Diff for /imach/src/imach.c between versions 1.16 and 1.154

version 1.16, 2002/02/20 17:12:32 version 1.154, 2014/06/20 17:32:08
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      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.154  2014/06/20 17:32:08  brouard
   individuals from different ages are interviewed on their health status    Summary: Outputs now all graphs of convergence to period prevalence
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.153  2014/06/20 16:45:46  brouard
   Health expectancies are computed from the transistions observed between    Summary: If 3 live state, convergence to period prevalence on same graph
   waves and are computed for each degree of severity of disability (number    Author: Brouard
   of life states). More degrees you consider, more time is necessary to  
   reach the Maximum Likelihood of the parameters involved in the model.    Revision 1.152  2014/06/18 17:54:09  brouard
   The simplest model is the multinomial logistic model where pij is    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   the probabibility to be observed in state j at the second wave conditional  
   to be observed in state i at the first wave. Therefore the model is:    Revision 1.151  2014/06/18 16:43:30  brouard
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    *** empty log message ***
   is a covariate. If you want to have a more complex model than "constant and  
   age", you should modify the program where the markup    Revision 1.150  2014/06/18 16:42:35  brouard
     *Covariates have to be included here again* invites you to do it.    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
   More covariates you add, less is the speed of the convergence.    Author: brouard
   
   The advantage that this computer programme claims, comes from that if the    Revision 1.149  2014/06/18 15:51:14  brouard
   delay between waves is not identical for each individual, or if some    Summary: Some fixes in parameter files errors
   individual missed an interview, the information is not rounded or lost, but    Author: Nicolas Brouard
   taken into account using an interpolation or extrapolation.  
   hPijx is the probability to be    Revision 1.148  2014/06/17 17:38:48  brouard
   observed in state i at age x+h conditional to the observed state i at age    Summary: Nothing new
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Author: Brouard
   unobserved intermediate  states. This elementary transition (by month or  
   quarter trimester, semester or year) is model as a multinomial logistic.    Just a new packaging for OS/X version 0.98nS
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply hPijx.    Revision 1.147  2014/06/16 10:33:11  brouard
     *** empty log message ***
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Revision 1.146  2014/06/16 10:20:28  brouard
      Summary: Merge
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Author: Brouard
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Merge, before building revised version.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.145  2014/06/10 21:23:15  brouard
   software can be distributed freely for non commercial use. Latest version    Summary: Debugging with valgrind
   can be accessed at http://euroreves.ined.fr/imach .    Author: Nicolas Brouard
   **********************************************************************/  
      Lot of changes in order to output the results with some covariates
 #include <math.h>    After the Edimburgh REVES conference 2014, it seems mandatory to
 #include <stdio.h>    improve the code.
 #include <stdlib.h>    No more memory valgrind error but a lot has to be done in order to
 #include <unistd.h>    continue the work of splitting the code into subroutines.
     Also, decodemodel has been improved. Tricode is still not
 #define MAXLINE 256    optimal. nbcode should be improved. Documentation has been added in
 #define FILENAMELENGTH 80    the source code.
 /*#define DEBUG*/  
 #define windows    Revision 1.143  2014/01/26 09:45:38  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.142  2014/01/26 03:57:36  brouard
 #define NINTERVMAX 8    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.141  2014/01/26 02:42:01  brouard
 #define YEARM 12. /* Number of months per year */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.140  2011/09/02 10:37:54  brouard
     Summary: times.h is ok with mingw32 now.
   
 int nvar;    Revision 1.139  2010/06/14 07:50:17  brouard
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 int npar=NPARMAX;    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.138  2010/04/30 18:19:40  brouard
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    *** empty log message ***
 int popbased=0;  
     Revision 1.137  2010/04/29 18:11:38  brouard
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): Checking covariates for more complex models
 int maxwav; /* Maxim number of waves */    than V1+V2. A lot of change to be done. Unstable.
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.136  2010/04/26 20:30:53  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): merging some libgsl code. Fixing computation
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    of likelione (using inter/intrapolation if mle = 0) in order to
 double jmean; /* Mean space between 2 waves */    get same likelihood as if mle=1.
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Some cleaning of code and comments added.
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    Revision 1.135  2009/10/29 15:33:14  brouard
 FILE *ficgp, *fichtm,*ficresprob,*ficpop;    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 FILE *ficreseij;  
   char filerese[FILENAMELENGTH];    Revision 1.134  2009/10/29 13:18:53  brouard
  FILE  *ficresvij;    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   char fileresv[FILENAMELENGTH];  
  FILE  *ficresvpl;    Revision 1.133  2009/07/06 10:21:25  brouard
   char fileresvpl[FILENAMELENGTH];    just nforces
   
 #define NR_END 1    Revision 1.132  2009/07/06 08:22:05  brouard
 #define FREE_ARG char*    Many tings
 #define FTOL 1.0e-10  
     Revision 1.131  2009/06/20 16:22:47  brouard
 #define NRANSI    Some dimensions resccaled
 #define ITMAX 200  
     Revision 1.130  2009/05/26 06:44:34  brouard
 #define TOL 2.0e-4    (Module): Max Covariate is now set to 20 instead of 8. A
     lot of cleaning with variables initialized to 0. Trying to make
 #define CGOLD 0.3819660    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.129  2007/08/31 13:49:27  lievre
     Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.128  2006/06/30 13:02:05  brouard
 #define TINY 1.0e-20    (Module): Clarifications on computing e.j
   
 static double maxarg1,maxarg2;    Revision 1.127  2006/04/28 18:11:50  brouard
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    (Module): Yes the sum of survivors was wrong since
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    imach-114 because nhstepm was no more computed in the age
      loop. Now we define nhstepma in the age loop.
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): In order to speed up (in case of numerous covariates) we
 #define rint(a) floor(a+0.5)    compute health expectancies (without variances) in a first step
     and then all the health expectancies with variances or standard
 static double sqrarg;    deviation (needs data from the Hessian matrices) which slows the
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    computation.
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
 int imx;  
 int stepm;    Revision 1.126  2006/04/28 17:23:28  brouard
 /* Stepm, step in month: minimum step interpolation*/    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 int m,nb;    loop. Now we define nhstepma in the age loop.
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Version 0.98h
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 double *weight;    Forecasting file added.
 int **s; /* Status */  
 double *agedc, **covar, idx;    Revision 1.124  2006/03/22 17:13:53  lievre
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    Parameters are printed with %lf instead of %f (more numbers after the comma).
     The log-likelihood is printed in the log file
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */    Revision 1.123  2006/03/20 10:52:43  brouard
     * imach.c (Module): <title> changed, corresponds to .htm file
 /**************** split *************************/    name. <head> headers where missing.
 static  int split( char *path, char *dirc, char *name )  
 {    * imach.c (Module): Weights can have a decimal point as for
    char *s;                             /* pointer */    English (a comma might work with a correct LC_NUMERIC environment,
    int  l1, l2;                         /* length counters */    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
    l1 = strlen( path );                 /* length of path */    1.
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Version 0.98g
    s = strrchr( path, '\\' );           /* find last / */  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.122  2006/03/20 09:45:41  brouard
 #if     defined(__bsd__)                /* get current working directory */    (Module): Weights can have a decimal point as for
       extern char       *getwd( );    English (a comma might work with a correct LC_NUMERIC environment,
     otherwise the weight is truncated).
       if ( getwd( dirc ) == NULL ) {    Modification of warning when the covariates values are not 0 or
 #else    1.
       extern char       *getcwd( );    Version 0.98g
   
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Revision 1.121  2006/03/16 17:45:01  lievre
 #endif    * imach.c (Module): Comments concerning covariates added
          return( GLOCK_ERROR_GETCWD );  
       }    * imach.c (Module): refinements in the computation of lli if
       strcpy( name, path );             /* we've got it */    status=-2 in order to have more reliable computation if stepm is
    } else {                             /* strip direcotry from path */    not 1 month. Version 0.98f
       s++;                              /* after this, the filename */  
       l2 = strlen( s );                 /* length of filename */    Revision 1.120  2006/03/16 15:10:38  lievre
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): refinements in the computation of lli if
       strcpy( name, s );                /* save file name */    status=-2 in order to have more reliable computation if stepm is
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    not 1 month. Version 0.98f
       dirc[l1-l2] = 0;                  /* add zero */  
    }    Revision 1.119  2006/03/15 17:42:26  brouard
    l1 = strlen( dirc );                 /* length of directory */    (Module): Bug if status = -2, the loglikelihood was
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    computed as likelihood omitting the logarithm. Version O.98e
    return( 0 );                         /* we're done */  
 }    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.
     (Module): Function pstamp added
 void replace(char *s, char*t)    (Module): Version 0.98d
 {  
   int i;    Revision 1.117  2006/03/14 17:16:22  brouard
   int lg=20;    (Module): varevsij Comments added explaining the second
   i=0;    table of variances if popbased=1 .
   lg=strlen(t);    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   for(i=0; i<= lg; i++) {    (Module): Function pstamp added
     (s[i] = t[i]);    (Module): Version 0.98d
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.116  2006/03/06 10:29:27  brouard
 }    (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 int nbocc(char *s, char occ)  
 {    Revision 1.115  2006/02/27 12:17:45  brouard
   int i,j=0;    (Module): One freematrix added in mlikeli! 0.98c
   int lg=20;  
   i=0;    Revision 1.114  2006/02/26 12:57:58  brouard
   lg=strlen(s);    (Module): Some improvements in processing parameter
   for(i=0; i<= lg; i++) {    filename with strsep.
   if  (s[i] == occ ) j++;  
   }    Revision 1.113  2006/02/24 14:20:24  brouard
   return j;    (Module): Memory leaks checks with valgrind and:
 }    datafile was not closed, some imatrix were not freed and on matrix
     allocation too.
 void cutv(char *u,char *v, char*t, char occ)  
 {    Revision 1.112  2006/01/30 09:55:26  brouard
   int i,lg,j,p=0;    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {    Revision 1.111  2006/01/25 20:38:18  brouard
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    (Module): Lots of cleaning and bugs added (Gompertz)
   }    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
   lg=strlen(t);  
   for(j=0; j<p; j++) {    Revision 1.110  2006/01/25 00:51:50  brouard
     (u[j] = t[j]);    (Module): Lots of cleaning and bugs added (Gompertz)
   }  
      u[p]='\0';    Revision 1.109  2006/01/24 19:37:15  brouard
     (Module): Comments (lines starting with a #) are allowed in data.
    for(j=0; j<= lg; j++) {  
     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
     Test existence of gnuplot in imach path
 void nrerror(char error_text[])  
 {    Revision 1.106  2006/01/19 13:24:36  brouard
   fprintf(stderr,"ERREUR ...\n");    Some cleaning and links added in html output
   fprintf(stderr,"%s\n",error_text);  
   exit(1);    Revision 1.105  2006/01/05 20:23:19  lievre
 }    *** empty log message ***
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    Revision 1.104  2005/09/30 16:11:43  lievre
 {    (Module): sump fixed, loop imx fixed, and simplifications.
   double *v;    (Module): If the status is missing at the last wave but we know
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    that the person is alive, then we can code his/her status as -2
   if (!v) nrerror("allocation failure in vector");    (instead of missing=-1 in earlier versions) and his/her
   return v-nl+NR_END;    contributions to the likelihood is 1 - Prob of dying from last
 }    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
 /************************ free vector ******************/  
 void free_vector(double*v, int nl, int nh)    Revision 1.103  2005/09/30 15:54:49  lievre
 {    (Module): sump fixed, loop imx fixed, and simplifications.
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.102  2004/09/15 17:31:30  brouard
     Add the possibility to read data file including tab characters.
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Revision 1.101  2004/09/15 10:38:38  brouard
 {    Fix on curr_time
   int *v;  
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Revision 1.100  2004/07/12 18:29:06  brouard
   if (!v) nrerror("allocation failure in ivector");    Add version for Mac OS X. Just define UNIX in Makefile
   return v-nl+NR_END;  
 }    Revision 1.99  2004/06/05 08:57:40  brouard
     *** empty log message ***
 /******************free ivector **************************/  
 void free_ivector(int *v, long nl, long nh)    Revision 1.98  2004/05/16 15:05:56  brouard
 {    New version 0.97 . First attempt to estimate force of mortality
   free((FREE_ARG)(v+nl-NR_END));    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 .
     This is the basic analysis of mortality and should be done before any
 /******************* imatrix *******************************/    other analysis, in order to test if the mortality estimated from the
 int **imatrix(long nrl, long nrh, long ncl, long nch)    cross-longitudinal survey is different from the mortality estimated
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    from other sources like vital statistic data.
 {  
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    The same imach parameter file can be used but the option for mle should be -3.
   int **m;  
      Agnès, who wrote this part of the code, tried to keep most of the
   /* allocate pointers to rows */    former routines in order to include the new code within the former code.
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    The output is very simple: only an estimate of the intercept and of
   m += NR_END;    the slope with 95% confident intervals.
   m -= nrl;  
      Current limitations:
      A) Even if you enter covariates, i.e. with the
   /* allocate rows and set pointers to them */    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    B) There is no computation of Life Expectancy nor Life Table.
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.97  2004/02/20 13:25:42  lievre
   m[nrl] -= ncl;    Version 0.96d. Population forecasting command line is (temporarily)
      suppressed.
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
      Revision 1.96  2003/07/15 15:38:55  brouard
   /* return pointer to array of pointers to rows */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
   return m;    rewritten within the same printf. Workaround: many printfs.
 }  
     Revision 1.95  2003/07/08 07:54:34  brouard
 /****************** free_imatrix *************************/    * imach.c (Repository):
 void free_imatrix(m,nrl,nrh,ncl,nch)    (Repository): Using imachwizard code to output a more meaningful covariance
       int **m;    matrix (cov(a12,c31) instead of numbers.
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */    Revision 1.94  2003/06/27 13:00:02  brouard
 {    Just cleaning
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   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
     exist so I changed back to asctime which exists.
 /******************* matrix *******************************/    (Module): Version 0.96b
 double **matrix(long nrl, long nrh, long ncl, long nch)  
 {    Revision 1.92  2003/06/25 16:30:45  brouard
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    (Module): On windows (cygwin) function asctime_r doesn't
   double **m;    exist so I changed back to asctime which exists.
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Revision 1.91  2003/06/25 15:30:29  brouard
   if (!m) nrerror("allocation failure 1 in matrix()");    * imach.c (Repository): Duplicated warning errors corrected.
   m += NR_END;    (Repository): Elapsed time after each iteration is now output. It
   m -= nrl;    helps to forecast when convergence will be reached. Elapsed time
     is stamped in powell.  We created a new html file for the graphs
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    concerning matrix of covariance. It has extension -cov.htm.
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.90  2003/06/24 12:34:15  brouard
   m[nrl] -= ncl;    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    of the covariance matrix to be input.
   return m;  
 }    Revision 1.89  2003/06/24 12:30:52  brouard
     (Module): Some bugs corrected for windows. Also, when
 /*************************free matrix ************************/    mle=-1 a template is output in file "or"mypar.txt with the design
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    of the covariance matrix to be input.
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.88  2003/06/23 17:54:56  brouard
   free((FREE_ARG)(m+nrl-NR_END));    * 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.
 }  
     Revision 1.87  2003/06/18 12:26:01  brouard
 /******************* ma3x *******************************/    Version 0.96
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  
 {    Revision 1.86  2003/06/17 20:04:08  brouard
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    (Module): Change position of html and gnuplot routines and added
   double ***m;    routine fileappend.
   
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Revision 1.85  2003/06/17 13:12:43  brouard
   if (!m) nrerror("allocation failure 1 in matrix()");    * imach.c (Repository): Check when date of death was earlier that
   m += NR_END;    current date of interview. It may happen when the death was just
   m -= nrl;    prior to the death. In this case, dh was negative and likelihood
     was wrong (infinity). We still send an "Error" but patch by
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    assuming that the date of death was just one stepm after the
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    interview.
   m[nrl] += NR_END;    (Repository): Because some people have very long ID (first column)
   m[nrl] -= ncl;    we changed int to long in num[] and we added a new lvector for
     memory allocation. But we also truncated to 8 characters (left
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    truncation)
     (Repository): No more line truncation errors.
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    Revision 1.84  2003/06/13 21:44:43  brouard
   m[nrl][ncl] += NR_END;    * imach.c (Repository): Replace "freqsummary" at a correct
   m[nrl][ncl] -= nll;    place. It differs from routine "prevalence" which may be called
   for (j=ncl+1; j<=nch; j++)    many times. Probs is memory consuming and must be used with
     m[nrl][j]=m[nrl][j-1]+nlay;    parcimony.
      Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   for (i=nrl+1; i<=nrh; i++) {  
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    Revision 1.83  2003/06/10 13:39:11  lievre
     for (j=ncl+1; j<=nch; j++)    *** empty log message ***
       m[i][j]=m[i][j-1]+nlay;  
   }    Revision 1.82  2003/06/05 15:57:20  brouard
   return m;    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));    Short summary of the programme:
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    
   free((FREE_ARG)(m+nrl-NR_END));    This program computes Healthy Life Expectancies from
 }    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     first survey ("cross") where individuals from different ages are
 /***************** f1dim *************************/    interviewed on their health status or degree of disability (in the
 extern int ncom;    case of a health survey which is our main interest) -2- at least a
 extern double *pcom,*xicom;    second wave of interviews ("longitudinal") which measure each change
 extern double (*nrfunc)(double []);    (if any) in individual health status.  Health expectancies are
      computed from the time spent in each health state according to a
 double f1dim(double x)    model. More health states you consider, more time is necessary to reach the
 {    Maximum Likelihood of the parameters involved in the model.  The
   int j;    simplest model is the multinomial logistic model where pij is the
   double f;    probability to be observed in state j at the second wave
   double *xt;    conditional to be observed in state i at the first wave. Therefore
      the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   xt=vector(1,ncom);    'age' is age and 'sex' is a covariate. If you want to have a more
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    complex model than "constant and age", you should modify the program
   f=(*nrfunc)(xt);    where the markup *Covariates have to be included here again* invites
   free_vector(xt,1,ncom);    you to do it.  More covariates you add, slower the
   return f;    convergence.
 }  
     The advantage of this computer programme, compared to a simple
 /*****************brent *************************/    multinomial logistic model, is clear when the delay between waves is not
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    identical for each individual. Also, if a individual missed an
 {    intermediate interview, the information is lost, but taken into
   int iter;    account using an interpolation or extrapolation.  
   double a,b,d,etemp;  
   double fu,fv,fw,fx;    hPijx is the probability to be observed in state i at age x+h
   double ftemp;    conditional to the observed state i at age x. The delay 'h' can be
   double p,q,r,tol1,tol2,u,v,w,x,xm;    split into an exact number (nh*stepm) of unobserved intermediate
   double e=0.0;    states. This elementary transition (by month, quarter,
      semester or year) is modelled as a multinomial logistic.  The hPx
   a=(ax < cx ? ax : cx);    matrix is simply the matrix product of nh*stepm elementary matrices
   b=(ax > cx ? ax : cx);    and the contribution of each individual to the likelihood is simply
   x=w=v=bx;    hPijx.
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {    Also this programme outputs the covariance matrix of the parameters but also
     xm=0.5*(a+b);    of the life expectancies. It also computes the period (stable) prevalence. 
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
     printf(".");fflush(stdout);             Institut national d'études démographiques, Paris.
 #ifdef DEBUG    This software have been partly granted by Euro-REVES, a concerted action
     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);    from the European Union.
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    It is copyrighted identically to a GNU software product, ie programme and
 #endif    software can be distributed freely for non commercial use. Latest version
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    can be accessed at http://euroreves.ined.fr/imach .
       *xmin=x;  
       return fx;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
     }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     ftemp=fu;    
     if (fabs(e) > tol1) {    **********************************************************************/
       r=(x-w)*(fx-fv);  /*
       q=(x-v)*(fx-fw);    main
       p=(x-v)*q-(x-w)*r;    read parameterfile
       q=2.0*(q-r);    read datafile
       if (q > 0.0) p = -p;    concatwav
       q=fabs(q);    freqsummary
       etemp=e;    if (mle >= 1)
       e=d;      mlikeli
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    print results files
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    if mle==1 
       else {       computes hessian
         d=p/q;    read end of parameter file: agemin, agemax, bage, fage, estepm
         u=x+d;        begin-prev-date,...
         if (u-a < tol2 || b-u < tol2)    open gnuplot file
           d=SIGN(tol1,xm-x);    open html file
       }    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
     } else {     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
       d=CGOLD*(e=(x >= xm ? a-x : b-x));                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
     }      freexexit2 possible for memory heap.
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  
     fu=(*f)(u);    h Pij x                         | pij_nom  ficrestpij
     if (fu <= fx) {     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
       if (u >= x) a=x; else b=x;         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
       SHFT(v,w,x,u)         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
         SHFT(fv,fw,fx,fu)  
         } else {         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
           if (u < x) a=u; else b=u;         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
           if (fu <= fw || w == x) {    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
             v=w;     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
             w=u;     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
             fv=fw;  
             fw=fu;    forecasting if prevfcast==1 prevforecast call prevalence()
           } else if (fu <= fv || v == x || v == w) {    health expectancies
             v=u;    Variance-covariance of DFLE
             fv=fu;    prevalence()
           }     movingaverage()
         }    varevsij() 
   }    if popbased==1 varevsij(,popbased)
   nrerror("Too many iterations in brent");    total life expectancies
   *xmin=x;    Variance of period (stable) prevalence
   return fx;   end
 }  */
   
 /****************** mnbrak ***********************/  
   
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,   
             double (*func)(double))  #include <math.h>
 {  #include <stdio.h>
   double ulim,u,r,q, dum;  #include <stdlib.h>
   double fu;  #include <string.h>
    #include <unistd.h>
   *fa=(*func)(*ax);  
   *fb=(*func)(*bx);  #include <limits.h>
   if (*fb > *fa) {  #include <sys/types.h>
     SHFT(dum,*ax,*bx,dum)  #include <sys/stat.h>
       SHFT(dum,*fb,*fa,dum)  #include <errno.h>
       }  extern int errno;
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);  #ifdef LINUX
   while (*fb > *fc) {  #include <time.h>
     r=(*bx-*ax)*(*fb-*fc);  #include "timeval.h"
     q=(*bx-*cx)*(*fb-*fa);  #else
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  #include <sys/time.h>
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #endif
     ulim=(*bx)+GLIMIT*(*cx-*bx);  
     if ((*bx-u)*(u-*cx) > 0.0) {  #ifdef GSL
       fu=(*func)(u);  #include <gsl/gsl_errno.h>
     } else if ((*cx-u)*(u-ulim) > 0.0) {  #include <gsl/gsl_multimin.h>
       fu=(*func)(u);  #endif
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  /* #include <libintl.h> */
           SHFT(*fb,*fc,fu,(*func)(u))  /* #define _(String) gettext (String) */
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
       u=ulim;  
       fu=(*func)(u);  #define GNUPLOTPROGRAM "gnuplot"
     } else {  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
       u=(*cx)+GOLD*(*cx-*bx);  #define FILENAMELENGTH 132
       fu=(*func)(u);  
     }  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
     SHFT(*ax,*bx,*cx,u)  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
       SHFT(*fa,*fb,*fc,fu)  
       }  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
 }  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
   
 /*************** linmin ************************/  #define NINTERVMAX 8
   #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
 int ncom;  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
 double *pcom,*xicom;  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
 double (*nrfunc)(double []);  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
    #define MAXN 20000
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #define YEARM 12. /**< Number of months per year */
 {  #define AGESUP 130
   double brent(double ax, double bx, double cx,  #define AGEBASE 40
                double (*f)(double), double tol, double *xmin);  #define AGEGOMP 10. /**< Minimal age for Gompertz adjustment */
   double f1dim(double x);  #ifdef UNIX
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #define DIRSEPARATOR '/'
               double *fc, double (*func)(double));  #define CHARSEPARATOR "/"
   int j;  #define ODIRSEPARATOR '\\'
   double xx,xmin,bx,ax;  #else
   double fx,fb,fa;  #define DIRSEPARATOR '\\'
    #define CHARSEPARATOR "\\"
   ncom=n;  #define ODIRSEPARATOR '/'
   pcom=vector(1,n);  #endif
   xicom=vector(1,n);  
   nrfunc=func;  /* $Id$ */
   for (j=1;j<=n;j++) {  /* $State$ */
     pcom[j]=p[j];  
     xicom[j]=xi[j];  char version[]="Imach version 0.98nU, January 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
   }  char fullversion[]="$Revision$ $Date$"; 
   ax=0.0;  char strstart[80];
   xx=1.0;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  int nvar=0, nforce=0; /* Number of variables, number of forces */
 #ifdef DEBUG  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
 #endif  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
   for (j=1;j<=n;j++) {  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
     xi[j] *= xmin;  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
     p[j] += xi[j];  int cptcovprodnoage=0; /**< Number of covariate products without age */   
   }  int cptcoveff=0; /* Total number of covariates to vary for printing results */
   free_vector(xicom,1,n);  int cptcov=0; /* Working variable */
   free_vector(pcom,1,n);  int npar=NPARMAX;
 }  int nlstate=2; /* Number of live states */
   int ndeath=1; /* Number of dead states */
 /*************** powell ************************/  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  int popbased=0;
             double (*func)(double []))  
 {  int *wav; /* Number of waves for this individuual 0 is possible */
   void linmin(double p[], double xi[], int n, double *fret,  int maxwav=0; /* Maxim number of waves */
               double (*func)(double []));  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
   int i,ibig,j;  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
   double del,t,*pt,*ptt,*xit;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
   double fp,fptt;                     to the likelihood and the sum of weights (done by funcone)*/
   double *xits;  int mle=1, weightopt=0;
   pt=vector(1,n);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   ptt=vector(1,n);  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   xit=vector(1,n);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   xits=vector(1,n);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   *fret=(*func)(p);  double jmean=1; /* Mean space between 2 waves */
   for (j=1;j<=n;j++) pt[j]=p[j];  double **matprod2(); /* test */
   for (*iter=1;;++(*iter)) {  double **oldm, **newm, **savm; /* Working pointers to matrices */
     fp=(*fret);  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
     ibig=0;  /*FILE *fic ; */ /* Used in readdata only */
     del=0.0;  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  FILE *ficlog, *ficrespow;
     for (i=1;i<=n;i++)  int globpr=0; /* Global variable for printing or not */
       printf(" %d %.12f",i, p[i]);  double fretone; /* Only one call to likelihood */
     printf("\n");  long ipmx=0; /* Number of contributions */
     for (i=1;i<=n;i++) {  double sw; /* Sum of weights */
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  char filerespow[FILENAMELENGTH];
       fptt=(*fret);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
 #ifdef DEBUG  FILE *ficresilk;
       printf("fret=%lf \n",*fret);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 #endif  FILE *ficresprobmorprev;
       printf("%d",i);fflush(stdout);  FILE *fichtm, *fichtmcov; /* Html File */
       linmin(p,xit,n,fret,func);  FILE *ficreseij;
       if (fabs(fptt-(*fret)) > del) {  char filerese[FILENAMELENGTH];
         del=fabs(fptt-(*fret));  FILE *ficresstdeij;
         ibig=i;  char fileresstde[FILENAMELENGTH];
       }  FILE *ficrescveij;
 #ifdef DEBUG  char filerescve[FILENAMELENGTH];
       printf("%d %.12e",i,(*fret));  FILE  *ficresvij;
       for (j=1;j<=n;j++) {  char fileresv[FILENAMELENGTH];
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  FILE  *ficresvpl;
         printf(" x(%d)=%.12e",j,xit[j]);  char fileresvpl[FILENAMELENGTH];
       }  char title[MAXLINE];
       for(j=1;j<=n;j++)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
         printf(" p=%.12e",p[j]);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       printf("\n");  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
 #endif  char command[FILENAMELENGTH];
     }  int  outcmd=0;
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
       int k[2],l;  
       k[0]=1;  char filelog[FILENAMELENGTH]; /* Log file */
       k[1]=-1;  char filerest[FILENAMELENGTH];
       printf("Max: %.12e",(*func)(p));  char fileregp[FILENAMELENGTH];
       for (j=1;j<=n;j++)  char popfile[FILENAMELENGTH];
         printf(" %.12e",p[j]);  
       printf("\n");  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       for(l=0;l<=1;l++) {  
         for (j=1;j<=n;j++) {  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  struct timezone tzp;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  extern int gettimeofday();
         }  struct tm tmg, tm, tmf, *gmtime(), *localtime();
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  long time_value;
       }  extern long time();
 #endif  char strcurr[80], strfor[80];
   
   char *endptr;
       free_vector(xit,1,n);  long lval;
       free_vector(xits,1,n);  double dval;
       free_vector(ptt,1,n);  
       free_vector(pt,1,n);  #define NR_END 1
       return;  #define FREE_ARG char*
     }  #define FTOL 1.0e-10
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  
     for (j=1;j<=n;j++) {  #define NRANSI 
       ptt[j]=2.0*p[j]-pt[j];  #define ITMAX 200 
       xit[j]=p[j]-pt[j];  
       pt[j]=p[j];  #define TOL 2.0e-4 
     }  
     fptt=(*func)(ptt);  #define CGOLD 0.3819660 
     if (fptt < fp) {  #define ZEPS 1.0e-10 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);  #define GOLD 1.618034 
         for (j=1;j<=n;j++) {  #define GLIMIT 100.0 
           xi[j][ibig]=xi[j][n];  #define TINY 1.0e-20 
           xi[j][n]=xit[j];  
         }  static double maxarg1,maxarg2;
 #ifdef DEBUG  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
         for(j=1;j<=n;j++)    
           printf(" %.12e",xit[j]);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
         printf("\n");  #define rint(a) floor(a+0.5)
 #endif  
       }  static double sqrarg;
     }  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
 }  int agegomp= AGEGOMP;
   
 /**** Prevalence limit ****************/  int imx; 
   int stepm=1;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  /* Stepm, step in month: minimum step interpolation*/
 {  
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  int estepm;
      matrix by transitions matrix until convergence is reached */  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   
   int i, ii,j,k;  int m,nb;
   double min, max, maxmin, maxmax,sumnew=0.;  long *num;
   double **matprod2();  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   double **out, cov[NCOVMAX], **pmij();  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   double **newm;  double **pmmij, ***probs;
   double agefin, delaymax=50 ; /* Max number of years to converge */  double *ageexmed,*agecens;
   double dateintmean=0;
   for (ii=1;ii<=nlstate+ndeath;ii++)  
     for (j=1;j<=nlstate+ndeath;j++){  double *weight;
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  int **s; /* Status */
     }  double *agedc;
   double  **covar; /**< covar[j,i], value of jth covariate for individual i,
    cov[1]=1.;                    * covar=matrix(0,NCOVMAX,1,n); 
                      * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  double  idx; 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
     newm=savm;  int *Ndum; /** Freq of modality (tricode */
     /* Covariates have to be included here again */  int **codtab; /**< codtab=imatrix(1,100,1,10); */
      cov[2]=agefin;  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
    double *lsurv, *lpop, *tpop;
       for (k=1; k<=cptcovn;k++) {  
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/  double ftolhess; /**< Tolerance for computing hessian */
       }  
       for (k=1; k<=cptcovage;k++)  /**************** split *************************/
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
       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]]];    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
        the name of the file (name), its extension only (ext) and its first part of the name (finame)
       /*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]);*/    char  *ss;                            /* pointer */
     int   l1, l2;                         /* length counters */
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  
     l1 = strlen(path );                   /* length of path */
     savm=oldm;    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     oldm=newm;    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     maxmax=0.;    if ( ss == NULL ) {                   /* no directory, so determine current directory */
     for(j=1;j<=nlstate;j++){      strcpy( name, path );               /* we got the fullname name because no directory */
       min=1.;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
       max=0.;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       for(i=1; i<=nlstate; i++) {      /* get current working directory */
         sumnew=0;      /*    extern  char* getcwd ( char *buf , int len);*/
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
         prlim[i][j]= newm[i][j]/(1-sumnew);        return( GLOCK_ERROR_GETCWD );
         max=FMAX(max,prlim[i][j]);      }
         min=FMIN(min,prlim[i][j]);      /* got dirc from getcwd*/
       }      printf(" DIRC = %s \n",dirc);
       maxmin=max-min;    } else {                              /* strip direcotry from path */
       maxmax=FMAX(maxmax,maxmin);      ss++;                               /* after this, the filename */
     }      l2 = strlen( ss );                  /* length of filename */
     if(maxmax < ftolpl){      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
       return prlim;      strcpy( name, ss );         /* save file name */
     }      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   }      dirc[l1-l2] = 0;                    /* add zero */
 }      printf(" DIRC2 = %s \n",dirc);
     }
 /*************** transition probabilities ***************/    /* We add a separator at the end of dirc if not exists */
     l1 = strlen( dirc );                  /* length of directory */
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    if( dirc[l1-1] != DIRSEPARATOR ){
 {      dirc[l1] =  DIRSEPARATOR;
   double s1, s2;      dirc[l1+1] = 0; 
   /*double t34;*/      printf(" DIRC3 = %s \n",dirc);
   int i,j,j1, nc, ii, jj;    }
     ss = strrchr( name, '.' );            /* find last / */
     for(i=1; i<= nlstate; i++){    if (ss >0){
     for(j=1; j<i;j++){      ss++;
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){      strcpy(ext,ss);                     /* save extension */
         /*s2 += param[i][j][nc]*cov[nc];*/      l1= strlen( name);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];      l2= strlen(ss)+1;
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/      strncpy( finame, name, l1-l2);
       }      finame[l1-l2]= 0;
       ps[i][j]=s2;    }
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  
     }    return( 0 );                          /* we're done */
     for(j=i+1; j<=nlstate+ndeath;j++){  }
       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];  
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  /******************************************/
       }  
       ps[i][j]=(s2);  void replace_back_to_slash(char *s, char*t)
     }  {
   }    int i;
     /*ps[3][2]=1;*/    int lg=0;
     i=0;
   for(i=1; i<= nlstate; i++){    lg=strlen(t);
      s1=0;    for(i=0; i<= lg; i++) {
     for(j=1; j<i; j++)      (s[i] = t[i]);
       s1+=exp(ps[i][j]);      if (t[i]== '\\') s[i]='/';
     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++)  char *trimbb(char *out, char *in)
       ps[i][j]= exp(ps[i][j])*ps[i][i];  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
     for(j=i+1; j<=nlstate+ndeath; j++)    char *s;
       ps[i][j]= exp(ps[i][j])*ps[i][i];    s=out;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    while (*in != '\0'){
   } /* end i */      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
         in++;
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      }
     for(jj=1; jj<= nlstate+ndeath; jj++){      *out++ = *in++;
       ps[ii][jj]=0;    }
       ps[ii][ii]=1;    *out='\0';
     }    return s;
   }  }
   
   char *cutl(char *blocc, char *alocc, char *in, char occ)
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  {
     for(jj=1; jj<= nlstate+ndeath; jj++){    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
      printf("%lf ",ps[ii][jj]);       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
    }       gives blocc="abcdef2ghi" and alocc="j".
     printf("\n ");       If occ is not found blocc is null and alocc is equal to in. Returns blocc
     }    */
     printf("\n ");printf("%lf ",cov[2]);*/    char *s, *t, *bl;
 /*    t=in;s=in;
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    while ((*in != occ) && (*in != '\0')){
   goto end;*/      *alocc++ = *in++;
     return ps;    }
 }    if( *in == occ){
       *(alocc)='\0';
 /**************** Product of 2 matrices ******************/      s=++in;
     }
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)   
 {    if (s == t) {/* occ not found */
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times      *(alocc-(in-s))='\0';
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */      in=s;
   /* in, b, out are matrice of pointers which should have been initialized    }
      before: only the contents of out is modified. The function returns    while ( *in != '\0'){
      a pointer to pointers identical to out */      *blocc++ = *in++;
   long i, j, k;    }
   for(i=nrl; i<= nrh; i++)  
     for(k=ncolol; k<=ncoloh; k++)    *blocc='\0';
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    return t;
         out[i][k] +=in[i][j]*b[j][k];  }
   char *cutv(char *blocc, char *alocc, char *in, char occ)
   return out;  {
 }    /* 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".
 /************* Higher Matrix Product ***************/       If occ is not found blocc is null and alocc is equal to in. Returns alocc
     */
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    char *s, *t;
 {    t=in;s=in;
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    while (*in != '\0'){
      duration (i.e. until      while( *in == occ){
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.        *blocc++ = *in++;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step        s=in;
      (typically every 2 years instead of every month which is too big).      }
      Model is determined by parameters x and covariates have to be      *blocc++ = *in++;
      included manually here.    }
     if (s == t) /* occ not found */
      */      *(blocc-(in-s))='\0';
     else
   int i, j, d, h, k;      *(blocc-(in-s)-1)='\0';
   double **out, cov[NCOVMAX];    in=s;
   double **newm;    while ( *in != '\0'){
       *alocc++ = *in++;
   /* Hstepm could be zero and should return the unit matrix */    }
   for (i=1;i<=nlstate+ndeath;i++)  
     for (j=1;j<=nlstate+ndeath;j++){    *alocc='\0';
       oldm[i][j]=(i==j ? 1.0 : 0.0);    return s;
       po[i][j][0]=(i==j ? 1.0 : 0.0);  }
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  int nbocc(char *s, char occ)
   for(h=1; h <=nhstepm; h++){  {
     for(d=1; d <=hstepm; d++){    int i,j=0;
       newm=savm;    int lg=20;
       /* Covariates have to be included here again */    i=0;
       cov[1]=1.;    lg=strlen(s);
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    for(i=0; i<= lg; i++) {
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    if  (s[i] == occ ) j++;
       for (k=1; k<=cptcovage;k++)    }
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    return j;
       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]]];  
   /* void cutv(char *u,char *v, char*t, char occ) */
   /* { */
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  /*      gives u="abcdef2ghi" and v="j" *\/ */
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  /*   int i,lg,j,p=0; */
       savm=oldm;  /*   i=0; */
       oldm=newm;  /*   lg=strlen(t); */
     }  /*   for(j=0; j<=lg-1; j++) { */
     for(i=1; i<=nlstate+ndeath; i++)  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
       for(j=1;j<=nlstate+ndeath;j++) {  /*   } */
         po[i][j][h]=newm[i][j];  
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  /*   for(j=0; j<p; j++) { */
          */  /*     (u[j] = t[j]); */
       }  /*   } */
   } /* end h */  /*      u[p]='\0'; */
   return po;  
 }  /*    for(j=0; j<= lg; j++) { */
   /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
   /*   } */
 /*************** log-likelihood *************/  /* } */
 double func( double *x)  
 {  /********************** nrerror ********************/
   int i, ii, j, k, mi, d, kk;  
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  void nrerror(char error_text[])
   double **out;  {
   double sw; /* Sum of weights */    fprintf(stderr,"ERREUR ...\n");
   double lli; /* Individual log likelihood */    fprintf(stderr,"%s\n",error_text);
   long ipmx;    exit(EXIT_FAILURE);
   /*extern weight */  }
   /* We are differentiating ll according to initial status */  /*********************** vector *******************/
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  double *vector(int nl, int nh)
   /*for(i=1;i<imx;i++)  {
     printf(" %d\n",s[4][i]);    double *v;
   */    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
   cov[1]=1.;    if (!v) nrerror("allocation failure in vector");
     return v-nl+NR_END;
   for(k=1; k<=nlstate; k++) ll[k]=0.;  }
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){  
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];  /************************ free vector ******************/
     for(mi=1; mi<= wav[i]-1; mi++){  void free_vector(double*v, int nl, int nh)
       for (ii=1;ii<=nlstate+ndeath;ii++)  {
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    free((FREE_ARG)(v+nl-NR_END));
       for(d=0; d<dh[mi][i]; d++){  }
         newm=savm;  
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  /************************ivector *******************************/
         for (kk=1; kk<=cptcovage;kk++) {  int *ivector(long nl,long nh)
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];  {
         }    int *v;
            v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    if (!v) nrerror("allocation failure in ivector");
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    return v-nl+NR_END;
         savm=oldm;  }
         oldm=newm;  
          /******************free ivector **************************/
          void free_ivector(int *v, long nl, long nh)
       } /* end mult */  {
          free((FREE_ARG)(v+nl-NR_END));
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  }
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  
       ipmx +=1;  /************************lvector *******************************/
       sw += weight[i];  long *lvector(long nl,long nh)
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  {
     } /* end of wave */    long *v;
   } /* end of individual */    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     if (!v) nrerror("allocation failure in ivector");
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    return v-nl+NR_END;
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  }
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  
   return -l;  /******************free lvector **************************/
 }  void free_lvector(long *v, long nl, long nh)
   {
     free((FREE_ARG)(v+nl-NR_END));
 /*********** Maximum Likelihood Estimation ***************/  }
   
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  /******************* imatrix *******************************/
 {  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   int i,j, iter;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   double **xi,*delti;  { 
   double fret;    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   xi=matrix(1,npar,1,npar);    int **m; 
   for (i=1;i<=npar;i++)    
     for (j=1;j<=npar;j++)    /* allocate pointers to rows */ 
       xi[i][j]=(i==j ? 1.0 : 0.0);    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
   printf("Powell\n");    if (!m) nrerror("allocation failure 1 in matrix()"); 
   powell(p,xi,npar,ftol,&iter,&fret,func);    m += NR_END; 
     m -= nrl; 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    
     /* allocate rows and set pointers to them */ 
 }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 /**** Computes Hessian and covariance matrix ***/    m[nrl] += NR_END; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    m[nrl] -= ncl; 
 {    
   double  **a,**y,*x,pd;    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   double **hess;    
   int i, j,jk;    /* return pointer to array of pointers to rows */ 
   int *indx;    return m; 
   } 
   double hessii(double p[], double delta, int theta, double delti[]);  
   double hessij(double p[], double delti[], int i, int j);  /****************** free_imatrix *************************/
   void lubksb(double **a, int npar, int *indx, double b[]) ;  void free_imatrix(m,nrl,nrh,ncl,nch)
   void ludcmp(double **a, int npar, int *indx, double *d) ;        int **m;
         long nch,ncl,nrh,nrl; 
   hess=matrix(1,npar,1,npar);       /* free an int matrix allocated by imatrix() */ 
   { 
   printf("\nCalculation of the hessian matrix. Wait...\n");    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   for (i=1;i<=npar;i++){    free((FREE_ARG) (m+nrl-NR_END)); 
     printf("%d",i);fflush(stdout);  } 
     hess[i][i]=hessii(p,ftolhess,i,delti);  
     /*printf(" %f ",p[i]);*/  /******************* matrix *******************************/
     /*printf(" %lf ",hess[i][i]);*/  double **matrix(long nrl, long nrh, long ncl, long nch)
   }  {
      long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   for (i=1;i<=npar;i++) {    double **m;
     for (j=1;j<=npar;j++)  {  
       if (j>i) {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         printf(".%d%d",i,j);fflush(stdout);    if (!m) nrerror("allocation failure 1 in matrix()");
         hess[i][j]=hessij(p,delti,i,j);    m += NR_END;
         hess[j][i]=hess[i][j];        m -= nrl;
         /*printf(" %lf ",hess[i][j]);*/  
       }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   }    m[nrl] += NR_END;
   printf("\n");    m[nrl] -= ncl;
   
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
      return m;
   a=matrix(1,npar,1,npar);    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
   y=matrix(1,npar,1,npar);  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
   x=vector(1,npar);  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
   indx=ivector(1,npar);     */
   for (i=1;i<=npar;i++)  }
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  
   ludcmp(a,npar,indx,&pd);  /*************************free matrix ************************/
   void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   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];  /******************* ma3x *******************************/
     }  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   }  {
     long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+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");  
     m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   for (j=1;j<=npar;j++) {    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     for (i=1;i<=npar;i++) x[i]=0;    m[nrl][ncl] += NR_END;
     x[j]=1;    m[nrl][ncl] -= nll;
     lubksb(a,npar,indx,x);    for (j=ncl+1; j<=nch; j++) 
     for (i=1;i<=npar;i++){      m[nrl][j]=m[nrl][j-1]+nlay;
       y[i][j]=x[i];    
       printf("%.3e ",y[i][j]);    for (i=nrl+1; i<=nrh; i++) {
     }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     printf("\n");      for (j=ncl+1; j<=nch; j++) 
   }        m[i][j]=m[i][j-1]+nlay;
   */    }
     return m; 
   free_matrix(a,1,npar,1,npar);    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   free_matrix(y,1,npar,1,npar);             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   free_vector(x,1,npar);    */
   free_ivector(indx,1,npar);  }
   free_matrix(hess,1,npar,1,npar);  
   /*************************free ma3x ************************/
   void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
 }  {
     free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
 /*************** hessian matrix ****************/    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 double hessii( double x[], double delta, int theta, double delti[])    free((FREE_ARG)(m+nrl-NR_END));
 {  }
   int i;  
   int l=1, lmax=20;  /*************** function subdirf ***********/
   double k1,k2;  char *subdirf(char fileres[])
   double p2[NPARMAX+1];  {
   double res;    /* Caution optionfilefiname is hidden */
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    strcpy(tmpout,optionfilefiname);
   double fx;    strcat(tmpout,"/"); /* Add to the right */
   int k=0,kmax=10;    strcat(tmpout,fileres);
   double l1;    return tmpout;
   }
   fx=func(x);  
   for (i=1;i<=npar;i++) p2[i]=x[i];  /*************** function subdirf2 ***********/
   for(l=0 ; l <=lmax; l++){  char *subdirf2(char fileres[], char *preop)
     l1=pow(10,l);  {
     delts=delt;    
     for(k=1 ; k <kmax; k=k+1){    /* Caution optionfilefiname is hidden */
       delt = delta*(l1*k);    strcpy(tmpout,optionfilefiname);
       p2[theta]=x[theta] +delt;    strcat(tmpout,"/");
       k1=func(p2)-fx;    strcat(tmpout,preop);
       p2[theta]=x[theta]-delt;    strcat(tmpout,fileres);
       k2=func(p2)-fx;    return tmpout;
       /*res= (k1-2.0*fx+k2)/delt/delt; */  }
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  
        /*************** function subdirf3 ***********/
 #ifdef DEBUG  char *subdirf3(char fileres[], char *preop, char *preop2)
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);  {
 #endif    
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    /* Caution optionfilefiname is hidden */
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    strcpy(tmpout,optionfilefiname);
         k=kmax;    strcat(tmpout,"/");
       }    strcat(tmpout,preop);
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    strcat(tmpout,preop2);
         k=kmax; l=lmax*10.;    strcat(tmpout,fileres);
       }    return tmpout;
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  }
         delts=delt;  
       }  /***************** f1dim *************************/
     }  extern int ncom; 
   }  extern double *pcom,*xicom;
   delti[theta]=delts;  extern double (*nrfunc)(double []); 
   return res;   
    double f1dim(double x) 
 }  { 
     int j; 
 double hessij( double x[], double delti[], int thetai,int thetaj)    double f;
 {    double *xt; 
   int i;   
   int l=1, l1, lmax=20;    xt=vector(1,ncom); 
   double k1,k2,k3,k4,res,fx;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   double p2[NPARMAX+1];    f=(*nrfunc)(xt); 
   int k;    free_vector(xt,1,ncom); 
     return f; 
   fx=func(x);  } 
   for (k=1; k<=2; k++) {  
     for (i=1;i<=npar;i++) p2[i]=x[i];  /*****************brent *************************/
     p2[thetai]=x[thetai]+delti[thetai]/k;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;  { 
     k1=func(p2)-fx;    int iter; 
      double a,b,d,etemp;
     p2[thetai]=x[thetai]+delti[thetai]/k;    double fu,fv,fw,fx;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    double ftemp;
     k2=func(p2)-fx;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
      double e=0.0; 
     p2[thetai]=x[thetai]-delti[thetai]/k;   
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    a=(ax < cx ? ax : cx); 
     k3=func(p2)-fx;    b=(ax > cx ? ax : cx); 
      x=w=v=bx; 
     p2[thetai]=x[thetai]-delti[thetai]/k;    fw=fv=fx=(*f)(x); 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    for (iter=1;iter<=ITMAX;iter++) { 
     k4=func(p2)-fx;      xm=0.5*(a+b); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
 #ifdef DEBUG      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
     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);      printf(".");fflush(stdout);
 #endif      fprintf(ficlog,".");fflush(ficlog);
   }  #ifdef DEBUG
   return res;      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
 }      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
       /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
 /************** Inverse of matrix **************/  #endif
 void ludcmp(double **a, int n, int *indx, double *d)      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
 {        *xmin=x; 
   int i,imax,j,k;        return fx; 
   double big,dum,sum,temp;      } 
   double *vv;      ftemp=fu;
        if (fabs(e) > tol1) { 
   vv=vector(1,n);        r=(x-w)*(fx-fv); 
   *d=1.0;        q=(x-v)*(fx-fw); 
   for (i=1;i<=n;i++) {        p=(x-v)*q-(x-w)*r; 
     big=0.0;        q=2.0*(q-r); 
     for (j=1;j<=n;j++)        if (q > 0.0) p = -p; 
       if ((temp=fabs(a[i][j])) > big) big=temp;        q=fabs(q); 
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");        etemp=e; 
     vv[i]=1.0/big;        e=d; 
   }        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   for (j=1;j<=n;j++) {          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
     for (i=1;i<j;i++) {        else { 
       sum=a[i][j];          d=p/q; 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          u=x+d; 
       a[i][j]=sum;          if (u-a < tol2 || b-u < tol2) 
     }            d=SIGN(tol1,xm-x); 
     big=0.0;        } 
     for (i=j;i<=n;i++) {      } else { 
       sum=a[i][j];        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       for (k=1;k<j;k++)      } 
         sum -= a[i][k]*a[k][j];      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       a[i][j]=sum;      fu=(*f)(u); 
       if ( (dum=vv[i]*fabs(sum)) >= big) {      if (fu <= fx) { 
         big=dum;        if (u >= x) a=x; else b=x; 
         imax=i;        SHFT(v,w,x,u) 
       }          SHFT(fv,fw,fx,fu) 
     }          } else { 
     if (j != imax) {            if (u < x) a=u; else b=u; 
       for (k=1;k<=n;k++) {            if (fu <= fw || w == x) { 
         dum=a[imax][k];              v=w; 
         a[imax][k]=a[j][k];              w=u; 
         a[j][k]=dum;              fv=fw; 
       }              fw=fu; 
       *d = -(*d);            } else if (fu <= fv || v == x || v == w) { 
       vv[imax]=vv[j];              v=u; 
     }              fv=fu; 
     indx[j]=imax;            } 
     if (a[j][j] == 0.0) a[j][j]=TINY;          } 
     if (j != n) {    } 
       dum=1.0/(a[j][j]);    nrerror("Too many iterations in brent"); 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    *xmin=x; 
     }    return fx; 
   }  } 
   free_vector(vv,1,n);  /* Doesn't work */  
 ;  /****************** mnbrak ***********************/
 }  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
 void lubksb(double **a, int n, int *indx, double b[])              double (*func)(double)) 
 {  { 
   int i,ii=0,ip,j;    double ulim,u,r,q, dum;
   double sum;    double fu; 
     
   for (i=1;i<=n;i++) {    *fa=(*func)(*ax); 
     ip=indx[i];    *fb=(*func)(*bx); 
     sum=b[ip];    if (*fb > *fa) { 
     b[ip]=b[i];      SHFT(dum,*ax,*bx,dum) 
     if (ii)        SHFT(dum,*fb,*fa,dum) 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        } 
     else if (sum) ii=i;    *cx=(*bx)+GOLD*(*bx-*ax); 
     b[i]=sum;    *fc=(*func)(*cx); 
   }    while (*fb > *fc) { 
   for (i=n;i>=1;i--) {      r=(*bx-*ax)*(*fb-*fc); 
     sum=b[i];      q=(*bx-*cx)*(*fb-*fa); 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     b[i]=sum/a[i][i];        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   }      ulim=(*bx)+GLIMIT*(*cx-*bx); 
 }      if ((*bx-u)*(u-*cx) > 0.0) { 
         fu=(*func)(u); 
 /************ Frequencies ********************/      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax, int fprev1,int lprev1)        fu=(*func)(u); 
 {  /* Some frequencies */        if (fu < *fc) { 
            SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;            SHFT(*fb,*fc,fu,(*func)(u)) 
   double ***freq; /* Frequencies */            } 
   double *pp;      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   double pos;        u=ulim; 
   FILE *ficresp;        fu=(*func)(u); 
   char fileresp[FILENAMELENGTH];      } else { 
         u=(*cx)+GOLD*(*cx-*bx); 
   pp=vector(1,nlstate);        fu=(*func)(u); 
  probs= ma3x(1,130 ,1,8, 1,8);      } 
   strcpy(fileresp,"p");      SHFT(*ax,*bx,*cx,u) 
   strcat(fileresp,fileres);        SHFT(*fa,*fb,*fc,fu) 
   if((ficresp=fopen(fileresp,"w"))==NULL) {        } 
     printf("Problem with prevalence resultfile: %s\n", fileresp);  } 
     exit(0);  
   }  /*************** linmin ************************/
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  
   j1=0;  int ncom; 
   double *pcom,*xicom;
   j=cptcoveff;  double (*nrfunc)(double []); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}   
   void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   for(k1=1; k1<=j;k1++){  { 
    for(i1=1; i1<=ncodemax[k1];i1++){    double brent(double ax, double bx, double cx, 
        j1++;                 double (*f)(double), double tol, double *xmin); 
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);    double f1dim(double x); 
          scanf("%d", i);*/    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
         for (i=-1; i<=nlstate+ndeath; i++)                  double *fc, double (*func)(double)); 
          for (jk=-1; jk<=nlstate+ndeath; jk++)      int j; 
            for(m=agemin; m <= agemax+3; m++)    double xx,xmin,bx,ax; 
              freq[i][jk][m]=0;    double fx,fb,fa;
           
        for (i=1; i<=imx; i++) {    ncom=n; 
          bool=1;    pcom=vector(1,n); 
          if  (cptcovn>0) {    xicom=vector(1,n); 
            for (z1=1; z1<=cptcoveff; z1++)    nrfunc=func; 
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])    for (j=1;j<=n;j++) { 
                bool=0;      pcom[j]=p[j]; 
          }      xicom[j]=xi[j]; 
           if (bool==1) {    } 
            for(m=fprev1; m<=lprev1; m++){    ax=0.0; 
              if(agev[m][i]==0) agev[m][i]=agemax+1;    xx=1.0; 
              if(agev[m][i]==1) agev[m][i]=agemax+2;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  #ifdef DEBUG
            }    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
          }    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
        }  #endif
         if  (cptcovn>0) {    for (j=1;j<=n;j++) { 
          fprintf(ficresp, "\n#********** Variable ");      xi[j] *= xmin; 
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      p[j] += xi[j]; 
        fprintf(ficresp, "**********\n#");    } 
         }    free_vector(xicom,1,n); 
        for(i=1; i<=nlstate;i++)    free_vector(pcom,1,n); 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);  } 
        fprintf(ficresp, "\n");  
          char *asc_diff_time(long time_sec, char ascdiff[])
   for(i=(int)agemin; i <= (int)agemax+3; i++){  {
     if(i==(int)agemax+3)    long sec_left, days, hours, minutes;
       printf("Total");    days = (time_sec) / (60*60*24);
     else    sec_left = (time_sec) % (60*60*24);
       printf("Age %d", i);    hours = (sec_left) / (60*60) ;
     for(jk=1; jk <=nlstate ; jk++){    sec_left = (sec_left) %(60*60);
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    minutes = (sec_left) /60;
         pp[jk] += freq[jk][m][i];    sec_left = (sec_left) % (60);
     }    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
     for(jk=1; jk <=nlstate ; jk++){    return ascdiff;
       for(m=-1, pos=0; m <=0 ; m++)  }
         pos += freq[jk][m][i];  
       if(pp[jk]>=1.e-10)  /*************** powell ************************/
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       else              double (*func)(double [])) 
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);  { 
     }    void linmin(double p[], double xi[], int n, double *fret, 
                 double (*func)(double [])); 
      for(jk=1; jk <=nlstate ; jk++){    int i,ibig,j; 
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    double del,t,*pt,*ptt,*xit;
         pp[jk] += freq[jk][m][i];    double fp,fptt;
      }    double *xits;
     int niterf, itmp;
     for(jk=1,pos=0; jk <=nlstate ; jk++)  
       pos += pp[jk];    pt=vector(1,n); 
     for(jk=1; jk <=nlstate ; jk++){    ptt=vector(1,n); 
       if(pos>=1.e-5)    xit=vector(1,n); 
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    xits=vector(1,n); 
       else    *fret=(*func)(p); 
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    for (j=1;j<=n;j++) pt[j]=p[j]; 
       if( i <= (int) agemax){    for (*iter=1;;++(*iter)) { 
         if(pos>=1.e-5){      fp=(*fret); 
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);      ibig=0; 
           probs[i][jk][j1]= pp[jk]/pos;      del=0.0; 
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/      last_time=curr_time;
         }      (void) gettimeofday(&curr_time,&tzp);
       else      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
       }  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
     }     for (i=1;i<=n;i++) {
     for(jk=-1; jk <=nlstate+ndeath; jk++)        printf(" %d %.12f",i, p[i]);
       for(m=-1; m <=nlstate+ndeath; m++)        fprintf(ficlog," %d %.12lf",i, p[i]);
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);        fprintf(ficrespow," %.12lf", p[i]);
     if(i <= (int) agemax)      }
       fprintf(ficresp,"\n");      printf("\n");
     printf("\n");      fprintf(ficlog,"\n");
     }      fprintf(ficrespow,"\n");fflush(ficrespow);
     }      if(*iter <=3){
  }        tm = *localtime(&curr_time.tv_sec);
          strcpy(strcurr,asctime(&tm));
   fclose(ficresp);  /*       asctime_r(&tm,strcurr); */
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        forecast_time=curr_time; 
   free_vector(pp,1,nlstate);        itmp = strlen(strcurr);
         if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
 }  /* End of Freq */          strcurr[itmp-1]='\0';
         printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 /************ Prevalence ********************/        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 void prevalence(int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax, int fprev1,int lprev1)        for(niterf=10;niterf<=30;niterf+=10){
 {  /* Some frequencies */          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
            tmf = *localtime(&forecast_time.tv_sec);
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  /*      asctime_r(&tmf,strfor); */
   double ***freq; /* Frequencies */          strcpy(strfor,asctime(&tmf));
   double *pp;          itmp = strlen(strfor);
   double pos;          if(strfor[itmp-1]=='\n')
           strfor[itmp-1]='\0';
   pp=vector(1,nlstate);          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   probs= ma3x(1,130 ,1,8, 1,8);          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
          }
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      }
   j1=0;      for (i=1;i<=n;i++) { 
          for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   j=cptcoveff;        fptt=(*fret); 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  #ifdef DEBUG
          printf("fret=%lf \n",*fret);
  for(k1=1; k1<=j;k1++){        fprintf(ficlog,"fret=%lf \n",*fret);
     for(i1=1; i1<=ncodemax[k1];i1++){  #endif
       j1++;        printf("%d",i);fflush(stdout);
          fprintf(ficlog,"%d",i);fflush(ficlog);
       for (i=-1; i<=nlstate+ndeath; i++)          linmin(p,xit,n,fret,func); 
         for (jk=-1; jk<=nlstate+ndeath; jk++)          if (fabs(fptt-(*fret)) > del) { 
           for(m=agemin; m <= agemax+3; m++)          del=fabs(fptt-(*fret)); 
           freq[i][jk][m]=0;          ibig=i; 
              } 
       for (i=1; i<=imx; i++) {  #ifdef DEBUG
         bool=1;        printf("%d %.12e",i,(*fret));
         if  (cptcovn>0) {        fprintf(ficlog,"%d %.12e",i,(*fret));
           for (z1=1; z1<=cptcoveff; z1++)        for (j=1;j<=n;j++) {
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
               bool=0;          printf(" x(%d)=%.12e",j,xit[j]);
               }          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         if (bool==1) {        }
           for(m=fprev1; m<=lprev1; m++){        for(j=1;j<=n;j++) {
             if(agev[m][i]==0) agev[m][i]=agemax+1;          printf(" p=%.12e",p[j]);
             if(agev[m][i]==1) agev[m][i]=agemax+2;          fprintf(ficlog," p=%.12e",p[j]);
             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];        printf("\n");
           }        fprintf(ficlog,"\n");
         }  #endif
       }      } 
        for(i=(int)agemin; i <= (int)agemax+3; i++){      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
         for(jk=1; jk <=nlstate ; jk++){  #ifdef DEBUG
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        int k[2],l;
             pp[jk] += freq[jk][m][i];        k[0]=1;
         }        k[1]=-1;
         for(jk=1; jk <=nlstate ; jk++){        printf("Max: %.12e",(*func)(p));
           for(m=-1, pos=0; m <=0 ; m++)        fprintf(ficlog,"Max: %.12e",(*func)(p));
             pos += freq[jk][m][i];        for (j=1;j<=n;j++) {
         }          printf(" %.12e",p[j]);
                  fprintf(ficlog," %.12e",p[j]);
          for(jk=1; jk <=nlstate ; jk++){        }
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        printf("\n");
              pp[jk] += freq[jk][m][i];        fprintf(ficlog,"\n");
          }        for(l=0;l<=1;l++) {
                    for (j=1;j<=n;j++) {
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
             printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
          for(jk=1; jk <=nlstate ; jk++){                      fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
            if( i <= (int) agemax){          }
              if(pos>=1.e-5){          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                probs[i][jk][j1]= pp[jk]/pos;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
              }        }
            }  #endif
          }  
            
          }        free_vector(xit,1,n); 
     }        free_vector(xits,1,n); 
   }        free_vector(ptt,1,n); 
          free_vector(pt,1,n); 
          return; 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      } 
   free_vector(pp,1,nlstate);      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
        for (j=1;j<=n;j++) { 
 }  /* End of Freq */        ptt[j]=2.0*p[j]-pt[j]; 
 /************* Waves Concatenation ***************/        xit[j]=p[j]-pt[j]; 
         pt[j]=p[j]; 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)      } 
 {      fptt=(*func)(ptt); 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.      if (fptt < fp) { 
      Death is a valid wave (if date is known).        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        if (t < 0.0) { 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          linmin(p,xit,n,fret,func); 
      and mw[mi+1][i]. dh depends on stepm.          for (j=1;j<=n;j++) { 
      */            xi[j][ibig]=xi[j][n]; 
             xi[j][n]=xit[j]; 
   int i, mi, m;          }
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  #ifdef DEBUG
      double sum=0., jmean=0.;*/          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
           fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   int j, k=0,jk, ju, jl;          for(j=1;j<=n;j++){
   double sum=0.;            printf(" %.12e",xit[j]);
   jmin=1e+5;            fprintf(ficlog," %.12e",xit[j]);
   jmax=-1;          }
   jmean=0.;          printf("\n");
   for(i=1; i<=imx; i++){          fprintf(ficlog,"\n");
     mi=0;  #endif
     m=firstpass;        }
     while(s[m][i] <= nlstate){      } 
       if(s[m][i]>=1)    } 
         mw[++mi][i]=m;  } 
       if(m >=lastpass)  
         break;  /**** Prevalence limit (stable or period prevalence)  ****************/
       else  
         m++;  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
     }/* end while */  {
     if (s[m][i] > nlstate){    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
       mi++;     /* Death is another wave */       matrix by transitions matrix until convergence is reached */
       /* if(mi==0)  never been interviewed correctly before death */  
          /* Only death is a correct wave */    int i, ii,j,k;
       mw[mi][i]=m;    double min, max, maxmin, maxmax,sumnew=0.;
     }    /* double **matprod2(); */ /* test */
     double **out, cov[NCOVMAX+1], **pmij();
     wav[i]=mi;    double **newm;
     if(mi==0)    double agefin, delaymax=50 ; /* Max number of years to converge */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  
   }    for (ii=1;ii<=nlstate+ndeath;ii++)
       for (j=1;j<=nlstate+ndeath;j++){
   for(i=1; i<=imx; i++){        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(mi=1; mi<wav[i];mi++){      }
       if (stepm <=0)  
         dh[mi][i]=1;     cov[1]=1.;
       else{   
         if (s[mw[mi+1][i]][i] > nlstate) {   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           if (agedc[i] < 2*AGESUP) {    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);      newm=savm;
           if(j==0) j=1;  /* Survives at least one month after exam */      /* Covariates have to be included here again */
           k=k+1;      cov[2]=agefin;
           if (j >= jmax) jmax=j;      
           if (j <= jmin) jmin=j;      for (k=1; k<=cptcovn;k++) {
           sum=sum+j;        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           /* if (j<10) printf("j=%d num=%d ",j,i); */        /*printf("prevalim ij=%d k=%d Tvar[%d]=%d nbcode=%d cov=%lf codtab[%d][Tvar[%d]]=%d \n",ij,k, k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], ij, k, codtab[ij][Tvar[k]]);*/
           }      }
         }      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
         else{      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));      /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
           k=k+1;      
           if (j >= jmax) jmax=j;      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
           else if (j <= jmin)jmin=j;      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
           sum=sum+j;      /* 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 *\/ */
         jk= j/stepm;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
         jl= j -jk*stepm;      
         ju= j -(jk+1)*stepm;      savm=oldm;
         if(jl <= -ju)      oldm=newm;
           dh[mi][i]=jk;      maxmax=0.;
         else      for(j=1;j<=nlstate;j++){
           dh[mi][i]=jk+1;        min=1.;
         if(dh[mi][i]==0)        max=0.;
           dh[mi][i]=1; /* At least one step */        for(i=1; i<=nlstate; i++) {
       }          sumnew=0;
     }          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   }          prlim[i][j]= newm[i][j]/(1-sumnew);
   jmean=sum/k;          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          max=FMAX(max,prlim[i][j]);
  }          min=FMIN(min,prlim[i][j]);
 /*********** Tricode ****************************/        }
 void tricode(int *Tvar, int **nbcode, int imx)        maxmin=max-min;
 {        maxmax=FMAX(maxmax,maxmin);
   int Ndum[20],ij=1, k, j, i;      }
   int cptcode=0;      if(maxmax < ftolpl){
   cptcoveff=0;        return prlim;
        }
   for (k=0; k<19; k++) Ndum[k]=0;    }
   for (k=1; k<=7; k++) ncodemax[k]=0;  }
   
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {  /*************** transition probabilities ***************/ 
     for (i=1; i<=imx; i++) {  
       ij=(int)(covar[Tvar[j]][i]);  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
       Ndum[ij]++;  {
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/    /* According to parameters values stored in x and the covariate's values stored in cov,
       if (ij > cptcode) cptcode=ij;       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]
     for (i=0; i<=cptcode; i++) {       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
       if(Ndum[i]!=0) ncodemax[j]++;       ncth covariate in the global vector x is given by the formula:
     }       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
     ij=1;       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
        Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
        sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
     for (i=1; i<=ncodemax[j]; i++) {       Outputs ps[i][j] the probability to be observed in j being in j according to
       for (k=0; k<=19; k++) {       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
         if (Ndum[k] != 0) {    */
           nbcode[Tvar[j]][ij]=k;    double s1, lnpijopii;
           ij++;    /*double t34;*/
         }    int i,j,j1, nc, ii, jj;
         if (ij > ncodemax[j]) break;  
       }        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];*/
  for (k=0; k<19; k++) Ndum[k]=0;            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
  for (i=1; i<=ncovmodel-2; i++) {          }
       ij=Tvar[i];          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
       Ndum[ij]++;  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
     }        }
         for(j=i+1; j<=nlstate+ndeath;j++){
  ij=1;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
  for (i=1; i<=10; i++) {            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
    if((Ndum[i]!=0) && (i<=ncov)){            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
      Tvaraff[ij]=i;  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
      ij++;          }
    }          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
  }        }
        }
     cptcoveff=ij-1;      
 }      for(i=1; i<= nlstate; i++){
         s1=0;
 /*********** Health Expectancies ****************/        for(j=1; j<i; j++){
           s1+=exp(ps[i][j]); /* In fact sums pij/pii */
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
 {        }
   /* Health expectancies */        for(j=i+1; j<=nlstate+ndeath; j++){
   int i, j, nhstepm, hstepm, h;          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   double age, agelim,hf;          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
   double ***p3mat;        }
          /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
   fprintf(ficreseij,"# Health expectancies\n");        ps[i][i]=1./(s1+1.);
   fprintf(ficreseij,"# Age");        /* Computing other pijs */
   for(i=1; i<=nlstate;i++)        for(j=1; j<i; j++)
     for(j=1; j<=nlstate;j++)          ps[i][j]= exp(ps[i][j])*ps[i][i];
       fprintf(ficreseij," %1d-%1d",i,j);        for(j=i+1; j<=nlstate+ndeath; j++)
   fprintf(ficreseij,"\n");          ps[i][j]= exp(ps[i][j])*ps[i][i];
         /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   hstepm=1*YEARM; /*  Every j years of age (in month) */      } /* end i */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */      
       for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
   agelim=AGESUP;        for(jj=1; jj<= nlstate+ndeath; jj++){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          ps[ii][jj]=0;
     /* nhstepm age range expressed in number of stepm */          ps[ii][ii]=1;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);        }
     /* Typically if 20 years = 20*12/6=40 stepm */      }
     if (stepm >= YEARM) hstepm=1;      
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
     /* Computed by stepm unit matrices, product of hstepm matrices, stored      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);        /*   } */
       /*   printf("\n "); */
       /* } */
     for(i=1; i<=nlstate;i++)      /* printf("\n ");printf("%lf ",cov[2]);*/
       for(j=1; j<=nlstate;j++)      /*
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){        for(i=1; i<= npar; i++) printf("%f ",x[i]);
           eij[i][j][(int)age] +=p3mat[i][j][h];        goto end;*/
         }      return ps;
      }
     hf=1;  
     if (stepm >= YEARM) hf=stepm/YEARM;  /**************** Product of 2 matrices ******************/
     fprintf(ficreseij,"%.0f",age );  
     for(i=1; i<=nlstate;i++)  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
       for(j=1; j<=nlstate;j++){  {
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       }       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     fprintf(ficreseij,"\n");    /* in, b, out are matrice of pointers which should have been initialized 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       before: only the contents of out is modified. The function returns
   }       a pointer to pointers identical to out */
 }    int i, j, k;
     for(i=nrl; i<= nrh; i++)
 /************ Variance ******************/      for(k=ncolol; k<=ncoloh; k++){
 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)        out[i][k]=0.;
 {        for(j=ncl; j<=nch; j++)
   /* Variance of health expectancies */          out[i][k] +=in[i][j]*b[j][k];
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      }
   double **newm;    return out;
   double **dnewm,**doldm;  }
   int i, j, nhstepm, hstepm, h;  
   int k, cptcode;  
   double *xp;  /************* Higher Matrix Product ***************/
   double **gp, **gm;  
   double ***gradg, ***trgradg;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   double ***p3mat;  {
   double age,agelim;    /* Computes the transition matrix starting at age 'age' over 
   int theta;       'nhstepm*hstepm*stepm' months (i.e. until
        age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
    fprintf(ficresvij,"# Covariances of life expectancies\n");       nhstepm*hstepm matrices. 
   fprintf(ficresvij,"# Age");       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   for(i=1; i<=nlstate;i++)       (typically every 2 years instead of every month which is too big 
     for(j=1; j<=nlstate;j++)       for the memory).
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);       Model is determined by parameters x and covariates have to be 
   fprintf(ficresvij,"\n");       included manually here. 
   
   xp=vector(1,npar);       */
   dnewm=matrix(1,nlstate,1,npar);  
   doldm=matrix(1,nlstate,1,nlstate);    int i, j, d, h, k;
      double **out, cov[NCOVMAX+1];
   hstepm=1*YEARM; /* Every year of age */    double **newm;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;    /* Hstepm could be zero and should return the unit matrix */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    for (i=1;i<=nlstate+ndeath;i++)
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for (j=1;j<=nlstate+ndeath;j++){
     if (stepm >= YEARM) hstepm=1;        oldm[i][j]=(i==j ? 1.0 : 0.0);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        po[i][j][0]=(i==j ? 1.0 : 0.0);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      }
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     gp=matrix(0,nhstepm,1,nlstate);    for(h=1; h <=nhstepm; h++){
     gm=matrix(0,nhstepm,1,nlstate);      for(d=1; d <=hstepm; d++){
         newm=savm;
     for(theta=1; theta <=npar; theta++){        /* Covariates have to be included here again */
       for(i=1; i<=npar; i++){ /* Computes gradient */        cov[1]=1.;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
       }        for (k=1; k<=cptcovn;k++) 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        for (k=1; k<=cptcovage;k++)
           cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       if (popbased==1) {        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
         for(i=1; i<=nlstate;i++)          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           prlim[i][i]=probs[(int)age][i][ij];  
       }  
              /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
       for(j=1; j<= nlstate; j++){        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         for(h=0; h<=nhstepm; h++){        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)                     pmij(pmmij,cov,ncovmodel,x,nlstate));
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];        savm=oldm;
         }        oldm=newm;
       }      }
          for(i=1; i<=nlstate+ndeath; i++)
       for(i=1; i<=npar; i++) /* Computes gradient */        for(j=1;j<=nlstate+ndeath;j++) {
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          po[i][j][h]=newm[i][j];
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        }
       /*printf("h=%d ",h);*/
       if (popbased==1) {    } /* end h */
         for(i=1; i<=nlstate;i++)  /*     printf("\n H=%d \n",h); */
           prlim[i][i]=probs[(int)age][i][ij];    return po;
       }  }
   
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){  /*************** log-likelihood *************/
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  double func( double *x)
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];  {
         }    int i, ii, j, k, mi, d, kk;
       }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     double **out;
       for(j=1; j<= nlstate; j++)    double sw; /* Sum of weights */
         for(h=0; h<=nhstepm; h++){    double lli; /* Individual log likelihood */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    int s1, s2;
         }    double bbh, survp;
     } /* End theta */    long ipmx;
     /*extern weight */
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     for(h=0; h<=nhstepm; h++)    /*for(i=1;i<imx;i++) 
       for(j=1; j<=nlstate;j++)      printf(" %d\n",s[4][i]);
         for(theta=1; theta <=npar; theta++)    */
           trgradg[h][j][theta]=gradg[h][theta][j];    cov[1]=1.;
   
     for(i=1;i<=nlstate;i++)    for(k=1; k<=nlstate; k++) ll[k]=0.;
       for(j=1;j<=nlstate;j++)  
         vareij[i][j][(int)age] =0.;    if(mle==1){
     for(h=0;h<=nhstepm;h++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(k=0;k<=nhstepm;k++){        /* Computes the values of the ncovmodel covariates of the model
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
         for(i=1;i<=nlstate;i++)           to be observed in j being in i according to the model.
           for(j=1;j<=nlstate;j++)         */
             vareij[i][j][(int)age] += doldm[i][j];        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
       }          cov[2+k]=covar[Tvar[k]][i];
     }        }
     h=1;        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
     if (stepm >= YEARM) h=stepm/YEARM;           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
     fprintf(ficresvij,"%.0f ",age );           has been calculated etc */
     for(i=1; i<=nlstate;i++)        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j<=nlstate;j++){          for (ii=1;ii<=nlstate+ndeath;ii++)
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);            for (j=1;j<=nlstate+ndeath;j++){
       }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     fprintf(ficresvij,"\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(gp,0,nhstepm,1,nlstate);            }
     free_matrix(gm,0,nhstepm,1,nlstate);          for(d=0; d<dh[mi][i]; d++){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);            newm=savm;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            for (kk=1; kk<=cptcovage;kk++) {
   } /* End age */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
              }
   free_vector(xp,1,npar);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   free_matrix(doldm,1,nlstate,1,npar);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   free_matrix(dnewm,1,nlstate,1,nlstate);            savm=oldm;
             oldm=newm;
 }          } /* end mult */
         
 /************ Variance of prevlim ******************/          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
 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)          /* 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 
   /* Variance of prevalence limit */           * (in months) between two waves is not a multiple of stepm, we rounded to 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/           * the nearest (and in case of equal distance, to the lowest) interval but now
   double **newm;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   double **dnewm,**doldm;           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
   int i, j, nhstepm, hstepm;           * probability in order to take into account the bias as a fraction of the way
   int k, cptcode;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
   double *xp;           * -stepm/2 to stepm/2 .
   double *gp, *gm;           * For stepm=1 the results are the same as for previous versions of Imach.
   double **gradg, **trgradg;           * For stepm > 1 the results are less biased than in previous versions. 
   double age,agelim;           */
   int theta;          s1=s[mw[mi][i]][i];
              s2=s[mw[mi+1][i]][i];
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");          bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficresvpl,"# Age");          /* bias bh is positive if real duration
   for(i=1; i<=nlstate;i++)           * is higher than the multiple of stepm and negative otherwise.
       fprintf(ficresvpl," %1d-%1d",i,i);           */
   fprintf(ficresvpl,"\n");          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           if( s2 > nlstate){ 
   xp=vector(1,npar);            /* i.e. if s2 is a death state and if the date of death is known 
   dnewm=matrix(1,nlstate,1,npar);               then the contribution to the likelihood is the probability to 
   doldm=matrix(1,nlstate,1,nlstate);               die between last step unit time and current  step unit time, 
                 which is also equal to probability to die before dh 
   hstepm=1*YEARM; /* Every year of age */               minus probability to die before dh-stepm . 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */               In version up to 0.92 likelihood was computed
   agelim = AGESUP;          as if date of death was unknown. Death was treated as any other
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          health state: the date of the interview describes the actual state
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          and not the date of a change in health state. The former idea was
     if (stepm >= YEARM) hstepm=1;          to consider that at each interview the state was recorded
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          (healthy, disable or death) and IMaCh was corrected; but when we
     gradg=matrix(1,npar,1,nlstate);          introduced the exact date of death then we should have modified
     gp=vector(1,nlstate);          the contribution of an exact death to the likelihood. This new
     gm=vector(1,nlstate);          contribution is smaller and very dependent of the step unit
           stepm. It is no more the probability to die between last interview
     for(theta=1; theta <=npar; theta++){          and month of death but the probability to survive from last
       for(i=1; i<=npar; i++){ /* Computes gradient */          interview up to one month before death multiplied by the
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          probability to die within a month. Thanks to Chris
       }          Jackson for correcting this bug.  Former versions increased
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          mortality artificially. The bad side is that we add another loop
       for(i=1;i<=nlstate;i++)          which slows down the processing. The difference can be up to 10%
         gp[i] = prlim[i][i];          lower mortality.
                */
       for(i=1; i<=npar; i++) /* Computes gradient */            lli=log(out[s1][s2] - savm[s1][s2]);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);  
       for(i=1;i<=nlstate;i++)          } else if  (s2==-2) {
         gm[i] = prlim[i][i];            for (j=1,survp=0. ; j<=nlstate; j++) 
               survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       for(i=1;i<=nlstate;i++)            /*survp += out[s1][j]; */
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];            lli= log(survp);
     } /* End theta */          }
           
     trgradg =matrix(1,nlstate,1,npar);          else if  (s2==-4) { 
             for (j=3,survp=0. ; j<=nlstate; j++)  
     for(j=1; j<=nlstate;j++)              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       for(theta=1; theta <=npar; theta++)            lli= log(survp); 
         trgradg[j][theta]=gradg[theta][j];          } 
   
     for(i=1;i<=nlstate;i++)          else if  (s2==-5) { 
       varpl[i][(int)age] =0.;            for (j=1,survp=0. ; j<=2; j++)  
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);              survp += (1.+bbh)*out[s1][j]- bbh*savm[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{
     fprintf(ficresvpl,"%.0f ",age );            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     for(i=1; i<=nlstate;i++)            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));          } 
     fprintf(ficresvpl,"\n");          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     free_vector(gp,1,nlstate);          /*if(lli ==000.0)*/
     free_vector(gm,1,nlstate);          /*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); */
     free_matrix(gradg,1,npar,1,nlstate);          ipmx +=1;
     free_matrix(trgradg,1,nlstate,1,npar);          sw += weight[i];
   } /* End age */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
   free_vector(xp,1,npar);      } /* end of individual */
   free_matrix(doldm,1,nlstate,1,npar);    }  else if(mle==2){
   free_matrix(dnewm,1,nlstate,1,nlstate);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 }        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
 /************ Variance of one-step probabilities  ******************/            for (j=1;j<=nlstate+ndeath;j++){
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
 {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j;            }
   int k=0, cptcode;          for(d=0; d<=dh[mi][i]; d++){
   double **dnewm,**doldm;            newm=savm;
   double *xp;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double *gp, *gm;            for (kk=1; kk<=cptcovage;kk++) {
   double **gradg, **trgradg;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double age,agelim, cov[NCOVMAX];            }
   int theta;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   char fileresprob[FILENAMELENGTH];                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   strcpy(fileresprob,"prob");            oldm=newm;
   strcat(fileresprob,fileres);          } /* end mult */
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {        
     printf("Problem with resultfile: %s\n", fileresprob);          s1=s[mw[mi][i]][i];
   }          s2=s[mw[mi+1][i]][i];
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);          bbh=(double)bh[mi][i]/(double)stepm; 
            lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
           ipmx +=1;
   xp=vector(1,npar);          sw += weight[i];
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));        } /* end of wave */
        } /* end of individual */
   cov[1]=1;    }  else if(mle==3){  /* exponential inter-extrapolation */
   for (age=bage; age<=fage; age ++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     cov[2]=age;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     gradg=matrix(1,npar,1,9);        for(mi=1; mi<= wav[i]-1; mi++){
     trgradg=matrix(1,9,1,npar);          for (ii=1;ii<=nlstate+ndeath;ii++)
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));            for (j=1;j<=nlstate+ndeath;j++){
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                  savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(theta=1; theta <=npar; theta++){            }
       for(i=1; i<=npar; i++)          for(d=0; d<dh[mi][i]; d++){
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            newm=savm;
                  cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       pmij(pmmij,cov,ncovmodel,xp,nlstate);            for (kk=1; kk<=cptcovage;kk++) {
                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       k=0;            }
       for(i=1; i<= (nlstate+ndeath); i++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(j=1; j<=(nlstate+ndeath);j++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
            k=k+1;            savm=oldm;
           gp[k]=pmmij[i][j];            oldm=newm;
         }          } /* end mult */
       }        
           s1=s[mw[mi][i]][i];
       for(i=1; i<=npar; i++)          s2=s[mw[mi+1][i]][i];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          bbh=(double)bh[mi][i]/(double)stepm; 
              lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           ipmx +=1;
       pmij(pmmij,cov,ncovmodel,xp,nlstate);          sw += weight[i];
       k=0;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1; i<=(nlstate+ndeath); i++){        } /* end of wave */
         for(j=1; j<=(nlstate+ndeath);j++){      } /* end of individual */
           k=k+1;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
           gm[k]=pmmij[i][j];      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       }        for(mi=1; mi<= wav[i]-1; mi++){
                for (ii=1;ii<=nlstate+ndeath;ii++)
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)            for (j=1;j<=nlstate+ndeath;j++){
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)          for(d=0; d<dh[mi][i]; d++){
       for(theta=1; theta <=npar; theta++)            newm=savm;
       trgradg[j][theta]=gradg[theta][j];            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);            }
           
      pmij(pmmij,cov,ncovmodel,x,nlstate);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
      k=0;            savm=oldm;
      for(i=1; i<=(nlstate+ndeath); i++){            oldm=newm;
        for(j=1; j<=(nlstate+ndeath);j++){          } /* end mult */
          k=k+1;        
          gm[k]=pmmij[i][j];          s1=s[mw[mi][i]][i];
         }          s2=s[mw[mi+1][i]][i];
      }          if( s2 > nlstate){ 
                  lli=log(out[s1][s2] - savm[s1][s2]);
      /*printf("\n%d ",(int)age);          }else{
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
                  }
           ipmx +=1;
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));          sw += weight[i];
      }*/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   fprintf(ficresprob,"\n%d ",(int)age);        } /* end of wave */
       } /* end of individual */
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   }        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));            for (j=1;j<=nlstate+ndeath;j++){
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);            }
 }          for(d=0; d<dh[mi][i]; d++){
  free_vector(xp,1,npar);            newm=savm;
 fclose(ficresprob);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
  exit(0);            for (kk=1; kk<=cptcovage;kk++) {
 }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
 /***********************************************/          
 /**************** Main Program *****************/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
 /***********************************************/                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
 /*int main(int argc, char *argv[])*/            oldm=newm;
 int main()          } /* end mult */
 {        
           s1=s[mw[mi][i]][i];
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;          s2=s[mw[mi+1][i]][i];
   double agedeb, agefin,hf;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   double agemin=1.e20, agemax=-1.e20;          ipmx +=1;
           sw += weight[i];
   double fret;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **xi,tmp,delta;          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
         } /* end of wave */
   double dum; /* Dummy variable */      } /* end of individual */
   double ***p3mat;    } /* End of if */
   int *indx;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   char line[MAXLINE], linepar[MAXLINE];    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   char title[MAXLINE];    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    return -l;
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];  }
   char filerest[FILENAMELENGTH];  
   char fileregp[FILENAMELENGTH];  /*************** log-likelihood *************/
   char popfile[FILENAMELENGTH];  double funcone( double *x)
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];  {
   int firstobs=1, lastobs=10;    /* Same as likeli but slower because of a lot of printf and if */
   int sdeb, sfin; /* Status at beginning and end */    int i, ii, j, k, mi, d, kk;
   int c,  h , cpt,l;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   int ju,jl, mi;    double **out;
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    double lli; /* Individual log likelihood */
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    double llt;
   int mobilav=0, fprev, lprev ,fprevfore=1, lprevfore=1,nforecast,popforecast=0;    int s1, s2;
   int hstepm, nhstepm;    double bbh, survp;
   int *popage;    /*extern weight */
     /* We are differentiating ll according to initial status */
   double bage, fage, age, agelim, agebase;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   double ftolpl=FTOL;    /*for(i=1;i<imx;i++) 
   double **prlim;      printf(" %d\n",s[4][i]);
   double *severity;    */
   double ***param; /* Matrix of parameters */    cov[1]=1.;
   double  *p;  
   double **matcov; /* Matrix of covariance */    for(k=1; k<=nlstate; k++) ll[k]=0.;
   double ***delti3; /* Scale */  
   double *delti; /* Scale */    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***eij, ***vareij;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double **varpl; /* Variances of prevalence limits by age */      for(mi=1; mi<= wav[i]-1; mi++){
   double *epj, vepp;        for (ii=1;ii<=nlstate+ndeath;ii++)
   double kk1, kk2;          for (j=1;j<=nlstate+ndeath;j++){
   double *popeffectif,*popcount;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             savm[ii][j]=(ii==j ? 1.0 : 0.0);
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";          }
   char *alph[]={"a","a","b","c","d","e"}, str[4];        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   char z[1]="c", occ;          for (kk=1; kk<=cptcovage;kk++) {
 #include <sys/time.h>            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 #include <time.h>          }
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   /* long total_usecs;          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   struct timeval start_time, end_time;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
            /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
           savm=oldm;
           oldm=newm;
   printf("\nIMACH, Version 0.7");        } /* end mult */
   printf("\nEnter the parameter file name: ");        
         s1=s[mw[mi][i]][i];
 #ifdef windows        s2=s[mw[mi+1][i]][i];
   scanf("%s",pathtot);        bbh=(double)bh[mi][i]/(double)stepm; 
   getcwd(pathcd, size);        /* bias is positive if real duration
   /*cygwin_split_path(pathtot,path,optionfile);         * is higher than the multiple of stepm and negative otherwise.
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/         */
   /* cutv(path,optionfile,pathtot,'\\');*/        if( s2 > nlstate && (mle <5) ){  /* Jackson */
           lli=log(out[s1][s2] - savm[s1][s2]);
 split(pathtot, path,optionfile);        } else if  (s2==-2) {
   chdir(path);          for (j=1,survp=0. ; j<=nlstate; j++) 
   replace(pathc,path);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
 #endif          lli= log(survp);
 #ifdef unix        }else if (mle==1){
   scanf("%s",optionfile);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
 #endif        } else if(mle==2){
           lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
 /*-------- arguments in the command line --------*/        } else if(mle==3){  /* exponential inter-extrapolation */
           lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
   strcpy(fileres,"r");        } else if (mle==4){  /* mle=4 no inter-extrapolation */
   strcat(fileres, optionfile);          lli=log(out[s1][s2]); /* Original formula */
         } else{  /* mle=0 back to 1 */
   /*---------arguments file --------*/          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
           /*lli=log(out[s1][s2]); */ /* Original formula */
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        } /* End of if */
     printf("Problem with optionfile %s\n",optionfile);        ipmx +=1;
     goto end;        sw += weight[i];
   }        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   strcpy(filereso,"o");        if(globpr){
   strcat(filereso,fileres);          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   if((ficparo=fopen(filereso,"w"))==NULL) {   %11.6f %11.6f %11.6f ", \
     printf("Problem with Output resultfile: %s\n", filereso);goto end;                  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]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   /* Reads comments: lines beginning with '#' */            llt +=ll[k]*gipmx/gsw;
   while((c=getc(ficpar))=='#' && c!= EOF){            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
     ungetc(c,ficpar);          }
     fgets(line, MAXLINE, ficpar);          fprintf(ficresilk," %10.6f\n", -llt);
     puts(line);        }
     fputs(line,ficparo);      } /* end of wave */
   }    } /* end of individual */
   ungetc(c,ficpar);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   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);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   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);    if(globpr==0){ /* First time we count the contributions and weights */
   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);      gipmx=ipmx;
 while((c=getc(ficpar))=='#' && c!= EOF){      gsw=sw;
     ungetc(c,ficpar);    }
     fgets(line, MAXLINE, ficpar);    return -l;
     puts(line);  }
     fputs(line,ficparo);  
   }  
   ungetc(c,ficpar);  /*************** function likelione ***********/
    void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   fscanf(ficpar,"fprevalence=%d lprevalence=%d pop_based=%d\n",&fprev,&lprev,&popbased);  {
   fprintf(ficparo,"fprevalence=%d lprevalence=%d pop_based=%d\n",fprev,lprev,popbased);    /* This routine should help understanding what is done with 
         the selection of individuals/waves and
  while((c=getc(ficpar))=='#' && c!= EOF){       to check the exact contribution to the likelihood.
     ungetc(c,ficpar);       Plotting could be done.
     fgets(line, MAXLINE, ficpar);     */
     puts(line);    int k;
     fputs(line,ficparo);  
   }    if(*globpri !=0){ /* Just counts and sums, no printings */
   ungetc(c,ficpar);      strcpy(fileresilk,"ilk"); 
        strcat(fileresilk,fileres);
   fscanf(ficpar,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",&fprevfore,&lprevfore,&nforecast,&mobilav);      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
   fprintf(ficparo,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",fprevfore,lprevfore,nforecast,mobilav);        printf("Problem with resultfile: %s\n", fileresilk);
              fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
        }
 while((c=getc(ficpar))=='#' && c!= EOF){      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");
     ungetc(c,ficpar);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
     fgets(line, MAXLINE, ficpar);      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
     puts(line);      for(k=1; k<=nlstate; k++) 
     fputs(line,ficparo);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
   }      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   ungetc(c,ficpar);    }
    
   fscanf(ficpar,"popforecast=%d popfile=%s\n",&popforecast,popfile);    *fretone=(*funcone)(p);
      if(*globpri !=0){
   covar=matrix(0,NCOVMAX,1,n);      fclose(ficresilk);
   cptcovn=0;      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;      fflush(fichtm); 
     } 
   ncovmodel=2+cptcovn;    return;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */  }
    
   /* Read guess parameters */  
   /* Reads comments: lines beginning with '#' */  /*********** Maximum Likelihood Estimation ***************/
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     fgets(line, MAXLINE, ficpar);  {
     puts(line);    int i,j, iter;
     fputs(line,ficparo);    double **xi;
   }    double fret;
   ungetc(c,ficpar);    double fretone; /* Only one call to likelihood */
      /*  char filerespow[FILENAMELENGTH];*/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    xi=matrix(1,npar,1,npar);
     for(i=1; i <=nlstate; i++)    for (i=1;i<=npar;i++)
     for(j=1; j <=nlstate+ndeath-1; j++){      for (j=1;j<=npar;j++)
       fscanf(ficpar,"%1d%1d",&i1,&j1);        xi[i][j]=(i==j ? 1.0 : 0.0);
       fprintf(ficparo,"%1d%1d",i1,j1);    printf("Powell\n");  fprintf(ficlog,"Powell\n");
       printf("%1d%1d",i,j);    strcpy(filerespow,"pow"); 
       for(k=1; k<=ncovmodel;k++){    strcat(filerespow,fileres);
         fscanf(ficpar," %lf",&param[i][j][k]);    if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf(" %lf",param[i][j][k]);      printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficparo," %lf",param[i][j][k]);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }    }
       fscanf(ficpar,"\n");    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       printf("\n");    for (i=1;i<=nlstate;i++)
       fprintf(ficparo,"\n");      for(j=1;j<=nlstate+ndeath;j++)
     }        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
      fprintf(ficrespow,"\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  
     powell(p,xi,npar,ftol,&iter,&fret,func);
   p=param[1][1];  
      free_matrix(xi,1,npar,1,npar);
   /* Reads comments: lines beginning with '#' */    fclose(ficrespow);
   while((c=getc(ficpar))=='#' && c!= EOF){    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     ungetc(c,ficpar);    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     fgets(line, MAXLINE, ficpar);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     puts(line);  
     fputs(line,ficparo);  }
   }  
   ungetc(c,ficpar);  /**** Computes Hessian and covariance matrix ***/
   void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  {
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    double  **a,**y,*x,pd;
   for(i=1; i <=nlstate; i++){    double **hess;
     for(j=1; j <=nlstate+ndeath-1; j++){    int i, j,jk;
       fscanf(ficpar,"%1d%1d",&i1,&j1);    int *indx;
       printf("%1d%1d",i,j);  
       fprintf(ficparo,"%1d%1d",i1,j1);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
       for(k=1; k<=ncovmodel;k++){    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
         fscanf(ficpar,"%le",&delti3[i][j][k]);    void lubksb(double **a, int npar, int *indx, double b[]) ;
         printf(" %le",delti3[i][j][k]);    void ludcmp(double **a, int npar, int *indx, double *d) ;
         fprintf(ficparo," %le",delti3[i][j][k]);    double gompertz(double p[]);
       }    hess=matrix(1,npar,1,npar);
       fscanf(ficpar,"\n");  
       printf("\n");    printf("\nCalculation of the hessian matrix. Wait...\n");
       fprintf(ficparo,"\n");    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     }    for (i=1;i<=npar;i++){
   }      printf("%d",i);fflush(stdout);
   delti=delti3[1][1];      fprintf(ficlog,"%d",i);fflush(ficlog);
       
   /* Reads comments: lines beginning with '#' */       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){      
     ungetc(c,ficpar);      /*  printf(" %f ",p[i]);
     fgets(line, MAXLINE, ficpar);          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     puts(line);    }
     fputs(line,ficparo);    
   }    for (i=1;i<=npar;i++) {
   ungetc(c,ficpar);      for (j=1;j<=npar;j++)  {
          if (j>i) { 
   matcov=matrix(1,npar,1,npar);          printf(".%d%d",i,j);fflush(stdout);
   for(i=1; i <=npar; i++){          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
     fscanf(ficpar,"%s",&str);          hess[i][j]=hessij(p,delti,i,j,func,npar);
     printf("%s",str);          
     fprintf(ficparo,"%s",str);          hess[j][i]=hess[i][j];    
     for(j=1; j <=i; j++){          /*printf(" %lf ",hess[i][j]);*/
       fscanf(ficpar," %le",&matcov[i][j]);        }
       printf(" %.5le",matcov[i][j]);      }
       fprintf(ficparo," %.5le",matcov[i][j]);    }
     }    printf("\n");
     fscanf(ficpar,"\n");    fprintf(ficlog,"\n");
     printf("\n");  
     fprintf(ficparo,"\n");    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   }    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   for(i=1; i <=npar; i++)    
     for(j=i+1;j<=npar;j++)    a=matrix(1,npar,1,npar);
       matcov[i][j]=matcov[j][i];    y=matrix(1,npar,1,npar);
        x=vector(1,npar);
   printf("\n");    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     /*-------- data file ----------*/    ludcmp(a,npar,indx,&pd);
     if((ficres =fopen(fileres,"w"))==NULL) {  
       printf("Problem with resultfile: %s\n", fileres);goto end;    for (j=1;j<=npar;j++) {
     }      for (i=1;i<=npar;i++) x[i]=0;
     fprintf(ficres,"#%s\n",version);      x[j]=1;
          lubksb(a,npar,indx,x);
     if((fic=fopen(datafile,"r"))==NULL)    {      for (i=1;i<=npar;i++){ 
       printf("Problem with datafile: %s\n", datafile);goto end;        matcov[i][j]=x[i];
     }      }
     }
     n= lastobs;  
     severity = vector(1,maxwav);    printf("\n#Hessian matrix#\n");
     outcome=imatrix(1,maxwav+1,1,n);    fprintf(ficlog,"\n#Hessian matrix#\n");
     num=ivector(1,n);    for (i=1;i<=npar;i++) { 
     moisnais=vector(1,n);      for (j=1;j<=npar;j++) { 
     annais=vector(1,n);        printf("%.3e ",hess[i][j]);
     moisdc=vector(1,n);        fprintf(ficlog,"%.3e ",hess[i][j]);
     andc=vector(1,n);      }
     agedc=vector(1,n);      printf("\n");
     cod=ivector(1,n);      fprintf(ficlog,"\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);    /* Recompute Inverse */
     anint=matrix(1,maxwav,1,n);    for (i=1;i<=npar;i++)
     s=imatrix(1,maxwav+1,1,n);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     adl=imatrix(1,maxwav+1,1,n);        ludcmp(a,npar,indx,&pd);
     tab=ivector(1,NCOVMAX);  
     ncodemax=ivector(1,8);    /*  printf("\n#Hessian matrix recomputed#\n");
   
     i=1;    for (j=1;j<=npar;j++) {
     while (fgets(line, MAXLINE, fic) != NULL)    {      for (i=1;i<=npar;i++) x[i]=0;
       if ((i >= firstobs) && (i <=lastobs)) {      x[j]=1;
              lubksb(a,npar,indx,x);
         for (j=maxwav;j>=1;j--){      for (i=1;i<=npar;i++){ 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);        y[i][j]=x[i];
           strcpy(line,stra);        printf("%.3e ",y[i][j]);
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);        fprintf(ficlog,"%.3e ",y[i][j]);
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);      }
         }      printf("\n");
              fprintf(ficlog,"\n");
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    }
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    */
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    free_matrix(a,1,npar,1,npar);
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);    free_matrix(y,1,npar,1,npar);
     free_vector(x,1,npar);
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);    free_ivector(indx,1,npar);
         for (j=ncov;j>=1;j--){    free_matrix(hess,1,npar,1,npar);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);  
         }  
         num[i]=atol(stra);  }
          
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){  /*************** hessian matrix ****************/
           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;}*/  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   {
         i=i+1;    int i;
       }    int l=1, lmax=20;
     }    double k1,k2;
     /* printf("ii=%d", ij);    double p2[MAXPARM+1]; /* identical to x */
        scanf("%d",i);*/    double res;
   imx=i-1; /* Number of individuals */    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     double fx;
   /* for (i=1; i<=imx; i++){    int k=0,kmax=10;
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    double l1;
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;  
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    fx=func(x);
     }    for (i=1;i<=npar;i++) p2[i]=x[i];
     for (i=1; i<=imx; 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]));*/    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
       l1=pow(10,l);
   /* Calculation of the number of parameter from char model*/      delts=delt;
   Tvar=ivector(1,15);      for(k=1 ; k <kmax; k=k+1){
   Tprod=ivector(1,15);        delt = delta*(l1*k);
   Tvaraff=ivector(1,15);        p2[theta]=x[theta] +delt;
   Tvard=imatrix(1,15,1,2);        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
   Tage=ivector(1,15);              p2[theta]=x[theta]-delt;
            k2=func(p2)-fx;
   if (strlen(model) >1){        /*res= (k1-2.0*fx+k2)/delt/delt; */
     j=0, j1=0, k1=1, k2=1;        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     j=nbocc(model,'+');        
     j1=nbocc(model,'*');  #ifdef DEBUGHESS
     cptcovn=j+1;        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);
     cptcovprod=j1;        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
      #endif
            /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
     strcpy(modelsav,model);        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){          k=kmax;
       printf("Error. Non available option model=%s ",model);        }
       goto end;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     }          k=kmax; l=lmax*10.;
            }
     for(i=(j+1); i>=1;i--){        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       cutv(stra,strb,modelsav,'+');          delts=delt;
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);        }
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/      }
       /*scanf("%d",i);*/    }
       if (strchr(strb,'*')) {    delti[theta]=delts;
         cutv(strd,strc,strb,'*');    return res; 
         if (strcmp(strc,"age")==0) {    
           cptcovprod--;  }
           cutv(strb,stre,strd,'V');  
           Tvar[i]=atoi(stre);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
           cptcovage++;  {
             Tage[cptcovage]=i;    int i;
             /*printf("stre=%s ", stre);*/    int l=1, l1, lmax=20;
         }    double k1,k2,k3,k4,res,fx;
         else if (strcmp(strd,"age")==0) {    double p2[MAXPARM+1];
           cptcovprod--;    int k;
           cutv(strb,stre,strc,'V');  
           Tvar[i]=atoi(stre);    fx=func(x);
           cptcovage++;    for (k=1; k<=2; k++) {
           Tage[cptcovage]=i;      for (i=1;i<=npar;i++) p2[i]=x[i];
         }      p2[thetai]=x[thetai]+delti[thetai]/k;
         else {      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           cutv(strb,stre,strc,'V');      k1=func(p2)-fx;
           Tvar[i]=ncov+k1;    
           cutv(strb,strc,strd,'V');      p2[thetai]=x[thetai]+delti[thetai]/k;
           Tprod[k1]=i;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           Tvard[k1][1]=atoi(strc);      k2=func(p2)-fx;
           Tvard[k1][2]=atoi(stre);    
           Tvar[cptcovn+k2]=Tvard[k1][1];      p2[thetai]=x[thetai]-delti[thetai]/k;
           Tvar[cptcovn+k2+1]=Tvard[k1][2];      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           for (k=1; k<=lastobs;k++)      k3=func(p2)-fx;
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    
           k1++;      p2[thetai]=x[thetai]-delti[thetai]/k;
           k2=k2+2;      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
         }      k4=func(p2)-fx;
       }      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
       else {  #ifdef DEBUG
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/      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);
        /*  scanf("%d",i);*/      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);
       cutv(strd,strc,strb,'V');  #endif
       Tvar[i]=atoi(strc);    }
       }    return res;
       strcpy(modelsav,stra);    }
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);  
         scanf("%d",i);*/  /************** Inverse of matrix **************/
     }  void ludcmp(double **a, int n, int *indx, double *d) 
 }  { 
      int i,imax,j,k; 
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);    double big,dum,sum,temp; 
   printf("cptcovprod=%d ", cptcovprod);    double *vv; 
   scanf("%d ",i);*/   
     fclose(fic);    vv=vector(1,n); 
     *d=1.0; 
     /*  if(mle==1){*/    for (i=1;i<=n;i++) { 
     if (weightopt != 1) { /* Maximisation without weights*/      big=0.0; 
       for(i=1;i<=n;i++) weight[i]=1.0;      for (j=1;j<=n;j++) 
     }        if ((temp=fabs(a[i][j])) > big) big=temp; 
     /*-calculation of age at interview from date of interview and age at death -*/      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     agev=matrix(1,maxwav,1,imx);      vv[i]=1.0/big; 
     } 
    for (i=1; i<=imx; i++)    for (j=1;j<=n;j++) { 
      for(m=2; (m<= maxwav); m++)      for (i=1;i<j;i++) { 
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){        sum=a[i][j]; 
          anint[m][i]=9999;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
          s[m][i]=-1;        a[i][j]=sum; 
        }      } 
          big=0.0; 
     for (i=1; i<=imx; i++)  {      for (i=j;i<=n;i++) { 
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        sum=a[i][j]; 
       for(m=1; (m<= maxwav); m++){        for (k=1;k<j;k++) 
         if(s[m][i] >0){          sum -= a[i][k]*a[k][j]; 
           if (s[m][i] == nlstate+1) {        a[i][j]=sum; 
             if(agedc[i]>0)        if ( (dum=vv[i]*fabs(sum)) >= big) { 
               if(moisdc[i]!=99 && andc[i]!=9999)          big=dum; 
               agev[m][i]=agedc[i];          imax=i; 
             else {        } 
               if (andc[i]!=9999){      } 
               printf("Warning negative age at death: %d line:%d\n",num[i],i);      if (j != imax) { 
               agev[m][i]=-1;        for (k=1;k<=n;k++) { 
               }          dum=a[imax][k]; 
             }          a[imax][k]=a[j][k]; 
           }          a[j][k]=dum; 
           else if(s[m][i] !=9){ /* Should no more exist */        } 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);        *d = -(*d); 
             if(mint[m][i]==99 || anint[m][i]==9999)        vv[imax]=vv[j]; 
               agev[m][i]=1;      } 
             else if(agev[m][i] <agemin){      indx[j]=imax; 
               agemin=agev[m][i];      if (a[j][j] == 0.0) a[j][j]=TINY; 
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/      if (j != n) { 
             }        dum=1.0/(a[j][j]); 
             else if(agev[m][i] >agemax){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
               agemax=agev[m][i];      } 
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    } 
             }    free_vector(vv,1,n);  /* Doesn't work */
             /*agev[m][i]=anint[m][i]-annais[i];*/  ;
             /*   agev[m][i] = age[i]+2*m;*/  } 
           }  
           else { /* =9 */  void lubksb(double **a, int n, int *indx, double b[]) 
             agev[m][i]=1;  { 
             s[m][i]=-1;    int i,ii=0,ip,j; 
           }    double sum; 
         }   
         else /*= 0 Unknown */    for (i=1;i<=n;i++) { 
           agev[m][i]=1;      ip=indx[i]; 
       }      sum=b[ip]; 
          b[ip]=b[i]; 
     }      if (ii) 
     for (i=1; i<=imx; i++)  {        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       for(m=1; (m<= maxwav); m++){      else if (sum) ii=i; 
         if (s[m][i] > (nlstate+ndeath)) {      b[i]=sum; 
           printf("Error: Wrong value in nlstate or ndeath\n");      } 
           goto end;    for (i=n;i>=1;i--) { 
         }      sum=b[i]; 
       }      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
     }      b[i]=sum/a[i][i]; 
     } 
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);  } 
   
     free_vector(severity,1,maxwav);  void pstamp(FILE *fichier)
     free_imatrix(outcome,1,maxwav+1,1,n);  {
     free_vector(moisnais,1,n);    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
     free_vector(annais,1,n);  }
     free_matrix(mint,1,maxwav,1,n);  
     free_matrix(anint,1,maxwav,1,n);  /************ Frequencies ********************/
     free_vector(moisdc,1,n);  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[])
     free_vector(andc,1,n);  {  /* Some frequencies */
     
        int i, m, jk, k1,i1, j1, bool, z1,j;
     wav=ivector(1,imx);    int first;
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    double ***freq; /* Frequencies */
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    double *pp, **prop;
        double pos,posprop, k2, dateintsum=0,k2cpt=0;
     /* Concatenates waves */    char fileresp[FILENAMELENGTH];
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);    
     pp=vector(1,nlstate);
     prop=matrix(1,nlstate,iagemin,iagemax+3);
       Tcode=ivector(1,100);    strcpy(fileresp,"p");
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    strcat(fileresp,fileres);
       ncodemax[1]=1;    if((ficresp=fopen(fileresp,"w"))==NULL) {
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      printf("Problem with prevalence resultfile: %s\n", fileresp);
            fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
    codtab=imatrix(1,100,1,10);      exit(0);
    h=0;    }
    m=pow(2,cptcoveff);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
      j1=0;
    for(k=1;k<=cptcoveff; k++){    
      for(i=1; i <=(m/pow(2,k));i++){    j=cptcoveff;
        for(j=1; j <= ncodemax[k]; j++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  
            h++;    first=1;
            if (h>m) h=1;codtab[h][k]=j;  
          }    /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
        }    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
      }    /*    j1++;
    }  */
     for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
         /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
    /*for(i=1; i <=m ;i++){          scanf("%d", i);*/
      for(k=1; k <=cptcovn; k++){        for (i=-5; i<=nlstate+ndeath; i++)  
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);          for (jk=-5; jk<=nlstate+ndeath; jk++)  
      }            for(m=iagemin; m <= iagemax+3; m++)
      printf("\n");              freq[i][jk][m]=0;
    }        
    scanf("%d",i);*/        for (i=1; i<=nlstate; i++)  
              for(m=iagemin; m <= iagemax+3; m++)
    /* Calculates basic frequencies. Computes observed prevalence at single age            prop[i][m]=0;
        and prints on file fileres'p'. */        
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprev, lprev);        dateintsum=0;
         k2cpt=0;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        for (i=1; i<=imx; i++) {
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          bool=1;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for (z1=1; z1<=cptcoveff; z1++)       
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
                        /* Tests if the value of each of the covariates of i is equal to filter j1 */
     /* For Powell, parameters are in a vector p[] starting at p[1]                bool=0;
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */                /* 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", 
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
                   j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
     if(mle==1){                /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);              } 
     }          }
       
     /*--------- results files --------------*/          if (bool==1){
     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=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);            for(m=firstpass; m<=lastpass; m++){
    fprintf(ficres,"fprevalence=%d lprevalence=%d pop_based=%d\n",fprev,lprev,popbased);              k2=anint[m][i]+(mint[m][i]/12.);
    fprintf(ficres,"fprevalence=%d lprevalence=%d nforecast=%d mob_average=%d\n",fprevfore,lprevfore,nforecast,mobilav);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
    jk=1;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
    fprintf(ficres,"# Parameters\n");                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
    printf("# Parameters\n");                if (m<lastpass) {
    for(i=1,jk=1; i <=nlstate; i++){                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
      for(k=1; k <=(nlstate+ndeath); k++){                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
        if (k != i)                }
          {                
            printf("%d%d ",i,k);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
            fprintf(ficres,"%1d%1d ",i,k);                  dateintsum=dateintsum+k2;
            for(j=1; j <=ncovmodel; j++){                  k2cpt++;
              printf("%f ",p[jk]);                }
              fprintf(ficres,"%f ",p[jk]);                /*}*/
              jk++;            }
            }          }
            printf("\n");        } /* end i */
            fprintf(ficres,"\n");         
          }        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
      }        pstamp(ficresp);
    }        if  (cptcovn>0) {
  if(mle==1){          fprintf(ficresp, "\n#********** Variable "); 
     /* Computing hessian and covariance matrix */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     ftolhess=ftol; /* Usually correct */          fprintf(ficresp, "**********\n#");
     hesscov(matcov, p, npar, delti, ftolhess, func);          fprintf(ficlog, "\n#********** Variable "); 
  }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     fprintf(ficres,"# Scales\n");          fprintf(ficlog, "**********\n#");
     printf("# Scales\n");        }
      for(i=1,jk=1; i <=nlstate; i++){        for(i=1; i<=nlstate;i++) 
       for(j=1; j <=nlstate+ndeath; j++){          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         if (j!=i) {        fprintf(ficresp, "\n");
           fprintf(ficres,"%1d%1d",i,j);        
           printf("%1d%1d",i,j);        for(i=iagemin; i <= iagemax+3; i++){
           for(k=1; k<=ncovmodel;k++){          if(i==iagemax+3){
             printf(" %.5e",delti[jk]);            fprintf(ficlog,"Total");
             fprintf(ficres," %.5e",delti[jk]);          }else{
             jk++;            if(first==1){
           }              first=0;
           printf("\n");              printf("See log file for details...\n");
           fprintf(ficres,"\n");            }
         }            fprintf(ficlog,"Age %d", i);
       }          }
       }          for(jk=1; jk <=nlstate ; jk++){
                for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     k=1;              pp[jk] += freq[jk][m][i]; 
     fprintf(ficres,"# Covariance\n");          }
     printf("# Covariance\n");          for(jk=1; jk <=nlstate ; jk++){
     for(i=1;i<=npar;i++){            for(m=-1, pos=0; m <=0 ; m++)
       /*  if (k>nlstate) k=1;              pos += freq[jk][m][i];
       i1=(i-1)/(ncovmodel*nlstate)+1;            if(pp[jk]>=1.e-10){
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);              if(first==1){
       printf("%s%d%d",alph[k],i1,tab[i]);*/                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       fprintf(ficres,"%3d",i);              }
       printf("%3d",i);              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       for(j=1; j<=i;j++){            }else{
         fprintf(ficres," %.5e",matcov[i][j]);              if(first==1)
         printf(" %.5e",matcov[i][j]);                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficres,"\n");            }
       printf("\n");          }
       k++;  
     }          for(jk=1; jk <=nlstate ; jk++){
                for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
     while((c=getc(ficpar))=='#' && c!= EOF){              pp[jk] += freq[jk][m][i];
       ungetc(c,ficpar);          }       
       fgets(line, MAXLINE, ficpar);          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
       puts(line);            pos += pp[jk];
       fputs(line,ficparo);            posprop += prop[jk][i];
     }          }
     ungetc(c,ficpar);          for(jk=1; jk <=nlstate ; jk++){
              if(pos>=1.e-5){
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);              if(first==1)
                    printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     if (fage <= 2) {              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       bage = agemin;            }else{
       fage = agemax;              if(first==1)
     }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     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,agemax,bage,fage);            if( i <= iagemax){
               if(pos>=1.e-5){
                    fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
 /*------------ gnuplot -------------*/                /*probs[i][jk][j1]= pp[jk]/pos;*/
 chdir(pathcd);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   if((ficgp=fopen("graph.plt","w"))==NULL) {              }
     printf("Problem with file graph.gp");goto end;              else
   }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
 #ifdef windows            }
   fprintf(ficgp,"cd \"%s\" \n",pathc);          }
 #endif          
 m=pow(2,cptcoveff);          for(jk=-1; jk <=nlstate+ndeath; jk++)
              for(m=-1; m <=nlstate+ndeath; m++)
  /* 1eme*/              if(freq[jk][m][i] !=0 ) {
   for (cpt=1; cpt<= nlstate ; cpt ++) {              if(first==1)
    for (k1=1; k1<= m ; k1 ++) {                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                 fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 #ifdef windows              }
     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);          if(i <= iagemax)
 #endif            fprintf(ficresp,"\n");
 #ifdef unix          if(first==1)
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);            printf("Others in log...\n");
 #endif          fprintf(ficlog,"\n");
         }
 for (i=1; i<= nlstate ; i ++) {        /*}*/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    }
   else fprintf(ficgp," \%%*lf (\%%*lf)");    dateintmean=dateintsum/k2cpt; 
 }   
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    fclose(ficresp);
     for (i=1; i<= nlstate ; i ++) {    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    free_vector(pp,1,nlstate);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
 }    /* End of Freq */
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  }
      for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  /************ Prevalence ********************/
   else fprintf(ficgp," \%%*lf (\%%*lf)");  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
 }    {  
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
 #ifdef unix       in each health status at the date of interview (if between dateprev1 and dateprev2).
 fprintf(ficgp,"\nset ter gif small size 400,300");       We still use firstpass and lastpass as another selection.
 #endif    */
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);   
    }    int i, m, jk, k1, i1, j1, bool, z1,j;
   }    double ***freq; /* Frequencies */
   /*2 eme*/    double *pp, **prop;
     double pos,posprop; 
   for (k1=1; k1<= m ; k1 ++) {    double  y2; /* in fractional years */
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);    int iagemin, iagemax;
        int first; /** to stop verbosity which is redirected to log file */
     for (i=1; i<= nlstate+1 ; i ++) {  
       k=2*i;    iagemin= (int) agemin;
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    iagemax= (int) agemax;
       for (j=1; j<= nlstate+1 ; j ++) {    /*pp=vector(1,nlstate);*/
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    prop=matrix(1,nlstate,iagemin,iagemax+3); 
   else fprintf(ficgp," \%%*lf (\%%*lf)");    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
 }      j1=0;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    /*j=cptcoveff;*/
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       for (j=1; j<= nlstate+1 ; j ++) {    
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    first=1;
         else fprintf(ficgp," \%%*lf (\%%*lf)");    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
 }        /*for(i1=1; i1<=ncodemax[k1];i1++){
       fprintf(ficgp,"\" t\"\" w l 0,");        j1++;*/
      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 ++) {        for (i=1; i<=nlstate; i++)  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          for(m=iagemin; m <= iagemax+3; m++)
   else fprintf(ficgp," \%%*lf (\%%*lf)");            prop[i][m]=0.0;
 }         
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        for (i=1; i<=imx; i++) { /* Each individual */
       else fprintf(ficgp,"\" t\"\" w l 0,");          bool=1;
     }          if  (cptcovn>0) {
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);            for (z1=1; z1<=cptcoveff; z1++) 
   }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                  bool=0;
   /*3eme*/          } 
           if (bool==1) { 
   for (k1=1; k1<= m ; k1 ++) {            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
       k=2+nlstate*(cpt-1);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
       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);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
       for (i=1; i< nlstate ; i ++) {                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         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((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) { 
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);                  /*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]]);*/
     }                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
   }                  prop[s[m][i]][iagemax+3] += weight[i]; 
                  } 
   /* CV preval stat */              }
   for (k1=1; k1<= m ; k1 ++) {            } /* end selection of waves */
     for (cpt=1; cpt<nlstate ; cpt ++) {          }
       k=3;        }
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);        for(i=iagemin; i <= iagemax+3; i++){  
       for (i=1; i< nlstate ; i ++)          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
         fprintf(ficgp,"+$%d",k+i+1);            posprop += prop[jk][i]; 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);          } 
                
       l=3+(nlstate+ndeath)*cpt;          for(jk=1; jk <=nlstate ; jk++){     
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);            if( i <=  iagemax){ 
       for (i=1; i< nlstate ; i ++) {              if(posprop>=1.e-5){ 
         l=3+(nlstate+ndeath)*cpt;                probs[i][jk][j1]= prop[jk][i]/posprop;
         fprintf(ficgp,"+$%d",l+i+1);              } else{
       }                if(first==1){
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                    first=0;
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);                  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]);
     }                }
   }                }
             } 
   /* proba elementaires */          }/* end jk */ 
    for(i=1,jk=1; i <=nlstate; i++){        }/* end i */ 
     for(k=1; k <=(nlstate+ndeath); k++){      /*} *//* end i1 */
       if (k != i) {    } /* end j1 */
         for(j=1; j <=ncovmodel; j++){    
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
           /*fprintf(ficgp,"%s",alph[1]);*/    /*free_vector(pp,1,nlstate);*/
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
           jk++;  }  /* End of prevalence */
           fprintf(ficgp,"\n");  
         }  /************* Waves Concatenation ***************/
       }  
     }  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)
     }  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
   for(jk=1; jk <=m; jk++) {       Death is a valid wave (if date is known).
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
    i=1;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
    for(k2=1; k2<=nlstate; k2++) {       and mw[mi+1][i]. dh depends on stepm.
      k3=i;       */
      for(k=1; k<=(nlstate+ndeath); k++) {  
        if (k != k2){    int i, mi, m;
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
 ij=1;       double sum=0., jmean=0.;*/
         for(j=3; j <=ncovmodel; j++) {    int first;
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {    int j, k=0,jk, ju, jl;
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);    double sum=0.;
             ij++;    first=0;
           }    jmin=1e+5;
           else    jmax=-1;
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    jmean=0.;
         }    for(i=1; i<=imx; i++){
           fprintf(ficgp,")/(1");      mi=0;
              m=firstpass;
         for(k1=1; k1 <=nlstate; k1++){        while(s[m][i] <= nlstate){
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
 ij=1;          mw[++mi][i]=m;
           for(j=3; j <=ncovmodel; j++){        if(m >=lastpass)
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {          break;
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);        else
             ij++;          m++;
           }      }/* end while */
           else      if (s[m][i] > nlstate){
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        mi++;     /* Death is another wave */
           }        /* if(mi==0)  never been interviewed correctly before death */
           fprintf(ficgp,")");           /* Only death is a correct wave */
         }        mw[mi][i]=m;
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);      }
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");  
         i=i+ncovmodel;      wav[i]=mi;
        }      if(mi==0){
      }        nbwarn++;
    }        if(first==0){
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
   }          first=1;
            }
   fclose(ficgp);        if(first==1){
              fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
 chdir(path);        }
          } /* end mi==0 */
     free_ivector(wav,1,imx);    } /* End individuals */
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);  
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      for(i=1; i<=imx; i++){
     free_ivector(num,1,n);      for(mi=1; mi<wav[i];mi++){
     free_vector(agedc,1,n);        if (stepm <=0)
     /*free_matrix(covar,1,NCOVMAX,1,n);*/          dh[mi][i]=1;
     fclose(ficparo);        else{
     fclose(ficres);          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); 
    /*________fin mle=1_________*/              if(j==0) j=1;  /* Survives at least one month after exam */
                  else if(j<0){
                 nberr++;
                  printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     /* No more information from the sample is required now */                j=1; /* Temporary Dangerous patch */
   /* Reads comments: lines beginning with '#' */                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);
   while((c=getc(ficpar))=='#' && c!= EOF){                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]);
     ungetc(c,ficpar);                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);
     fgets(line, MAXLINE, ficpar);              }
     puts(line);              k=k+1;
     fputs(line,ficparo);              if (j >= jmax){
   }                jmax=j;
   ungetc(c,ficpar);                ijmax=i;
                }
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);              if (j <= jmin){
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);                jmin=j;
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);                ijmin=i;
 /*--------- index.htm --------*/              }
               sum=sum+j;
   strcpy(optionfilehtm,optionfile);              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
   strcat(optionfilehtm,".htm");              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {            }
     printf("Problem with %s \n",optionfilehtm);goto end;          }
   }          else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">  /*        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]); */
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>  
 Total number of observations=%d <br>            k=k+1;
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>            if (j >= jmax) {
 <hr  size=\"2\" color=\"#EC5E5E\">              jmax=j;
 <li>Outputs files<br><br>\n              ijmax=i;
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n            }
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>            else if (j <= jmin){
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>              jmin=j;
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>              ijmin=i;
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>            }
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>            /*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]);*/
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>            if(j<0){
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>              nberr++;
         - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>              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]);
 <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
             }
  fprintf(fichtm," <li>Graphs</li><p>");            sum=sum+j;
           }
  m=cptcoveff;          jk= j/stepm;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}          jl= j -jk*stepm;
           ju= j -(jk+1)*stepm;
  j1=0;          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
  for(k1=1; k1<=m;k1++){            if(jl==0){
    for(i1=1; i1<=ncodemax[k1];i1++){              dh[mi][i]=jk;
        j1++;              bh[mi][i]=0;
        if (cptcovn > 0) {            }else{ /* We want a negative bias in order to only have interpolation ie
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");                    * to avoid the price of an extra matrix product in likelihood */
          for (cpt=1; cpt<=cptcoveff;cpt++)              dh[mi][i]=jk+1;
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);              bh[mi][i]=ju;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");            }
        }          }else{
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>            if(jl <= -ju){
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);                  dh[mi][i]=jk;
        for(cpt=1; cpt<nlstate;cpt++){              bh[mi][i]=jl;       /* bias is positive if real duration
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>                                   * is higher than the multiple of stepm and negative otherwise.
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);                                   */
        }            }
     for(cpt=1; cpt<=nlstate;cpt++) {            else{
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident              dh[mi][i]=jk+1;
 interval) in state (%d): v%s%d%d.gif <br>              bh[mi][i]=ju;
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);              }
      }            if(dh[mi][i]==0){
      for(cpt=1; cpt<=nlstate;cpt++) {              dh[mi][i]=1; /* At least one step */
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>              bh[mi][i]=ju; /* At least one step */
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);              /*  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);*/
      }            }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          } /* end if mle */
 health expectancies in states (1) and (2): e%s%d.gif<br>        }
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);      } /* end wave */
 fprintf(fichtm,"\n</body>");    }
    }    jmean=sum/k;
  }    printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
 fclose(fichtm);    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);
    }
   /*--------------- Prevalence limit --------------*/  
    /*********** Tricode ****************************/
   strcpy(filerespl,"pl");  void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
   strcat(filerespl,fileres);  {
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    /**< Uses cptcovn+2*cptcovprod as the number of covariates */
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    /*      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]
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);     * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
   fprintf(ficrespl,"#Prevalence limit\n");    /* nbcode[Tvar[j]][1]= 
   fprintf(ficrespl,"#Age ");    */
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");    int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
      int modmaxcovj=0; /* Modality max of covariates j */
   prlim=matrix(1,nlstate,1,nlstate);    int cptcode=0; /* Modality max of covariates j */
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    int modmincovj=0; /* Modality min of covariates j */
   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 */    cptcoveff=0; 
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */   
   k=0;    for (k=-1; k < maxncov; k++) Ndum[k]=0;
   agebase=agemin;    for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
   agelim=agemax;  
   ftolpl=1.e-10;    /* Loop on covariates without age and products */
   i1=cptcoveff;    for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
   if (cptcovn < 1){i1=1;}      for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
                                  modality of this covariate Vj*/ 
   for(cptcov=1;cptcov<=i1;cptcov++){        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                                      * If product of Vn*Vm, still boolean *:
         k=k+1;                                      * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/                                      * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
         fprintf(ficrespl,"\n#******");        /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
         for(j=1;j<=cptcoveff;j++)                                        modality of the nth covariate of individual i. */
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        if (ij > modmaxcovj)
         fprintf(ficrespl,"******\n");          modmaxcovj=ij; 
                else if (ij < modmincovj) 
         for (age=agebase; age<=agelim; age++){          modmincovj=ij; 
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);        if ((ij < -1) && (ij > NCOVMAX)){
           fprintf(ficrespl,"%.0f",age );          printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
           for(i=1; i<=nlstate;i++)          exit(1);
           fprintf(ficrespl," %.5f", prlim[i][i]);        }else
           fprintf(ficrespl,"\n");        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
         }        /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
       }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     }        /* getting the maximum value of the modality of the covariate
   fclose(ficrespl);           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
            female is 1, then modmaxcovj=1.*/
   /*------------- h Pij x at various ages ------------*/      }
        printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      cptcode=modmaxcovj;
   if((ficrespij=fopen(filerespij,"w"))==NULL) {      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;     /*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("Computing pij: result on file '%s' \n", filerespij);        printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
          if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
   stepsize=(int) (stepm+YEARM-1)/YEARM;          ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
   /*if (stepm<=24) stepsize=2;*/        }
         /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
   agelim=AGESUP;           historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
   hstepm=stepsize*YEARM; /* Every year of age */      } /* Ndum[-1] number of undefined modalities */
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
        /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
   k=0;      /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
   for(cptcov=1;cptcov<=i1;cptcov++){      /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){         modmincovj=3; modmaxcovj = 7;
       k=k+1;         There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
         fprintf(ficrespij,"\n#****** ");         which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
         for(j=1;j<=cptcoveff;j++)         variables V1_1 and V1_2.
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);         nbcode[Tvar[j]][ij]=k;
         fprintf(ficrespij,"******\n");         nbcode[Tvar[j]][1]=0;
                 nbcode[Tvar[j]][2]=1;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */         nbcode[Tvar[j]][3]=2;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      */
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      ij=1; /* ij is similar to i but can jumps over null modalities */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
           oldm=oldms;savm=savms;        for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            /*recode from 0 */
           fprintf(ficrespij,"# Age");          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
           for(i=1; i<=nlstate;i++)            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
             for(j=1; j<=nlstate+ndeath;j++)                                       k is a modality. If we have model=V1+V1*sex 
               fprintf(ficrespij," %1d-%1d",i,j);                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
           fprintf(ficrespij,"\n");            ij++;
           for (h=0; h<=nhstepm; h++){          }
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );          if (ij > ncodemax[j]) break; 
             for(i=1; i<=nlstate;i++)        }  /* end of loop on */
               for(j=1; j<=nlstate+ndeath;j++)      } /* end of loop on modality */ 
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
             fprintf(ficrespij,"\n");    
           }   for (k=-1; k< maxncov; k++) Ndum[k]=0; 
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    
           fprintf(ficrespij,"\n");    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
         }     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
     }     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
   }     Ndum[ij]++; 
    } 
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/  
    ij=1;
   fclose(ficrespij);   for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
      /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
   /*---------- Forecasting ------------------*/     if((Ndum[i]!=0) && (i<=ncovcol)){
        /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
   strcpy(fileresf,"f");       Tvaraff[ij]=i; /*For printing (unclear) */
   strcat(fileresf,fileres);       ij++;
   if((ficresf=fopen(fileresf,"w"))==NULL) {     }else
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;         Tvaraff[ij]=0;
   }   }
   printf("Computing forecasting: result on file '%s' \n", fileresf);   ij--;
    cptcoveff=ij; /*Number of total covariates*/
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax, fprevfore, lprevfore);  
   }
  free_matrix(agev,1,maxwav,1,imx);  
   /* Mobile average */  
   /*********** Health Expectancies ****************/
   if (cptcoveff==0) ncodemax[cptcoveff]=1;  
   void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   if (mobilav==1) {  
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  {
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)    /* Health expectancies, no variances */
       for (i=1; i<=nlstate;i++)    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    int nhstepma, nstepma; /* Decreasing with age */
           mobaverage[(int)agedeb][i][cptcod]=0.;    double age, agelim, hf;
        double ***p3mat;
     for (agedeb=bage+4; agedeb<=fage; agedeb++){    double eip;
       for (i=1; i<=nlstate;i++){  
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    pstamp(ficreseij);
           for (cpt=0;cpt<=4;cpt++){    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    fprintf(ficreseij,"# Age");
           }    for(i=1; i<=nlstate;i++){
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;      for(j=1; j<=nlstate;j++){
         }        fprintf(ficreseij," e%1d%1d ",i,j);
       }      }
     }        fprintf(ficreseij," e%1d. ",i);
   }    }
     fprintf(ficreseij,"\n");
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=12) stepsize=1;    
     if(estepm < stepm){
   agelim=AGESUP;      printf ("Problem %d lower than %d\n",estepm, stepm);
   hstepm=stepsize*YEARM; /* Every year of age */    }
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */    else  hstepm=estepm;   
      /* We compute the life expectancy from trapezoids spaced every estepm months
   if (popforecast==1) {     * This is mainly to measure the difference between two models: for example
     if((ficpop=fopen(popfile,"r"))==NULL)    {     * if stepm=24 months pijx are given only every 2 years and by summing them
       printf("Problem with population file : %s\n",popfile);goto end;     * we are calculating an estimate of the Life Expectancy assuming a linear 
     }     * progression in between and thus overestimating or underestimating according
     popage=ivector(0,AGESUP);     * to the curvature of the survival function. If, for the same date, we 
     popeffectif=vector(0,AGESUP);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     popcount=vector(0,AGESUP);     * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
     i=1;       * curvature will be obtained if estepm is as small as stepm. */
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)  
       {    /* For example we decided to compute the life expectancy with the smallest unit */
         i=i+1;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       }       nhstepm is the number of hstepm from age to agelim 
     imx=i;       nstepm is the number of stepm from age to agelin. 
         Look at hpijx to understand the reason of that which relies in memory size
   for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];       and note for a fixed period like estepm months */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
   for(cptcov=1;cptcov<=i1;cptcov++){       means that if the survival funtion is printed only each two years of age and if
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       k=k+1;       results. So we changed our mind and took the option of the best precision.
       fprintf(ficresf,"\n#****** ");    */
       for(j=1;j<=cptcoveff;j++) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         fprintf(ficresf,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       }    agelim=AGESUP;
       fprintf(ficresf,"******\n");    /* If stepm=6 months */
       fprintf(ficresf,"# StartingAge FinalAge Horizon(in years)");      /* Computed by stepm unit matrices, product of hstepm matrices, stored
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
       if (popforecast==1)  fprintf(ficresf," [Population]");      
   /* nhstepm age range expressed in number of stepm */
       for (agedeb=fage; agedeb>=bage; agedeb--){    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
         fprintf(ficresf,"\n%.f %.f 0",agedeb, agedeb);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
        if (mobilav==1) {    /* if (stepm >= YEARM) hstepm=1;*/
         for(j=1; j<=nlstate;j++)    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
           fprintf(ficresf," %.3f",mobaverage[(int)agedeb][j][cptcod]);    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         }  
         else {    for (age=bage; age<=fage; age ++){ 
           for(j=1; j<=nlstate;j++)      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           fprintf(ficresf," %.3f",probs[(int)agedeb][j][cptcod]);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         }        /* if (stepm >= YEARM) hstepm=1;*/
       nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
        for(j=1; j<=ndeath;j++) fprintf(ficresf," 0.00000");  
        if (popforecast==1) fprintf(ficresf," [%.f] ",popeffectif[(int)agedeb]);      /* If stepm=6 months */
       }      /* Computed by stepm unit matrices, product of hstepma matrices, stored
               in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       for (cpt=1; cpt<=nforecast;cpt++) {      
         fprintf(ficresf,"\n");      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         nhstepm = nhstepm/hstepm;      
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/      printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      
         oldm=oldms;savm=savms;      /* Computing expectancies */
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        for(i=1; i<=nlstate;i++)
                        for(j=1; j<=nlstate;j++)
         for (h=0; h<=nhstepm; h++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
                    eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
          if (h*hstepm/YEARM*stepm==cpt)            
             fprintf(ficresf,"\n%.f %.f %.f",agedeb, agedeb+ h*hstepm/YEARM*stepm, h*hstepm/YEARM*stepm);            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
            
                    }
          for(j=1; j<=nlstate+ndeath;j++) {  
            kk1=0.;kk2=0;      fprintf(ficreseij,"%3.0f",age );
            for(i=1; i<=nlstate;i++) {              for(i=1; i<=nlstate;i++){
              if (mobilav==1)        eip=0;
                 kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb][i][cptcod];        for(j=1; j<=nlstate;j++){
              else kk1=kk1+p3mat[i][j][h]*probs[(int)agedeb][i][cptcod];          eip +=eij[i][j][(int)age];
              if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
             }        }
            if (h*hstepm/YEARM*stepm==cpt) {        fprintf(ficreseij,"%9.4f", eip );
              fprintf(ficresf," %.3f", kk1);      }
                if (popforecast==1) fprintf(ficresf," [%.f]", kk2);      fprintf(ficreseij,"\n");
            }      
           }    }
         }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    printf("\n");
            fprintf(ficlog,"\n");
       }    
       }  }
     }  
   }  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   if (popforecast==1) {  {
     free_ivector(popage,0,AGESUP);    /* Covariances of health expectancies eij and of total life expectancies according
     free_vector(popeffectif,0,AGESUP);     to initial status i, ei. .
     free_vector(popcount,0,AGESUP);    */
   }    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   free_imatrix(s,1,maxwav+1,1,n);    int nhstepma, nstepma; /* Decreasing with age */
   free_vector(weight,1,n);    double age, agelim, hf;
   fclose(ficresf);    double ***p3matp, ***p3matm, ***varhe;
   /*---------- Health expectancies and variances ------------*/    double **dnewm,**doldm;
     double *xp, *xm;
   strcpy(filerest,"t");    double **gp, **gm;
   strcat(filerest,fileres);    double ***gradg, ***trgradg;
   if((ficrest=fopen(filerest,"w"))==NULL) {    int theta;
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;  
   }    double eip, vip;
   printf("Computing Total LEs with variances: file '%s' \n", filerest);  
     varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     xp=vector(1,npar);
   strcpy(filerese,"e");    xm=vector(1,npar);
   strcat(filerese,fileres);    dnewm=matrix(1,nlstate*nlstate,1,npar);
   if((ficreseij=fopen(filerese,"w"))==NULL) {    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    
   }    pstamp(ficresstdeij);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
     fprintf(ficresstdeij,"# Age");
  strcpy(fileresv,"v");    for(i=1; i<=nlstate;i++){
   strcat(fileresv,fileres);      for(j=1; j<=nlstate;j++)
   if((ficresvij=fopen(fileresv,"w"))==NULL) {        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      fprintf(ficresstdeij," e%1d. ",i);
   }    }
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    fprintf(ficresstdeij,"\n");
   
   k=0;    pstamp(ficrescveij);
   for(cptcov=1;cptcov<=i1;cptcov++){    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    fprintf(ficrescveij,"# Age");
       k=k+1;    for(i=1; i<=nlstate;i++)
       fprintf(ficrest,"\n#****** ");      for(j=1; j<=nlstate;j++){
       for(j=1;j<=cptcoveff;j++)        cptj= (j-1)*nlstate+i;
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(i2=1; i2<=nlstate;i2++)
       fprintf(ficrest,"******\n");          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
       fprintf(ficreseij,"\n#****** ");            if(cptj2 <= cptj)
       for(j=1;j<=cptcoveff;j++)              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);          }
       fprintf(ficreseij,"******\n");      }
     fprintf(ficrescveij,"\n");
       fprintf(ficresvij,"\n#****** ");    
       for(j=1;j<=cptcoveff;j++)    if(estepm < stepm){
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      printf ("Problem %d lower than %d\n",estepm, stepm);
       fprintf(ficresvij,"******\n");    }
     else  hstepm=estepm;   
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    /* We compute the life expectancy from trapezoids spaced every estepm months
       oldm=oldms;savm=savms;     * This is mainly to measure the difference between two models: for example
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);       * if stepm=24 months pijx are given only every 2 years and by summing them
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);     * we are calculating an estimate of the Life Expectancy assuming a linear 
       oldm=oldms;savm=savms;     * progression in between and thus overestimating or underestimating according
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);     * 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
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");     * to compare the new estimate of Life expectancy with the same linear 
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);     * hypothesis. A more precise result, taking into account a more precise
       fprintf(ficrest,"\n");     * curvature will be obtained if estepm is as small as stepm. */
          
       hf=1;    /* For example we decided to compute the life expectancy with the smallest unit */
       if (stepm >= YEARM) hf=stepm/YEARM;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       epj=vector(1,nlstate+1);       nhstepm is the number of hstepm from age to agelim 
       for(age=bage; age <=fage ;age++){       nstepm is the number of stepm from age to agelin. 
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);       Look at hpijx to understand the reason of that which relies in memory size
         if (popbased==1) {       and note for a fixed period like estepm months */
           for(i=1; i<=nlstate;i++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
             prlim[i][i]=probs[(int)age][i][k];       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 
         fprintf(ficrest," %.0f",age);       results. So we changed our mind and took the option of the best precision.
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    */
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];  
           }    /* If stepm=6 months */
           epj[nlstate+1] +=epj[j];    /* nhstepm age range expressed in number of stepm */
         }    agelim=AGESUP;
         for(i=1, vepp=0.;i <=nlstate;i++)    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
           for(j=1;j <=nlstate;j++)    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             vepp += vareij[i][j][(int)age];    /* if (stepm >= YEARM) hstepm=1;*/
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         for(j=1;j <=nlstate;j++){    
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         }    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         fprintf(ficrest,"\n");    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
       }    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     }    gp=matrix(0,nhstepm,1,nlstate*nlstate);
   }    gm=matrix(0,nhstepm,1,nlstate*nlstate);
          
            for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
  fclose(ficreseij);      /* if (stepm >= YEARM) hstepm=1;*/
  fclose(ficresvij);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   fclose(ficrest);  
   fclose(ficpar);      /* If stepm=6 months */
   free_vector(epj,1,nlstate+1);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
   /*  scanf("%d ",i); */         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   /*------- Variance limit prevalence------*/        hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
 strcpy(fileresvpl,"vpl");      /* Computing  Variances of health expectancies */
   strcat(fileresvpl,fileres);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {         decrease memory allocation */
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);      for(theta=1; theta <=npar; theta++){
     exit(0);        for(i=1; i<=npar; i++){ 
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
  k=0;        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
  for(cptcov=1;cptcov<=i1;cptcov++){        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    
      k=k+1;        for(j=1; j<= nlstate; j++){
      fprintf(ficresvpl,"\n#****** ");          for(i=1; i<=nlstate; i++){
      for(j=1;j<=cptcoveff;j++)            for(h=0; h<=nhstepm-1; h++){
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
      fprintf(ficresvpl,"******\n");              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
                  }
      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);       
    }        for(ij=1; ij<= nlstate*nlstate; ij++)
  }          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   fclose(ficresvpl);          }
       }/* End theta */
   /*---------- End : free ----------------*/      
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      
        for(h=0; h<=nhstepm-1; h++)
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        for(j=1; j<=nlstate*nlstate;j++)
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);          for(theta=1; theta <=npar; theta++)
              trgradg[h][j][theta]=gradg[h][theta][j];
        
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);       for(ij=1;ij<=nlstate*nlstate;ij++)
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(ji=1;ji<=nlstate*nlstate;ji++)
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          varhe[ij][ji][(int)age] =0.;
    
   free_matrix(matcov,1,npar,1,npar);       printf("%d|",(int)age);fflush(stdout);
   free_vector(delti,1,npar);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         for(h=0;h<=nhstepm-1;h++){
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);        for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   printf("End of Imach\n");          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          for(ij=1;ij<=nlstate*nlstate;ij++)
              for(ji=1;ji<=nlstate*nlstate;ji++)
   /* 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);*/              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   /*printf("Total time was %d uSec.\n", total_usecs);*/        }
   /*------ End -----------*/      }
   
       /* Computing expectancies */
  end:      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
 #ifdef windows      for(i=1; i<=nlstate;i++)
  chdir(pathcd);        for(j=1; j<=nlstate;j++)
 #endif          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
              eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
  system("..\\gp37mgw\\wgnuplot graph.plt");            
             /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
 #ifdef windows  
   while (z[0] != 'q') {          }
     chdir(pathcd);  
     printf("\nType e to edit output files, c to start again, and q for exiting: ");      fprintf(ficresstdeij,"%3.0f",age );
     scanf("%s",z);      for(i=1; i<=nlstate;i++){
     if (z[0] == 'c') system("./imach");        eip=0.;
     else if (z[0] == 'e') {        vip=0.;
       chdir(path);        for(j=1; j<=nlstate;j++){
       system(optionfilehtm);          eip += eij[i][j][(int)age];
     }          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
     else if (z[0] == 'q') exit(0);            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
   }          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
 #endif        }
 }        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }
       fprintf(ficresstdeij,"\n");
   
       fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
               if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
         }
       fprintf(ficrescveij,"\n");
      
     }
     free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
     fprintf(ficlog,"\n");
   
     free_vector(xm,1,npar);
     free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
   
   /************ Variance ******************/
   void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   {
     /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /* double **newm;*/
     double **dnewm,**doldm;
     double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
     int k, cptcode;
     double *xp;
     double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
     double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
     double age,agelim, hf;
     double ***mobaverage;
     int theta;
     char digit[4];
     char digitp[25];
   
     char fileresprobmorprev[FILENAMELENGTH];
   
     if(popbased==1){
       if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
     }
     else 
       strcpy(digitp,"-stablbased-");
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     pstamp(ficresprobmorprev);
     fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }  
     fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
     /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
     fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pstamp(ficresvij);
     fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     if(popbased==1)
       fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
     else
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
     /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at function hpijx to understand why (it is linked to memory size questions) */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
       gm=matrix(0,nhstepm,1,nlstate);
   
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
     
         for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
             for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
   
         for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
           for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
   
       } /* End theta */
   
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
       for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **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 */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s with errno=%s\n",optionfile,strerror(errno));
       fprintf(ficlog,"Problem with optionfile %s with errno=%s\n",optionfile,strerror(errno));
       fflush(ficlog);
       /* goto end; */
       exit(70); 
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line,stdout);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n);  /**< used in readdata */
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       ncovmodel=2+nbocc(model,'+')+1; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     else
       ncovmodel=2;
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guessed parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       /* Reads scales values */
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       /* Reads covariance matrix */
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,NCOVMAX); /* Number of code per covariate; if O and 1 only, 2**ncov; V1+V2+V3+V4=>16 */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,NCOVMAX); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,NCOVMAX); /* Unclear */
     Tvard=imatrix(1,NCOVMAX,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,NCOVMAX); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
     /* */
     
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
     /* */
    
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     Ndum =ivector(-1,NCOVMAX);  
     if (ncovmodel > 2)
       tricode(Tvar,nbcode,imx, Ndum); /**< Fills nbcode[Tvar[j]][l]; */
   
     codtab=imatrix(1,100,1,10); /* codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) */
     /*printf(" codtab[1,1],codtab[100,10]=%d,%d\n", codtab[1][1],codtab[100][10]);*/
     h=0;
   
   
     /*if (cptcovn > 0) */
         
    
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=pow(2,cptcoveff-k);i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) 
               h=1;
             /**< codtab(h,k)  k   = codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) + 1
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     1
              */
             codtab[h][k]=j;
             /*codtab[h][Tvar[k]]=j;*/
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
   
    free_ivector(Ndum,-1,NCOVMAX);
   
   
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       //fprintf(ficgp,"set missing 'NaNq'\n");
       fprintf(ficgp,"set datafile missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       /*p[1]=0.0268; p[NDIM]=0.083;*/
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         fputs(line,stdout);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
        /* freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint); */
       /* ,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2); */
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
   #include "prevlim.h"  /* Use ficrespl, ficlog */
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
   #include "hpijx.h"
       fclose(ficrespij);
   
     /*-------------- Variance of one-step probabilities---*/
       k=1;
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
           /*
            */
           /* goto endfree; */
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
   
   
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms; /* Segmentation fault */
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);
             fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         /*}*/
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,NCOVMAX,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       /*for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         /*}*/
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
     }  /* mle==-3 arrives here for freeing */
    endfree:
       free_matrix(prlim,1,nlstate,1,nlstate); /*here or after loop ? */
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,NCOVMAX);
       free_ivector(Tvar,1,NCOVMAX);
       free_ivector(Tprod,1,NCOVMAX);
       free_ivector(Tvaraff,1,NCOVMAX);
       free_ivector(Tage,1,NCOVMAX);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("gnuplot command might not be in your path: %s, err=%d\n", plotcmd, outcmd);
       printf("\n Trying if gnuplot resides on the same directory that IMaCh\n");
       sprintf(plotcmd,"%sgnuplot %s", pathimach, optionfilegnuplot);
       if((outcmd=system(plotcmd)) != 0)
         printf("\n Still a problem with gnuplot command %s, err=%d\n", plotcmd, outcmd);
     }
     printf(" Successul, please wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit results with your browser, g to graph again and q for exit: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
   #ifdef OSX
         sprintf(pplotcmd, "open %s", optionfilehtm);
   #else
         sprintf(pplotcmd, "%s", optionfilehtm);
   #endif
         printf("Starting browser with: %s",pplotcmd);fflush(stdout);
         system(pplotcmd);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.16  
changed lines
  Added in v.1.154


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