");    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
     int first;
     /*-------- Rewriting paramater file ----------*/    int j, k=0,jk, ju, jl;
      strcpy(rfileres,"r");    /* "Rparameterfile */    double sum=0.;
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/    first=0;
      strcat(rfileres,".");    /* */    jmin=1e+5;
      strcat(rfileres,optionfilext);    /* Other files have txt extension */    jmax=-1;
     if((ficres =fopen(rfileres,"w"))==NULL) {    jmean=0.;
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    for(i=1; i<=imx; i++){
     }      mi=0;
     fprintf(ficres,"#%s\n",version);      m=firstpass;
          while(s[m][i] <= nlstate){
     /*-------- data file ----------*/        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     if((fic=fopen(datafile,"r"))==NULL)    {          mw[++mi][i]=m;
       printf("Problem with datafile: %s\n", datafile);goto end;        if(m >=lastpass)
     }          break;
         else
     n= lastobs;          m++;
     severity = vector(1,maxwav);      }/* end while */
     outcome=imatrix(1,maxwav+1,1,n);      if (s[m][i] > nlstate){
     num=ivector(1,n);        mi++;     /* Death is another wave */
     moisnais=vector(1,n);        /* if(mi==0)  never been interviewed correctly before death */
     annais=vector(1,n);           /* Only death is a correct wave */
     moisdc=vector(1,n);        mw[mi][i]=m;
     andc=vector(1,n);      }
     agedc=vector(1,n);  
     cod=ivector(1,n);      wav[i]=mi;
     weight=vector(1,n);      if(mi==0){
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */        nbwarn++;
     mint=matrix(1,maxwav,1,n);        if(first==0){
     anint=matrix(1,maxwav,1,n);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     s=imatrix(1,maxwav+1,1,n);          first=1;
     adl=imatrix(1,maxwav+1,1,n);            }
     tab=ivector(1,NCOVMAX);        if(first==1){
     ncodemax=ivector(1,8);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
         }
     i=1;      } /* end mi==0 */
     while (fgets(line, MAXLINE, fic) != NULL)    {    } /* End individuals */
       if ((i >= firstobs) && (i <=lastobs)) {  
            for(i=1; i<=imx; i++){
         for (j=maxwav;j>=1;j--){      for(mi=1; mi<wav[i];mi++){
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        if (stepm <=0)
           strcpy(line,stra);          dh[mi][i]=1;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        else{
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
         }            if (agedc[i] < 2*AGESUP) {
                      j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);              if(j==0) j=1;  /* Survives at least one month after exam */
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);              else if(j<0){
                 nberr++;
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);                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]);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);                j=1; /* Temporary Dangerous patch */
                 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);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);                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]);
         for (j=ncov;j>=1;j--){                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);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);              }
         }              k=k+1;
         num[i]=atol(stra);              if (j >= jmax){
                        jmax=j;
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){                ijmax=i;
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/              }
               if (j <= jmin){
         i=i+1;                jmin=j;
       }                ijmin=i;
     }              }
     /* printf("ii=%d", ij);              sum=sum+j;
        scanf("%d",i);*/              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   imx=i-1; /* Number of individuals */              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
             }
   /* for (i=1; i<=imx; i++){          }
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;          else{
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;  /*        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]); */
     }  
             k=k+1;
     for (i=1; i<=imx; i++)            if (j >= jmax) {
     if (covar[1][i]==0) 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]));*/              jmax=j;
               ijmax=i;
   /* Calculation of the number of parameter from char model*/            }
   Tvar=ivector(1,15);            else if (j <= jmin){
   Tprod=ivector(1,15);              jmin=j;
   Tvaraff=ivector(1,15);              ijmin=i;
   Tvard=imatrix(1,15,1,2);            }
   Tage=ivector(1,15);                  /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
                /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
   if (strlen(model) >1){            if(j<0){
     j=0, j1=0, k1=1, k2=1;              nberr++;
     j=nbocc(model,'+');              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]);
     j1=nbocc(model,'*');              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]);
     cptcovn=j+1;            }
     cptcovprod=j1;            sum=sum+j;
              }
              jk= j/stepm;
     strcpy(modelsav,model);          jl= j -jk*stepm;
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          ju= j -(jk+1)*stepm;
       printf("Error. Non available option model=%s ",model);          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       goto end;            if(jl==0){
     }              dh[mi][i]=jk;
                  bh[mi][i]=0;
     for(i=(j+1); i>=1;i--){            }else{ /* We want a negative bias in order to only have interpolation ie
       cutv(stra,strb,modelsav,'+');                    * to avoid the price of an extra matrix product in likelihood */
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);              dh[mi][i]=jk+1;
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/              bh[mi][i]=ju;
       /*scanf("%d",i);*/            }
       if (strchr(strb,'*')) {          }else{
         cutv(strd,strc,strb,'*');            if(jl <= -ju){
         if (strcmp(strc,"age")==0) {              dh[mi][i]=jk;
           cptcovprod--;              bh[mi][i]=jl;       /* bias is positive if real duration
           cutv(strb,stre,strd,'V');                                   * is higher than the multiple of stepm and negative otherwise.
           Tvar[i]=atoi(stre);                                   */
           cptcovage++;            }
             Tage[cptcovage]=i;            else{
             /*printf("stre=%s ", stre);*/              dh[mi][i]=jk+1;
         }              bh[mi][i]=ju;
         else if (strcmp(strd,"age")==0) {            }
           cptcovprod--;            if(dh[mi][i]==0){
           cutv(strb,stre,strc,'V');              dh[mi][i]=1; /* At least one step */
           Tvar[i]=atoi(stre);              bh[mi][i]=ju; /* At least one step */
           cptcovage++;              /*  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);*/
           Tage[cptcovage]=i;            }
         }          } /* end if mle */
         else {        }
           cutv(strb,stre,strc,'V');      } /* end wave */
           Tvar[i]=ncov+k1;    }
           cutv(strb,strc,strd,'V');    jmean=sum/k;
           Tprod[k1]=i;    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
           Tvard[k1][1]=atoi(strc);    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);
           Tvard[k1][2]=atoi(stre);   }
           Tvar[cptcovn+k2]=Tvard[k1][1];  
           Tvar[cptcovn+k2+1]=Tvard[k1][2];  /*********** Tricode ****************************/
           for (k=1; k<=lastobs;k++)  void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];  {
           k1++;    /**< Uses cptcovn+2*cptcovprod as the number of covariates */
           k2=k2+2;    /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
         }    /* Boring subroutine which should only output nbcode[Tvar[j]][k]
       }     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
       else {    /* nbcode[Tvar[j]][1]= 
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    */
        /*  scanf("%d",i);*/  
       cutv(strd,strc,strb,'V');    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
       Tvar[i]=atoi(strc);    int modmaxcovj=0; /* Modality max of covariates j */
       }    int cptcode=0; /* Modality max of covariates j */
       strcpy(modelsav,stra);      int modmincovj=0; /* Modality min of covariates j */
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);  
         scanf("%d",i);*/  
     }    cptcoveff=0; 
 }   
      for (k=-1; k < maxncov; k++) Ndum[k]=0;
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
   printf("cptcovprod=%d ", cptcovprod);  
   scanf("%d ",i);*/    /* Loop on covariates without age and products */
     fclose(fic);    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
       for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
     /*  if(mle==1){*/                                 modality of this covariate Vj*/ 
     if (weightopt != 1) { /* Maximisation without weights*/        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
       for(i=1;i<=n;i++) weight[i]=1.0;                                      * If product of Vn*Vm, still boolean *:
     }                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
     /*-calculation of age at interview from date of interview and age at death -*/                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
     agev=matrix(1,maxwav,1,imx);        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
                                         modality of the nth covariate of individual i. */
    for (i=1; i<=imx; i++)        if (ij > modmaxcovj)
      for(m=2; (m<= maxwav); m++)          modmaxcovj=ij; 
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){        else if (ij < modmincovj) 
          anint[m][i]=9999;          modmincovj=ij; 
          s[m][i]=-1;        if ((ij < -1) && (ij > NCOVMAX)){
        }          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
              exit(1);
     for (i=1; i<=imx; i++)  {        }else
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
       for(m=1; (m<= maxwav); m++){        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
         if(s[m][i] >0){        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
           if (s[m][i] == nlstate+1) {        /* getting the maximum value of the modality of the covariate
             if(agedc[i]>0)           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
               if(moisdc[i]!=99 && andc[i]!=9999)           female is 1, then modmaxcovj=1.*/
               agev[m][i]=agedc[i];      }
             else {      printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
               if (andc[i]!=9999){      cptcode=modmaxcovj;
               printf("Warning negative age at death: %d line:%d\n",num[i],i);      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
               agev[m][i]=-1;     /*for (i=0; i<=cptcode; i++) {*/
               }      for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
             }        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
           }        if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
           else if(s[m][i] !=9){ /* Should no more exist */          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);        }
             if(mint[m][i]==99 || anint[m][i]==9999)        /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
               agev[m][i]=1;           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
             else if(agev[m][i] <agemin){      } /* Ndum[-1] number of undefined modalities */
               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);*/      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
             }      /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
             else if(agev[m][i] >agemax){      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
               agemax=agev[m][i];         modmincovj=3; modmaxcovj = 7;
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/         There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
             }         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
             /*agev[m][i]=anint[m][i]-annais[i];*/         variables V1_1 and V1_2.
             /*   agev[m][i] = age[i]+2*m;*/         nbcode[Tvar[j]][ij]=k;
           }         nbcode[Tvar[j]][1]=0;
           else { /* =9 */         nbcode[Tvar[j]][2]=1;
             agev[m][i]=1;         nbcode[Tvar[j]][3]=2;
             s[m][i]=-1;      */
           }      ij=1; /* ij is similar to i but can jumps over null modalities */
         }      for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
         else /*= 0 Unknown */        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
           agev[m][i]=1;          /*recode from 0 */
       }          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. 
     }                                       k is a modality. If we have model=V1+V1*sex 
     for (i=1; i<=imx; i++)  {                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
       for(m=1; (m<= maxwav); m++){            ij++;
         if (s[m][i] > (nlstate+ndeath)) {          }
           printf("Error: Wrong value in nlstate or ndeath\n");            if (ij > ncodemax[j]) break; 
           goto end;        }  /* end of loop on */
         }      } /* end of loop on modality */ 
       }    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
     }    
    for (k=-1; k< maxncov; k++) Ndum[k]=0; 
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    
     for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
     free_vector(severity,1,maxwav);     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
     free_imatrix(outcome,1,maxwav+1,1,n);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
     free_vector(moisnais,1,n);     Ndum[ij]++; 
     free_vector(annais,1,n);   } 
     /* free_matrix(mint,1,maxwav,1,n);  
        free_matrix(anint,1,maxwav,1,n);*/   ij=1;
     free_vector(moisdc,1,n);   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
     free_vector(andc,1,n);     /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
      if((Ndum[i]!=0) && (i<=ncovcol)){
           /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
     wav=ivector(1,imx);       Tvaraff[ij]=i; /*For printing (unclear) */
     dh=imatrix(1,lastpass-firstpass+1,1,imx);       ij++;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);     }else
             Tvaraff[ij]=0;
     /* Concatenates waves */   }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);   ij--;
    cptcoveff=ij; /*Number of total covariates*/
   
       Tcode=ivector(1,100);  }
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);  
       ncodemax[1]=1;  
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);  /*********** Health Expectancies ****************/
        
    codtab=imatrix(1,100,1,10);  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
    h=0;  
    m=pow(2,cptcoveff);  {
      /* Health expectancies, no variances */
    for(k=1;k<=cptcoveff; k++){    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
      for(i=1; i <=(m/pow(2,k));i++){    int nhstepma, nstepma; /* Decreasing with age */
        for(j=1; j <= ncodemax[k]; j++){    double age, agelim, hf;
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    double ***p3mat;
            h++;    double eip;
            if (h>m) h=1;codtab[h][k]=j;  
          }    pstamp(ficreseij);
        }    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
      }    fprintf(ficreseij,"# Age");
    }    for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++){
         fprintf(ficreseij," e%1d%1d ",i,j);
    /*for(i=1; i <=m ;i++){      }
      for(k=1; k <=cptcovn; k++){      fprintf(ficreseij," e%1d. ",i);
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);    }
      }    fprintf(ficreseij,"\n");
      printf("\n");  
    }    
    scanf("%d",i);*/    if(estepm < stepm){
          printf ("Problem %d lower than %d\n",estepm, stepm);
    /* Calculates basic frequencies. Computes observed prevalence at single age    }
        and prints on file fileres'p'. */    else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
         * This is mainly to measure the difference between two models: for example
         * if stepm=24 months pijx are given only every 2 years and by summing them
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     * we are calculating an estimate of the Life Expectancy assuming a linear 
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     * progression in between and thus overestimating or underestimating according
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     * to the curvature of the survival function. If, for the same date, we 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */     * to compare the new estimate of Life expectancy with the same linear 
           * hypothesis. A more precise result, taking into account a more precise
     /* For Powell, parameters are in a vector p[] starting at p[1]     * curvature will be obtained if estepm is as small as stepm. */
        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) */    /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     if(mle==1){       nhstepm is the number of hstepm from age to agelim 
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);       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 */
     /*--------- results files --------------*/    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, weightopt,model);       survival function given by stepm (the optimization length). Unfortunately it
         means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
    jk=1;       results. So we changed our mind and took the option of the best precision.
    fprintf(ficres,"# Parameters\n");    */
    printf("# Parameters\n");    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
    for(i=1,jk=1; i <=nlstate; i++){  
      for(k=1; k <=(nlstate+ndeath); k++){    agelim=AGESUP;
        if (k != i)    /* If stepm=6 months */
          {      /* Computed by stepm unit matrices, product of hstepm matrices, stored
            printf("%d%d ",i,k);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
            fprintf(ficres,"%1d%1d ",i,k);      
            for(j=1; j <=ncovmodel; j++){  /* nhstepm age range expressed in number of stepm */
              printf("%f ",p[jk]);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
              fprintf(ficres,"%f ",p[jk]);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
              jk++;    /* if (stepm >= YEARM) hstepm=1;*/
            }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
            printf("\n");    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
            fprintf(ficres,"\n");  
          }    for (age=bage; age<=fage; age ++){ 
      }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
    }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
  if(mle==1){      /* if (stepm >= YEARM) hstepm=1;*/
     /* Computing hessian and covariance matrix */      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     ftolhess=ftol; /* Usually correct */  
     hesscov(matcov, p, npar, delti, ftolhess, func);      /* If stepm=6 months */
  }      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     fprintf(ficres,"# Scales\n");         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     printf("# Scales\n");      
      for(i=1,jk=1; i <=nlstate; i++){      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(j=1; j <=nlstate+ndeath; j++){      
         if (j!=i) {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
           fprintf(ficres,"%1d%1d",i,j);      
           printf("%1d%1d",i,j);      printf("%d|",(int)age);fflush(stdout);
           for(k=1; k<=ncovmodel;k++){      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
             printf(" %.5e",delti[jk]);      
             fprintf(ficres," %.5e",delti[jk]);      /* Computing expectancies */
             jk++;      for(i=1; i<=nlstate;i++)
           }        for(j=1; j<=nlstate;j++)
           printf("\n");          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
           fprintf(ficres,"\n");            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
         }            
       }            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
      }  
              }
     k=1;  
     fprintf(ficres,"# Covariance\n");      fprintf(ficreseij,"%3.0f",age );
     printf("# Covariance\n");      for(i=1; i<=nlstate;i++){
     for(i=1;i<=npar;i++){        eip=0;
       /*  if (k>nlstate) k=1;        for(j=1; j<=nlstate;j++){
       i1=(i-1)/(ncovmodel*nlstate)+1;          eip +=eij[i][j][(int)age];
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
       printf("%s%d%d",alph[k],i1,tab[i]);*/        }
       fprintf(ficres,"%3d",i);        fprintf(ficreseij,"%9.4f", eip );
       printf("%3d",i);      }
       for(j=1; j<=i;j++){      fprintf(ficreseij,"\n");
         fprintf(ficres," %.5e",matcov[i][j]);      
         printf(" %.5e",matcov[i][j]);    }
       }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficres,"\n");    printf("\n");
       printf("\n");    fprintf(ficlog,"\n");
       k++;    
     }  }
      
     while((c=getc(ficpar))=='#' && c!= EOF){  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[] )
       ungetc(c,ficpar);  
       fgets(line, MAXLINE, ficpar);  {
       puts(line);    /* Covariances of health expectancies eij and of total life expectancies according
       fputs(line,ficparo);     to initial status i, ei. .
     }    */
     ungetc(c,ficpar);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
      int nhstepma, nstepma; /* Decreasing with age */
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemaxpar, &bage, &fage);    double age, agelim, hf;
        double ***p3matp, ***p3matm, ***varhe;
     if (fage <= 2) {    double **dnewm,**doldm;
       bage = agemin;    double *xp, *xm;
       fage = agemaxpar;    double **gp, **gm;
     }    double ***gradg, ***trgradg;
        int theta;
     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\n",agemin,agemaxpar,bage,fage);    double eip, vip;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemaxpar,bage,fage);  
      varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     while((c=getc(ficpar))=='#' && c!= EOF){    xp=vector(1,npar);
     ungetc(c,ficpar);    xm=vector(1,npar);
     fgets(line, MAXLINE, ficpar);    dnewm=matrix(1,nlstate*nlstate,1,npar);
     puts(line);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     fputs(line,ficparo);    
   }    pstamp(ficresstdeij);
   ungetc(c,ficpar);    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
      fprintf(ficresstdeij,"# Age");
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);    for(i=1; i<=nlstate;i++){
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      for(j=1; j<=nlstate;j++)
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
            fprintf(ficresstdeij," e%1d. ",i);
   while((c=getc(ficpar))=='#' && c!= EOF){    }
     ungetc(c,ficpar);    fprintf(ficresstdeij,"\n");
     fgets(line, MAXLINE, ficpar);  
     puts(line);    pstamp(ficrescveij);
     fputs(line,ficparo);    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   }    fprintf(ficrescveij,"# Age");
   ungetc(c,ficpar);    for(i=1; i<=nlstate;i++)
        for(j=1; j<=nlstate;j++){
         cptj= (j-1)*nlstate+i;
    dateprev1=anprev1+mprev1/12.+jprev1/365.;        for(i2=1; i2<=nlstate;i2++)
    dateprev2=anprev2+mprev2/12.+jprev2/365.;          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
   fscanf(ficpar,"pop_based=%d\n",&popbased);            if(cptj2 <= cptj)
   fprintf(ficparo,"pop_based=%d\n",popbased);                fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
   fprintf(ficres,"pop_based=%d\n",popbased);            }
        }
   while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficrescveij,"\n");
     ungetc(c,ficpar);    
     fgets(line, MAXLINE, ficpar);    if(estepm < stepm){
     puts(line);      printf ("Problem %d lower than %d\n",estepm, stepm);
     fputs(line,ficparo);    }
   }    else  hstepm=estepm;   
   ungetc(c,ficpar);    /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
   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);     * if stepm=24 months pijx are given only every 2 years and by summing them
 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);     * we are calculating an estimate of the Life Expectancy assuming a linear 
 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);     * 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
 while((c=getc(ficpar))=='#' && c!= EOF){     * to compare the new estimate of Life expectancy with the same linear 
     ungetc(c,ficpar);     * hypothesis. A more precise result, taking into account a more precise
     fgets(line, MAXLINE, ficpar);     * curvature will be obtained if estepm is as small as stepm. */
     puts(line);  
     fputs(line,ficparo);    /* For example we decided to compute the life expectancy with the smallest unit */
   }    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   ungetc(c,ficpar);       nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);       Look at hpijx to understand the reason of that which relies in memory size
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);       and note for a fixed period like estepm months */
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    /* 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
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);       means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
 /*------------ gnuplot -------------*/       results. So we changed our mind and took the option of the best precision.
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, agemin,agemaxpar,fage, pathc,p);    */
      hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
 /*------------ free_vector  -------------*/  
  chdir(path);    /* If stepm=6 months */
      /* nhstepm age range expressed in number of stepm */
  free_ivector(wav,1,imx);    agelim=AGESUP;
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
  free_ivector(num,1,n);    /* if (stepm >= YEARM) hstepm=1;*/
  free_vector(agedc,1,n);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
  /*free_matrix(covar,1,NCOVMAX,1,n);*/    
  fclose(ficparo);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  fclose(ficres);    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
 /*--------- index.htm --------*/    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     gp=matrix(0,nhstepm,1,nlstate*nlstate);
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
      for (age=bage; age<=fage; age ++){ 
   /*--------------- Prevalence limit --------------*/      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
        /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   strcpy(filerespl,"pl");      /* if (stepm >= YEARM) hstepm=1;*/
   strcat(filerespl,fileres);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   if((ficrespl=fopen(filerespl,"w"))==NULL) {  
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;      /* If stepm=6 months */
   }      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
   fprintf(ficrespl,"#Prevalence limit\n");      
   fprintf(ficrespl,"#Age ");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");      /* Computing  Variances of health expectancies */
        /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   prlim=matrix(1,nlstate,1,nlstate);         decrease memory allocation */
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(theta=1; theta <=npar; theta++){
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for(i=1; i<=npar; i++){ 
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          xm[i] = x[i] - (i==theta ?delti[theta]:0);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        }
   k=0;        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   agebase=agemin;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   agelim=agemaxpar;    
   ftolpl=1.e-10;        for(j=1; j<= nlstate; j++){
   i1=cptcoveff;          for(i=1; i<=nlstate; i++){
   if (cptcovn < 1){i1=1;}            for(h=0; h<=nhstepm-1; h++){
               gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   for(cptcov=1;cptcov<=i1;cptcov++){              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            }
         k=k+1;          }
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/        }
         fprintf(ficrespl,"\n#******");       
         for(j=1;j<=cptcoveff;j++)        for(ij=1; ij<= nlstate*nlstate; ij++)
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          for(h=0; h<=nhstepm-1; h++){
         fprintf(ficrespl,"******\n");            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
                  }
         for (age=agebase; age<=agelim; age++){      }/* End theta */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      
           fprintf(ficrespl,"%.0f",age );      
           for(i=1; i<=nlstate;i++)      for(h=0; h<=nhstepm-1; h++)
           fprintf(ficrespl," %.5f", prlim[i][i]);        for(j=1; j<=nlstate*nlstate;j++)
           fprintf(ficrespl,"\n");          for(theta=1; theta <=npar; theta++)
         }            trgradg[h][j][theta]=gradg[h][theta][j];
       }      
     }  
   fclose(ficrespl);       for(ij=1;ij<=nlstate*nlstate;ij++)
         for(ji=1;ji<=nlstate*nlstate;ji++)
   /*------------- h Pij x at various ages ------------*/          varhe[ij][ji][(int)age] =0.;
    
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);       printf("%d|",(int)age);fflush(stdout);
   if((ficrespij=fopen(filerespij,"w"))==NULL) {       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;       for(h=0;h<=nhstepm-1;h++){
   }        for(k=0;k<=nhstepm-1;k++){
   printf("Computing pij: result on file '%s' \n", filerespij);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
            matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   stepsize=(int) (stepm+YEARM-1)/YEARM;          for(ij=1;ij<=nlstate*nlstate;ij++)
   /*if (stepm<=24) stepsize=2;*/            for(ji=1;ji<=nlstate*nlstate;ji++)
               varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   agelim=AGESUP;        }
   hstepm=stepsize*YEARM; /* Every year of age */      }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
        /* Computing expectancies */
   k=0;      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   for(cptcov=1;cptcov<=i1;cptcov++){      for(i=1; i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        for(j=1; j<=nlstate;j++)
       k=k+1;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
         fprintf(ficrespij,"\n#****** ");            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
         for(j=1;j<=cptcoveff;j++)            
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
         fprintf(ficrespij,"******\n");  
                  }
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      fprintf(ficresstdeij,"%3.0f",age );
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      for(i=1; i<=nlstate;i++){
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        eip=0.;
           oldm=oldms;savm=savms;        vip=0.;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          for(j=1; j<=nlstate;j++){
           fprintf(ficrespij,"# Age");          eip += eij[i][j][(int)age];
           for(i=1; i<=nlstate;i++)          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
             for(j=1; j<=nlstate+ndeath;j++)            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
               fprintf(ficrespij," %1d-%1d",i,j);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
           fprintf(ficrespij,"\n");        }
           for (h=0; h<=nhstepm; h++){        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      }
             for(i=1; i<=nlstate;i++)      fprintf(ficresstdeij,"\n");
               for(j=1; j<=nlstate+ndeath;j++)  
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);      fprintf(ficrescveij,"%3.0f",age );
             fprintf(ficrespij,"\n");      for(i=1; i<=nlstate;i++)
           }        for(j=1; j<=nlstate;j++){
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          cptj= (j-1)*nlstate+i;
           fprintf(ficrespij,"\n");          for(i2=1; i2<=nlstate;i2++)
         }            for(j2=1; j2<=nlstate;j2++){
     }              cptj2= (j2-1)*nlstate+i2;
   }              if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/            }
         }
   fclose(ficrespij);      fprintf(ficrescveij,"\n");
      
     }
   /*---------- Forecasting ------------------*/    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   if((stepm == 1) && (model==".")){    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
 if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_matrix(mint,1,maxwav,1,n);    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_vector(weight,1,n);}    printf("\n");
   else{    fprintf(ficlog,"\n");
     erreur=108;  
     printf("Error %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d\n", erreur, stepm);    free_vector(xm,1,npar);
   }    free_vector(xp,1,npar);
      free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   /*---------- Health expectancies and variances ------------*/    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
   strcpy(filerest,"t");  
   strcat(filerest,fileres);  /************ Variance ******************/
   if((ficrest=fopen(filerest,"w"))==NULL) {  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[])
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  {
   }    /* Variance of health expectancies */
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /* double **newm;*/
     double **dnewm,**doldm;
   strcpy(filerese,"e");    double **dnewmp,**doldmp;
   strcat(filerese,fileres);    int i, j, nhstepm, hstepm, h, nstepm ;
   if((ficreseij=fopen(filerese,"w"))==NULL) {    int k, cptcode;
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    double *xp;
   }    double **gp, **gm;  /* for var eij */
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
  strcpy(fileresv,"v");    double *gpp, *gmp; /* for var p point j */
   strcat(fileresv,fileres);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    double ***p3mat;
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    double age,agelim, hf;
   }    double ***mobaverage;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    int theta;
     char digit[4];
   k=0;    char digitp[25];
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    char fileresprobmorprev[FILENAMELENGTH];
       k=k+1;  
       fprintf(ficrest,"\n#****** ");    if(popbased==1){
       for(j=1;j<=cptcoveff;j++)      if(mobilav!=0)
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        strcpy(digitp,"-populbased-mobilav-");
       fprintf(ficrest,"******\n");      else strcpy(digitp,"-populbased-nomobil-");
     }
       fprintf(ficreseij,"\n#****** ");    else 
       for(j=1;j<=cptcoveff;j++)      strcpy(digitp,"-stablbased-");
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficreseij,"******\n");    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       fprintf(ficresvij,"\n#****** ");      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
       for(j=1;j<=cptcoveff;j++)        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
       fprintf(ficresvij,"******\n");      }
     }
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  
       oldm=oldms;savm=savms;    strcpy(fileresprobmorprev,"prmorprev"); 
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);      sprintf(digit,"%-d",ij);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
       oldm=oldms;savm=savms;    strcat(fileresprobmorprev,digit); /* Tvar to be done */
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
        strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
        printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    }
       fprintf(ficrest,"\n");    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
       hf=1;    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       if (stepm >= YEARM) hf=stepm/YEARM;    pstamp(ficresprobmorprev);
       epj=vector(1,nlstate+1);    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
       for(age=bage; age <=fage ;age++){    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         if (popbased==1) {      fprintf(ficresprobmorprev," p.%-d SE",j);
           for(i=1; i<=nlstate;i++)      for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][k];        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
         }    }  
            fprintf(ficresprobmorprev,"\n");
         fprintf(ficrest," %.0f",age);    fprintf(ficgp,"\n# Routine varevsij");
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    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");
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           }  /*   } */
           epj[nlstate+1] +=epj[j];    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         }    pstamp(ficresvij);
         for(i=1, vepp=0.;i <=nlstate;i++)    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
           for(j=1;j <=nlstate;j++)    if(popbased==1)
             vepp += vareij[i][j][(int)age];      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    else
         for(j=1;j <=nlstate;j++){      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    fprintf(ficresvij,"# Age");
         }    for(i=1; i<=nlstate;i++)
         fprintf(ficrest,"\n");      for(j=1; j<=nlstate;j++)
       }        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     }    fprintf(ficresvij,"\n");
   }  
     xp=vector(1,npar);
   fclose(ficreseij);    dnewm=matrix(1,nlstate,1,npar);
   fclose(ficresvij);    doldm=matrix(1,nlstate,1,nlstate);
   fclose(ficrest);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
   fclose(ficpar);    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   free_vector(epj,1,nlstate+1);  
      gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   /*------- Variance limit prevalence------*/      gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
   strcpy(fileresvpl,"vpl");    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   strcat(fileresvpl,fileres);    
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    if(estepm < stepm){
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);      printf ("Problem %d lower than %d\n",estepm, stepm);
     exit(0);    }
   }    else  hstepm=estepm;   
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   k=0;       nhstepm is the number of hstepm from age to agelim 
   for(cptcov=1;cptcov<=i1;cptcov++){       nstepm is the number of stepm from age to agelin. 
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){       Look at function hpijx to understand why (it is linked to memory size questions) */
       k=k+1;    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       fprintf(ficresvpl,"\n#****** ");       survival function given by stepm (the optimization length). Unfortunately it
       for(j=1;j<=cptcoveff;j++)       means that if the survival funtion is printed every two years of age and if
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       fprintf(ficresvpl,"******\n");       results. So we changed our mind and took the option of the best precision.
          */
       varpl=matrix(1,nlstate,(int) bage, (int) fage);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
       oldm=oldms;savm=savms;    agelim = AGESUP;
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     }      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
  }      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   fclose(ficresvpl);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
   /*---------- End : free ----------------*/      gm=matrix(0,nhstepm,1,nlstate);
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);  
    
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      for(theta=1; theta <=npar; theta++){
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
            xp[i] = x[i] + (i==theta ?delti[theta]:0);
          }
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);        if (popbased==1) {
            if(mobilav ==0){
   free_matrix(matcov,1,npar,1,npar);            for(i=1; i<=nlstate;i++)
   free_vector(delti,1,npar);              prlim[i][i]=probs[(int)age][i][ij];
   free_matrix(agev,1,maxwav,1,imx);          }else{ /* mobilav */ 
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);            for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
   if(erreur >0)          }
     printf("End of Imach with error %d\n",erreur);        }
   else   printf("End of Imach\n");    
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        for(j=1; j<= nlstate; j++){
            for(h=0; h<=nhstepm; h++){
   /* 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);*/            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
   /*printf("Total time was %d uSec.\n", total_usecs);*/              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
   /*------ End -----------*/          }
         }
         /* This for computing probability of death (h=1 means
  end:           computed over hstepm matrices product = hstepm*stepm months) 
 #ifdef windows           as a weighted average of prlim.
   /* chdir(pathcd);*/        */
 #endif        for(j=nlstate+1;j<=nlstate+ndeath;j++){
  /*system("wgnuplot graph.plt");*/          for(i=1,gpp[j]=0.; i<= nlstate; i++)
  /*system("../gp37mgw/wgnuplot graph.plt");*/            gpp[j] += prlim[i][i]*p3mat[i][j][1];
  /*system("cd ../gp37mgw");*/        }    
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/        /* end probability of death */
  strcpy(plotcmd,GNUPLOTPROGRAM);  
  strcat(plotcmd," ");        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
  strcat(plotcmd,optionfilegnuplot);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
  system(plotcmd);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
 #ifdef windows   
   while (z[0] != 'q') {        if (popbased==1) {
     chdir(path);          if(mobilav ==0){
     printf("\nType e to edit output files, c to start again, and q for exiting: ");            for(i=1; i<=nlstate;i++)
     scanf("%s",z);              prlim[i][i]=probs[(int)age][i][ij];
     if (z[0] == 'c') system("./imach");          }else{ /* mobilav */ 
     else if (z[0] == 'e') {            for(i=1; i<=nlstate;i++)
       chdir(path);              prlim[i][i]=mobaverage[(int)age][i][ij];
       system(optionfilehtm);          }
     }        }
     else if (z[0] == 'q') exit(0);  
   }        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
 #endif          for(h=0; h<=nhstepm; h++){
 }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
   
       } /* End theta */
   
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
       for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     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,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     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,agelim, 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 from each state (1 to %d) to period (stable) prevalence in state %d <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
   <img src=\"%s%d_%d.png\">",nlstate, cpt, 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 m0,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, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small size 320, 240\n set log y\n"); 
     /* fprintf(ficgp, "set size 0.65,0.65\n"); */
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.",dummy) != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.", dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %d for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%ld' at line number %d for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   void removespace(char *str) {
     char *p1 = str, *p2 = str;
     do
       while (*p2 == ' ')
         p2++;
     while (*p1++ = *p2++);
   }
   
   int decodemodel ( char model[], int lastobs) /**< This routine decode the model and returns:
      * Model  V1+V2+V3+V8+V7*V8+V5*V6+V8*age+V3*age
      * - cptcovt total number of covariates of the model nbocc(+)+1 = 8
      * - cptcovn or number of covariates k of the models excluding age*products =6
      * - cptcovage number of covariates with age*products =2
      * - cptcovs number of simple covariates
      * - Tvar[k] is the id of the kth covariate Tvar[1]@12 {1, 2, 3, 8, 10, 11, 8, 3, 7, 8, 5, 6}, thus Tvar[5=V7*V8]=10
      *     which is a new column after the 9 (ncovcol) variables. 
      * - if k is a product Vn*Vm covar[k][i] is filled with correct values for each individual
      * - Tprod[l] gives the kth covariates of the product Vn*Vm l=1 to cptcovprod-cptcovage
      *    Tprod[1]@2 {5, 6}: position of first product V7*V8 is 5, and second V5*V6 is 6.
      * - Tvard[k]  p Tvard[1][1]@4 {7, 8, 5, 6} for V7*V8 and V5*V6 .
    */
   {
     int i, j, k, ks;
     int i1, j1, k1, k2;
     char modelsav[80];
     char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     /*removespace(model);*/
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=0, k2=-1, ks=0, cptcovn=0;
       j=nbocc(model,'+'); /**< j=Number of '+' */
       j1=nbocc(model,'*'); /**< j1=Number of '*' */
       cptcovs=j+1-j1; /**<  Number of simple covariates V1+V2*age+V3 +V3*V4=> V1 + V3 =2  */
       cptcovt= j+1; /* Number of total covariates in the model V1 + V2*age+ V3 + V3*V4=> 4*/
                     /* including age products which are counted in cptcovage.
                     /* but the covariates which are products must be treated separately: ncovn=4- 2=2 (V1+V3). */
       cptcovprod=j1; /**< Number of products  V1*V2 +v3*age = 2 */
       cptcovprodnoage=0; /**< Number of covariate products without age: V3*V4 =1  */
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /*   Design
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9 Weight
        *  <          ncovcol=8                >
        * Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8
        *   k=  1    2      3       4     5       6      7        8
        *  cptcovn number of covariates (not including constant and age ) = # of + plus 1 = 7+1=8
        *  covar[k,i], value of kth covariate if not including age for individual i:
        *       covar[1][i]= (V2), covar[4][i]=(V3), covar[8][i]=(V8)
        *  Tvar[k] # of the kth covariate:  Tvar[1]=2  Tvar[4]=3 Tvar[8]=8
        *       if multiplied by age: V3*age Tvar[3=V3*age]=3 (V3) Tvar[7]=8 and 
        *  Tage[++cptcovage]=k
        *       if products, new covar are created after ncovcol with k1
        *  Tvar[k]=ncovcol+k1; # of the kth covariate product:  Tvar[5]=ncovcol+1=10  Tvar[6]=ncovcol+1=11
        *  Tprod[k1]=k; Tprod[1]=5 Tprod[2]= 6; gives the position of the k1th product
        *  Tvard[k1][1]=m Tvard[k1][2]=m; Tvard[1][1]=5 (V5) Tvard[1][2]=6 Tvard[2][1]=7 (V7) Tvard[2][2]=8
        *  Tvar[cptcovn+k2]=Tvard[k1][1];Tvar[cptcovn+k2+1]=Tvard[k1][2];
        *  Tvar[8+1]=5;Tvar[8+2]=6;Tvar[8+3]=7;Tvar[8+4]=8 inverted
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9  V10  V11
        *  <          ncovcol=8                >
        *       Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8    d1   d1   d2  d2
        *          k=  1    2      3       4     5       6      7        8    9   10   11  12
        *     Tvar[k]= 2    1      3       3    10      11      8        8    5    6    7   8
        * p Tvar[1]@12={2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        * p Tprod[1]@2={                         6, 5}
        *p Tvard[1][1]@4= {7, 8, 5, 6}
        * covar[k][i]= V2   V1      ?      V3    V5*V6?   V7*V8?  ?       V8   
        *  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
        *How to reorganize?
        * Model V1 + V2 + V3 + V8 + V5*V6 + V7*V8 + V3*age + V8*age
        * Tvars {2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        *       {2,   1,     4,      8,    5,      6,     3,       7}
        * Struct []
        */
   
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       /*
        * Treating invertedly V2+V1+V3*age+V2*V4 is as if written V2*V4 +V3*age + V1 + V2 */
       for(k=cptcovt; k>=1;k--) /**< Number of covariates */
           Tvar[k]=0;
       cptcovage=0;
       for(k=1; k<=cptcovt;k++){ /* Loop on total covariates of the model */
         cutl(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /**< Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutl(strc,strd,strb,'*'); /**< strd*strc  Vm*Vn: strb=V3*age(input) strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /**< Model includes age: Vn*age */
             /* covar is not filled and then is empty */
             cptcovprod--;
             cutl(stre,strb,strd,'V'); /* strd=V3(input): stre="3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=3 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutl(stre,strb,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cptcovn++;
             cptcovprodnoage++;k1++;
             cutl(stre,strb,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1; /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutl(strc,strb,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1] =atoi(strc); /* m 1 for V1*/
             Tvard[k1][2] =atoi(stre); /* n 4 for V4*/
             k2=k2+2;
             Tvar[cptcovt+k2]=Tvard[k1][1]; /* Tvar[(cptcovt=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovt+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovt=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 May not be defined */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutl(strd,strc,strb,'V');
           ks++; /**< Number of simple covariates */
           cptcovn++;
           Tvar[k]=atoi(strd);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               /* printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4]="1234";
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     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);
   
     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");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
        /* freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint); */
       /* ,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2); */
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
   #include "prevlim.h"  /* Use ficrespl, ficlog */
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
   #include "hpijx.h"
       fclose(ficrespij);
   
     /*-------------- Variance of one-step probabilities---*/
       k=1;
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
           /*
            */
           /* goto endfree; */
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
   
   
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms; /* Segmentation fault */
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);
             fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         /*}*/
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,NCOVMAX,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*here or after loop ? */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,NCOVMAX);
       free_ivector(Tvar,1,NCOVMAX);
       free_ivector(Tprod,1,NCOVMAX);
       free_ivector(Tvaraff,1,NCOVMAX);
       free_ivector(Tage,1,NCOVMAX);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     /*(void) gettimeofday(&end_time,&tzp);*/
     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.1.30  
changed lines
  Added in v.1.160


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