Diff for /imach/src/imach.c between versions 1.13 and 1.123

version 1.13, 2002/02/20 17:02:08 version 1.123, 2006/03/20 10:52:43
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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 1.123  2006/03/20 10:52:43  brouard
   individuals from different ages are interviewed on their health status    * imach.c (Module): <title> changed, corresponds to .htm file
   or degree of  disability. At least a second wave of interviews    name. <head> headers where missing.
   ("longitudinal") should  measure each new individual health status.  
   Health expectancies are computed from the transistions observed between    * imach.c (Module): Weights can have a decimal point as for
   waves and are computed for each degree of severity of disability (number    English (a comma might work with a correct LC_NUMERIC environment,
   of life states). More degrees you consider, more time is necessary to    otherwise the weight is truncated).
   reach the Maximum Likelihood of the parameters involved in the model.    Modification of warning when the covariates values are not 0 or
   The simplest model is the multinomial logistic model where pij is    1.
   the probabibility to be observed in state j at the second wave conditional    Version 0.98g
   to be observed in state i at the first wave. Therefore the model is:  
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Revision 1.122  2006/03/20 09:45:41  brouard
   is a covariate. If you want to have a more complex model than "constant and    (Module): Weights can have a decimal point as for
   age", you should modify the program where the markup    English (a comma might work with a correct LC_NUMERIC environment,
     *Covariates have to be included here again* invites you to do it.    otherwise the weight is truncated).
   More covariates you add, less is the speed of the convergence.    Modification of warning when the covariates values are not 0 or
     1.
   The advantage that this computer programme claims, comes from that if the    Version 0.98g
   delay between waves is not identical for each individual, or if some  
   individual missed an interview, the information is not rounded or lost, but    Revision 1.121  2006/03/16 17:45:01  lievre
   taken into account using an interpolation or extrapolation.    * imach.c (Module): Comments concerning covariates added
   hPijx is the probability to be  
   observed in state i at age x+h conditional to the observed state i at age    * imach.c (Module): refinements in the computation of lli if
   x. The delay 'h' can be split into an exact number (nh*stepm) of    status=-2 in order to have more reliable computation if stepm is
   unobserved intermediate  states. This elementary transition (by month or    not 1 month. Version 0.98f
   quarter trimester, semester or year) is model as a multinomial logistic.  
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.120  2006/03/16 15:10:38  lievre
   and the contribution of each individual to the likelihood is simply hPijx.    (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
   Also this programme outputs the covariance matrix of the parameters but also    not 1 month. Version 0.98f
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.119  2006/03/15 17:42:26  brouard
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    (Module): Bug if status = -2, the loglikelihood was
            Institut national d'études démographiques, Paris.    computed as likelihood omitting the logarithm. Version O.98e
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.118  2006/03/14 18:20:07  brouard
   It is copyrighted identically to a GNU software product, ie programme and    (Module): varevsij Comments added explaining the second
   software can be distributed freely for non commercial use. Latest version    table of variances if popbased=1 .
   can be accessed at http://euroreves.ined.fr/imach .    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   **********************************************************************/    (Module): Function pstamp added
      (Module): Version 0.98d
 #include <math.h>  
 #include <stdio.h>    Revision 1.117  2006/03/14 17:16:22  brouard
 #include <stdlib.h>    (Module): varevsij Comments added explaining the second
 #include <unistd.h>    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define MAXLINE 256    (Module): Function pstamp added
 #define FILENAMELENGTH 80    (Module): Version 0.98d
 /*#define DEBUG*/  
 #define windows    Revision 1.116  2006/03/06 10:29:27  brouard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    (Module): Variance-covariance wrong links and
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    varian-covariance of ej. is needed (Saito).
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.115  2006/02/27 12:17:45  brouard
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    (Module): One freematrix added in mlikeli! 0.98c
   
 #define NINTERVMAX 8    Revision 1.114  2006/02/26 12:57:58  brouard
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    (Module): Some improvements in processing parameter
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    filename with strsep.
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.113  2006/02/24 14:20:24  brouard
 #define YEARM 12. /* Number of months per year */    (Module): Memory leaks checks with valgrind and:
 #define AGESUP 130    datafile was not closed, some imatrix were not freed and on matrix
 #define AGEBASE 40    allocation too.
   
     Revision 1.112  2006/01/30 09:55:26  brouard
 int nvar;    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.111  2006/01/25 20:38:18  brouard
 int nlstate=2; /* Number of live states */    (Module): Lots of cleaning and bugs added (Gompertz)
 int ndeath=1; /* Number of dead states */    (Module): Comments can be added in data file. Missing date values
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    can be a simple dot '.'.
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.110  2006/01/25 00:51:50  brouard
 int maxwav; /* Maxim number of waves */    (Module): Lots of cleaning and bugs added (Gompertz)
 int jmin, jmax; /* min, max spacing between 2 waves */  
 int mle, weightopt;    Revision 1.109  2006/01/24 19:37:15  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    (Module): Comments (lines starting with a #) are allowed in data.
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.108  2006/01/19 18:05:42  lievre
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Gnuplot problem appeared...
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    To be fixed
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;  
 FILE *ficgp, *fichtm,*ficresprob;    Revision 1.107  2006/01/19 16:20:37  brouard
 FILE *ficreseij;    Test existence of gnuplot in imach path
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.106  2006/01/19 13:24:36  brouard
   char fileresv[FILENAMELENGTH];    Some cleaning and links added in html output
  FILE  *ficresvpl;  
   char fileresvpl[FILENAMELENGTH];    Revision 1.105  2006/01/05 20:23:19  lievre
     *** empty log message ***
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.104  2005/09/30 16:11:43  lievre
 #define FTOL 1.0e-10    (Module): sump fixed, loop imx fixed, and simplifications.
     (Module): If the status is missing at the last wave but we know
 #define NRANSI    that the person is alive, then we can code his/her status as -2
 #define ITMAX 200    (instead of missing=-1 in earlier versions) and his/her
     contributions to the likelihood is 1 - Prob of dying from last
 #define TOL 2.0e-4    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
 #define CGOLD 0.3819660  
 #define ZEPS 1.0e-10    Revision 1.103  2005/09/30 15:54:49  lievre
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    (Module): sump fixed, loop imx fixed, and simplifications.
   
 #define GOLD 1.618034    Revision 1.102  2004/09/15 17:31:30  brouard
 #define GLIMIT 100.0    Add the possibility to read data file including tab characters.
 #define TINY 1.0e-20  
     Revision 1.101  2004/09/15 10:38:38  brouard
 static double maxarg1,maxarg2;    Fix on curr_time
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.100  2004/07/12 18:29:06  brouard
      Add version for Mac OS X. Just define UNIX in Makefile
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.99  2004/06/05 08:57:40  brouard
     *** empty log message ***
 static double sqrarg;  
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    Revision 1.98  2004/05/16 15:05:56  brouard
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 int imx;    state at each age, but using a Gompertz model: log u =a + b*age .
 int stepm;    This is the basic analysis of mortality and should be done before any
 /* Stepm, step in month: minimum step interpolation*/    other analysis, in order to test if the mortality estimated from the
     cross-longitudinal survey is different from the mortality estimated
 int m,nb;    from other sources like vital statistic data.
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    The same imach parameter file can be used but the option for mle should be -3.
 double **pmmij, ***probs, ***mobaverage;  
     Agnès, who wrote this part of the code, tried to keep most of the
 double *weight;    former routines in order to include the new code within the former code.
 int **s; /* Status */  
 double *agedc, **covar, idx;    The output is very simple: only an estimate of the intercept and of
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    the slope with 95% confident intervals.
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Current limitations:
 double ftolhess; /* Tolerance for computing hessian */    A) Even if you enter covariates, i.e. with the
     model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 /**************** split *************************/    B) There is no computation of Life Expectancy nor Life Table.
 static  int split( char *path, char *dirc, char *name )  
 {    Revision 1.97  2004/02/20 13:25:42  lievre
    char *s;                             /* pointer */    Version 0.96d. Population forecasting command line is (temporarily)
    int  l1, l2;                         /* length counters */    suppressed.
   
    l1 = strlen( path );                 /* length of path */    Revision 1.96  2003/07/15 15:38:55  brouard
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
    s = strrchr( path, '\\' );           /* find last / */    rewritten within the same printf. Workaround: many printfs.
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.95  2003/07/08 07:54:34  brouard
       extern char       *getwd( );    * imach.c (Repository):
     (Repository): Using imachwizard code to output a more meaningful covariance
       if ( getwd( dirc ) == NULL ) {    matrix (cov(a12,c31) instead of numbers.
 #else  
       extern char       *getcwd( );    Revision 1.94  2003/06/27 13:00:02  brouard
     Just cleaning
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    Revision 1.93  2003/06/25 16:33:55  brouard
          return( GLOCK_ERROR_GETCWD );    (Module): On windows (cygwin) function asctime_r doesn't
       }    exist so I changed back to asctime which exists.
       strcpy( name, path );             /* we've got it */    (Module): Version 0.96b
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */    Revision 1.92  2003/06/25 16:30:45  brouard
       l2 = strlen( s );                 /* length of filename */    (Module): On windows (cygwin) function asctime_r doesn't
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    exist so I changed back to asctime which exists.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.91  2003/06/25 15:30:29  brouard
       dirc[l1-l2] = 0;                  /* add zero */    * imach.c (Repository): Duplicated warning errors corrected.
    }    (Repository): Elapsed time after each iteration is now output. It
    l1 = strlen( dirc );                 /* length of directory */    helps to forecast when convergence will be reached. Elapsed time
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    is stamped in powell.  We created a new html file for the graphs
    return( 0 );                         /* we're done */    concerning matrix of covariance. It has extension -cov.htm.
 }  
     Revision 1.90  2003/06/24 12:34:15  brouard
     (Module): Some bugs corrected for windows. Also, when
 /******************************************/    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 void replace(char *s, char*t)  
 {    Revision 1.89  2003/06/24 12:30:52  brouard
   int i;    (Module): Some bugs corrected for windows. Also, when
   int lg=20;    mle=-1 a template is output in file "or"mypar.txt with the design
   i=0;    of the covariance matrix to be input.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.88  2003/06/23 17:54:56  brouard
     (s[i] = t[i]);    * 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.
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.87  2003/06/18 12:26:01  brouard
 }    Version 0.96
   
 int nbocc(char *s, char occ)    Revision 1.86  2003/06/17 20:04:08  brouard
 {    (Module): Change position of html and gnuplot routines and added
   int i,j=0;    routine fileappend.
   int lg=20;  
   i=0;    Revision 1.85  2003/06/17 13:12:43  brouard
   lg=strlen(s);    * imach.c (Repository): Check when date of death was earlier that
   for(i=0; i<= lg; i++) {    current date of interview. It may happen when the death was just
   if  (s[i] == occ ) j++;    prior to the death. In this case, dh was negative and likelihood
   }    was wrong (infinity). We still send an "Error" but patch by
   return j;    assuming that the date of death was just one stepm after the
 }    interview.
     (Repository): Because some people have very long ID (first column)
 void cutv(char *u,char *v, char*t, char occ)    we changed int to long in num[] and we added a new lvector for
 {    memory allocation. But we also truncated to 8 characters (left
   int i,lg,j,p=0;    truncation)
   i=0;    (Repository): No more line truncation errors.
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    Revision 1.84  2003/06/13 21:44:43  brouard
   }    * imach.c (Repository): Replace "freqsummary" at a correct
     place. It differs from routine "prevalence" which may be called
   lg=strlen(t);    many times. Probs is memory consuming and must be used with
   for(j=0; j<p; j++) {    parcimony.
     (u[j] = t[j]);    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   }  
      u[p]='\0';    Revision 1.83  2003/06/10 13:39:11  lievre
     *** empty log message ***
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);    Revision 1.82  2003/06/05 15:57:20  brouard
   }    Add log in  imach.c and  fullversion number is now printed.
 }  
   */
 /********************** nrerror ********************/  /*
      Interpolated Markov Chain
 void nrerror(char error_text[])  
 {    Short summary of the programme:
   fprintf(stderr,"ERREUR ...\n");    
   fprintf(stderr,"%s\n",error_text);    This program computes Healthy Life Expectancies from
   exit(1);    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 }    first survey ("cross") where individuals from different ages are
 /*********************** vector *******************/    interviewed on their health status or degree of disability (in the
 double *vector(int nl, int nh)    case of a health survey which is our main interest) -2- at least a
 {    second wave of interviews ("longitudinal") which measure each change
   double *v;    (if any) in individual health status.  Health expectancies are
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    computed from the time spent in each health state according to a
   if (!v) nrerror("allocation failure in vector");    model. More health states you consider, more time is necessary to reach the
   return v-nl+NR_END;    Maximum Likelihood of the parameters involved in the model.  The
 }    simplest model is the multinomial logistic model where pij is the
     probability to be observed in state j at the second wave
 /************************ free vector ******************/    conditional to be observed in state i at the first wave. Therefore
 void free_vector(double*v, int nl, int nh)    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 {    'age' is age and 'sex' is a covariate. If you want to have a more
   free((FREE_ARG)(v+nl-NR_END));    complex model than "constant and age", you should modify the program
 }    where the markup *Covariates have to be included here again* invites
     you to do it.  More covariates you add, slower the
 /************************ivector *******************************/    convergence.
 int *ivector(long nl,long nh)  
 {    The advantage of this computer programme, compared to a simple
   int *v;    multinomial logistic model, is clear when the delay between waves is not
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    identical for each individual. Also, if a individual missed an
   if (!v) nrerror("allocation failure in ivector");    intermediate interview, the information is lost, but taken into
   return v-nl+NR_END;    account using an interpolation or extrapolation.  
 }  
     hPijx is the probability to be observed in state i at age x+h
 /******************free ivector **************************/    conditional to the observed state i at age x. The delay 'h' can be
 void free_ivector(int *v, long nl, long nh)    split into an exact number (nh*stepm) of unobserved intermediate
 {    states. This elementary transition (by month, quarter,
   free((FREE_ARG)(v+nl-NR_END));    semester or year) is modelled as a multinomial logistic.  The hPx
 }    matrix is simply the matrix product of nh*stepm elementary matrices
     and the contribution of each individual to the likelihood is simply
 /******************* imatrix *******************************/    hPijx.
 int **imatrix(long nrl, long nrh, long ncl, long nch)  
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    Also this programme outputs the covariance matrix of the parameters but also
 {    of the life expectancies. It also computes the period (stable) prevalence. 
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    
   int **m;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
               Institut national d'études démographiques, Paris.
   /* allocate pointers to rows */    This software have been partly granted by Euro-REVES, a concerted action
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    from the European Union.
   if (!m) nrerror("allocation failure 1 in matrix()");    It is copyrighted identically to a GNU software product, ie programme and
   m += NR_END;    software can be distributed freely for non commercial use. Latest version
   m -= nrl;    can be accessed at http://euroreves.ined.fr/imach .
    
      Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   /* allocate rows and set pointers to them */    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    **********************************************************************/
   m[nrl] += NR_END;  /*
   m[nrl] -= ncl;    main
      read parameterfile
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    read datafile
      concatwav
   /* return pointer to array of pointers to rows */    freqsummary
   return m;    if (mle >= 1)
 }      mlikeli
     print results files
 /****************** free_imatrix *************************/    if mle==1 
 void free_imatrix(m,nrl,nrh,ncl,nch)       computes hessian
       int **m;    read end of parameter file: agemin, agemax, bage, fage, estepm
       long nch,ncl,nrh,nrl;        begin-prev-date,...
      /* free an int matrix allocated by imatrix() */    open gnuplot file
 {    open html file
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    period (stable) prevalence
   free((FREE_ARG) (m+nrl-NR_END));     for age prevalim()
 }    h Pij x
     variance of p varprob
 /******************* matrix *******************************/    forecasting if prevfcast==1 prevforecast call prevalence()
 double **matrix(long nrl, long nrh, long ncl, long nch)    health expectancies
 {    Variance-covariance of DFLE
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    prevalence()
   double **m;     movingaverage()
     varevsij() 
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    if popbased==1 varevsij(,popbased)
   if (!m) nrerror("allocation failure 1 in matrix()");    total life expectancies
   m += NR_END;    Variance of period (stable) prevalence
   m -= nrl;   end
   */
   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;  
   m[nrl] -= ncl;   
   #include <math.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include <stdio.h>
   return m;  #include <stdlib.h>
 }  #include <string.h>
   #include <unistd.h>
 /*************************free matrix ************************/  
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  #include <limits.h>
 {  #include <sys/types.h>
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #include <sys/stat.h>
   free((FREE_ARG)(m+nrl-NR_END));  #include <errno.h>
 }  extern int errno;
   
 /******************* ma3x *******************************/  /* #include <sys/time.h> */
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #include <time.h>
 {  #include "timeval.h"
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  
   double ***m;  /* #include <libintl.h> */
   /* #define _(String) gettext (String) */
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");  #define MAXLINE 256
   m += NR_END;  
   m -= nrl;  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define FILENAMELENGTH 132
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
   m[nrl] -= ncl;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
   #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #define NINTERVMAX 8
   m[nrl][ncl] += NR_END;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   m[nrl][ncl] -= nll;  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   for (j=ncl+1; j<=nch; j++)  #define NCOVMAX 8 /* Maximum number of covariates */
     m[nrl][j]=m[nrl][j-1]+nlay;  #define MAXN 20000
    #define YEARM 12. /* Number of months per year */
   for (i=nrl+1; i<=nrh; i++) {  #define AGESUP 130
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #define AGEBASE 40
     for (j=ncl+1; j<=nch; j++)  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
       m[i][j]=m[i][j-1]+nlay;  #ifdef UNIX
   }  #define DIRSEPARATOR '/'
   return m;  #define CHARSEPARATOR "/"
 }  #define ODIRSEPARATOR '\\'
   #else
 /*************************free ma3x ************************/  #define DIRSEPARATOR '\\'
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #define CHARSEPARATOR "\\"
 {  #define ODIRSEPARATOR '/'
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #endif
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  /* $Id$ */
 }  /* $State$ */
   
 /***************** f1dim *************************/  char version[]="Imach version 0.98g, March 2006, INED-EUROREVES-Institut de longevite ";
 extern int ncom;  char fullversion[]="$Revision$ $Date$"; 
 extern double *pcom,*xicom;  char strstart[80];
 extern double (*nrfunc)(double []);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
    int erreur, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 double f1dim(double x)  int nvar;
 {  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;
   int j;  int npar=NPARMAX;
   double f;  int nlstate=2; /* Number of live states */
   double *xt;  int ndeath=1; /* Number of dead states */
    int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   xt=vector(1,ncom);  int popbased=0;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);  int *wav; /* Number of waves for this individuual 0 is possible */
   free_vector(xt,1,ncom);  int maxwav; /* Maxim number of waves */
   return f;  int jmin, jmax; /* min, max spacing between 2 waves */
 }  int ijmin, ijmax; /* Individuals having jmin and jmax */ 
   int gipmx, gsw; /* Global variables on the number of contributions 
 /*****************brent *************************/                     to the likelihood and the sum of weights (done by funcone)*/
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  int mle, weightopt;
 {  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   int iter;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   double a,b,d,etemp;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   double fu,fv,fw,fx;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   double ftemp;  double jmean; /* Mean space between 2 waves */
   double p,q,r,tol1,tol2,u,v,w,x,xm;  double **oldm, **newm, **savm; /* Working pointers to matrices */
   double e=0.0;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
    FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   a=(ax < cx ? ax : cx);  FILE *ficlog, *ficrespow;
   b=(ax > cx ? ax : cx);  int globpr; /* Global variable for printing or not */
   x=w=v=bx;  double fretone; /* Only one call to likelihood */
   fw=fv=fx=(*f)(x);  long ipmx; /* Number of contributions */
   for (iter=1;iter<=ITMAX;iter++) {  double sw; /* Sum of weights */
     xm=0.5*(a+b);  char filerespow[FILENAMELENGTH];
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  FILE *ficresilk;
     printf(".");fflush(stdout);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
 #ifdef DEBUG  FILE *ficresprobmorprev;
     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);  FILE *fichtm, *fichtmcov; /* Html File */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  FILE *ficreseij;
 #endif  char filerese[FILENAMELENGTH];
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  FILE *ficresstdeij;
       *xmin=x;  char fileresstde[FILENAMELENGTH];
       return fx;  FILE *ficrescveij;
     }  char filerescve[FILENAMELENGTH];
     ftemp=fu;  FILE  *ficresvij;
     if (fabs(e) > tol1) {  char fileresv[FILENAMELENGTH];
       r=(x-w)*(fx-fv);  FILE  *ficresvpl;
       q=(x-v)*(fx-fw);  char fileresvpl[FILENAMELENGTH];
       p=(x-v)*q-(x-w)*r;  char title[MAXLINE];
       q=2.0*(q-r);  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       if (q > 0.0) p = -p;  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       q=fabs(q);  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
       etemp=e;  char command[FILENAMELENGTH];
       e=d;  int  outcmd=0;
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
       else {  
         d=p/q;  char filelog[FILENAMELENGTH]; /* Log file */
         u=x+d;  char filerest[FILENAMELENGTH];
         if (u-a < tol2 || b-u < tol2)  char fileregp[FILENAMELENGTH];
           d=SIGN(tol1,xm-x);  char popfile[FILENAMELENGTH];
       }  
     } else {  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  
     }  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  struct timezone tzp;
     fu=(*f)(u);  extern int gettimeofday();
     if (fu <= fx) {  struct tm tmg, tm, tmf, *gmtime(), *localtime();
       if (u >= x) a=x; else b=x;  long time_value;
       SHFT(v,w,x,u)  extern long time();
         SHFT(fv,fw,fx,fu)  char strcurr[80], strfor[80];
         } else {  
           if (u < x) a=u; else b=u;  char *endptr;
           if (fu <= fw || w == x) {  long lval;
             v=w;  double dval;
             w=u;  
             fv=fw;  #define NR_END 1
             fw=fu;  #define FREE_ARG char*
           } else if (fu <= fv || v == x || v == w) {  #define FTOL 1.0e-10
             v=u;  
             fv=fu;  #define NRANSI 
           }  #define ITMAX 200 
         }  
   }  #define TOL 2.0e-4 
   nrerror("Too many iterations in brent");  
   *xmin=x;  #define CGOLD 0.3819660 
   return fx;  #define ZEPS 1.0e-10 
 }  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   
 /****************** mnbrak ***********************/  #define GOLD 1.618034 
   #define GLIMIT 100.0 
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  #define TINY 1.0e-20 
             double (*func)(double))  
 {  static double maxarg1,maxarg2;
   double ulim,u,r,q, dum;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   double fu;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
      
   *fa=(*func)(*ax);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   *fb=(*func)(*bx);  #define rint(a) floor(a+0.5)
   if (*fb > *fa) {  
     SHFT(dum,*ax,*bx,dum)  static double sqrarg;
       SHFT(dum,*fb,*fa,dum)  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       }  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   *cx=(*bx)+GOLD*(*bx-*ax);  int agegomp= AGEGOMP;
   *fc=(*func)(*cx);  
   while (*fb > *fc) {  int imx; 
     r=(*bx-*ax)*(*fb-*fc);  int stepm=1;
     q=(*bx-*cx)*(*fb-*fa);  /* Stepm, step in month: minimum step interpolation*/
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  int estepm;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
     if ((*bx-u)*(u-*cx) > 0.0) {  
       fu=(*func)(u);  int m,nb;
     } else if ((*cx-u)*(u-ulim) > 0.0) {  long *num;
       fu=(*func)(u);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
       if (fu < *fc) {  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  double **pmmij, ***probs;
           SHFT(*fb,*fc,fu,(*func)(u))  double *ageexmed,*agecens;
           }  double dateintmean=0;
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;  double *weight;
       fu=(*func)(u);  int **s; /* Status */
     } else {  double *agedc, **covar, idx;
       u=(*cx)+GOLD*(*cx-*bx);  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
       fu=(*func)(u);  double *lsurv, *lpop, *tpop;
     }  
     SHFT(*ax,*bx,*cx,u)  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
       SHFT(*fa,*fb,*fc,fu)  double ftolhess; /* Tolerance for computing hessian */
       }  
 }  /**************** split *************************/
   static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
 /*************** linmin ************************/  {
     /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
 int ncom;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
 double *pcom,*xicom;    */ 
 double (*nrfunc)(double []);    char  *ss;                            /* pointer */
      int   l1, l2;                         /* length counters */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {    l1 = strlen(path );                   /* length of path */
   double brent(double ax, double bx, double cx,    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
                double (*f)(double), double tol, double *xmin);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   double f1dim(double x);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,      strcpy( name, path );               /* we got the fullname name because no directory */
               double *fc, double (*func)(double));      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   int j;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   double xx,xmin,bx,ax;      /* get current working directory */
   double fx,fb,fa;      /*    extern  char* getcwd ( char *buf , int len);*/
        if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   ncom=n;        return( GLOCK_ERROR_GETCWD );
   pcom=vector(1,n);      }
   xicom=vector(1,n);      /* got dirc from getcwd*/
   nrfunc=func;      printf(" DIRC = %s \n",dirc);
   for (j=1;j<=n;j++) {    } else {                              /* strip direcotry from path */
     pcom[j]=p[j];      ss++;                               /* after this, the filename */
     xicom[j]=xi[j];      l2 = strlen( ss );                  /* length of filename */
   }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   ax=0.0;      strcpy( name, ss );         /* save file name */
   xx=1.0;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);      dirc[l1-l2] = 0;                    /* add zero */
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);      printf(" DIRC2 = %s \n",dirc);
 #ifdef DEBUG    }
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);    /* We add a separator at the end of dirc if not exists */
 #endif    l1 = strlen( dirc );                  /* length of directory */
   for (j=1;j<=n;j++) {    if( dirc[l1-1] != DIRSEPARATOR ){
     xi[j] *= xmin;      dirc[l1] =  DIRSEPARATOR;
     p[j] += xi[j];      dirc[l1+1] = 0; 
   }      printf(" DIRC3 = %s \n",dirc);
   free_vector(xicom,1,n);    }
   free_vector(pcom,1,n);    ss = strrchr( name, '.' );            /* find last / */
 }    if (ss >0){
       ss++;
 /*************** powell ************************/      strcpy(ext,ss);                     /* save extension */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,      l1= strlen( name);
             double (*func)(double []))      l2= strlen(ss)+1;
 {      strncpy( finame, name, l1-l2);
   void linmin(double p[], double xi[], int n, double *fret,      finame[l1-l2]= 0;
               double (*func)(double []));    }
   int i,ibig,j;  
   double del,t,*pt,*ptt,*xit;    return( 0 );                          /* we're done */
   double fp,fptt;  }
   double *xits;  
   pt=vector(1,n);  
   ptt=vector(1,n);  /******************************************/
   xit=vector(1,n);  
   xits=vector(1,n);  void replace_back_to_slash(char *s, char*t)
   *fret=(*func)(p);  {
   for (j=1;j<=n;j++) pt[j]=p[j];    int i;
   for (*iter=1;;++(*iter)) {    int lg=0;
     fp=(*fret);    i=0;
     ibig=0;    lg=strlen(t);
     del=0.0;    for(i=0; i<= lg; i++) {
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      (s[i] = t[i]);
     for (i=1;i<=n;i++)      if (t[i]== '\\') s[i]='/';
       printf(" %d %.12f",i, p[i]);    }
     printf("\n");  }
     for (i=1;i<=n;i++) {  
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  int nbocc(char *s, char occ)
       fptt=(*fret);  {
 #ifdef DEBUG    int i,j=0;
       printf("fret=%lf \n",*fret);    int lg=20;
 #endif    i=0;
       printf("%d",i);fflush(stdout);    lg=strlen(s);
       linmin(p,xit,n,fret,func);    for(i=0; i<= lg; i++) {
       if (fabs(fptt-(*fret)) > del) {    if  (s[i] == occ ) j++;
         del=fabs(fptt-(*fret));    }
         ibig=i;    return j;
       }  }
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  void cutv(char *u,char *v, char*t, char occ)
       for (j=1;j<=n;j++) {  {
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
         printf(" x(%d)=%.12e",j,xit[j]);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       }       gives u="abcedf" and v="ghi2j" */
       for(j=1;j<=n;j++)    int i,lg,j,p=0;
         printf(" p=%.12e",p[j]);    i=0;
       printf("\n");    for(j=0; j<=strlen(t)-1; j++) {
 #endif      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     }    }
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  
 #ifdef DEBUG    lg=strlen(t);
       int k[2],l;    for(j=0; j<p; j++) {
       k[0]=1;      (u[j] = t[j]);
       k[1]=-1;    }
       printf("Max: %.12e",(*func)(p));       u[p]='\0';
       for (j=1;j<=n;j++)  
         printf(" %.12e",p[j]);     for(j=0; j<= lg; j++) {
       printf("\n");      if (j>=(p+1))(v[j-p-1] = t[j]);
       for(l=0;l<=1;l++) {    }
         for (j=1;j<=n;j++) {  }
           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]);  /********************** nrerror ********************/
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  void nrerror(char error_text[])
       }  {
 #endif    fprintf(stderr,"ERREUR ...\n");
     fprintf(stderr,"%s\n",error_text);
     exit(EXIT_FAILURE);
       free_vector(xit,1,n);  }
       free_vector(xits,1,n);  /*********************** vector *******************/
       free_vector(ptt,1,n);  double *vector(int nl, int nh)
       free_vector(pt,1,n);  {
       return;    double *v;
     }    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");    if (!v) nrerror("allocation failure in vector");
     for (j=1;j<=n;j++) {    return v-nl+NR_END;
       ptt[j]=2.0*p[j]-pt[j];  }
       xit[j]=p[j]-pt[j];  
       pt[j]=p[j];  /************************ free vector ******************/
     }  void free_vector(double*v, int nl, int nh)
     fptt=(*func)(ptt);  {
     if (fptt < fp) {    free((FREE_ARG)(v+nl-NR_END));
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  }
       if (t < 0.0) {  
         linmin(p,xit,n,fret,func);  /************************ivector *******************************/
         for (j=1;j<=n;j++) {  int *ivector(long nl,long nh)
           xi[j][ibig]=xi[j][n];  {
           xi[j][n]=xit[j];    int *v;
         }    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
 #ifdef DEBUG    if (!v) nrerror("allocation failure in ivector");
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    return v-nl+NR_END;
         for(j=1;j<=n;j++)  }
           printf(" %.12e",xit[j]);  
         printf("\n");  /******************free ivector **************************/
 #endif  void free_ivector(int *v, long nl, long nh)
       }  {
     }    free((FREE_ARG)(v+nl-NR_END));
   }  }
 }  
   /************************lvector *******************************/
 /**** Prevalence limit ****************/  long *lvector(long nl,long nh)
   {
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    long *v;
 {    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    if (!v) nrerror("allocation failure in ivector");
      matrix by transitions matrix until convergence is reached */    return v-nl+NR_END;
   }
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  /******************free lvector **************************/
   double **matprod2();  void free_lvector(long *v, long nl, long nh)
   double **out, cov[NCOVMAX], **pmij();  {
   double **newm;    free((FREE_ARG)(v+nl-NR_END));
   double agefin, delaymax=50 ; /* Max number of years to converge */  }
   
   for (ii=1;ii<=nlstate+ndeath;ii++)  /******************* imatrix *******************************/
     for (j=1;j<=nlstate+ndeath;j++){  int **imatrix(long nrl, long nrh, long ncl, long nch) 
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     }  { 
     long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
    cov[1]=1.;    int **m; 
      
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    /* allocate pointers to rows */ 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     newm=savm;    if (!m) nrerror("allocation failure 1 in matrix()"); 
     /* Covariates have to be included here again */    m += NR_END; 
      cov[2]=agefin;    m -= nrl; 
      
       for (k=1; k<=cptcovn;k++) {    
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    /* allocate rows and set pointers to them */ 
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       for (k=1; k<=cptcovage;k++)    m[nrl] += NR_END; 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m[nrl] -= ncl; 
       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(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    /* return pointer to array of pointers to rows */ 
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    return m; 
   } 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  
   /****************** free_imatrix *************************/
     savm=oldm;  void free_imatrix(m,nrl,nrh,ncl,nch)
     oldm=newm;        int **m;
     maxmax=0.;        long nch,ncl,nrh,nrl; 
     for(j=1;j<=nlstate;j++){       /* free an int matrix allocated by imatrix() */ 
       min=1.;  { 
       max=0.;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       for(i=1; i<=nlstate; i++) {    free((FREE_ARG) (m+nrl-NR_END)); 
         sumnew=0;  } 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  
         prlim[i][j]= newm[i][j]/(1-sumnew);  /******************* matrix *******************************/
         max=FMAX(max,prlim[i][j]);  double **matrix(long nrl, long nrh, long ncl, long nch)
         min=FMIN(min,prlim[i][j]);  {
       }    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
       maxmin=max-min;    double **m;
       maxmax=FMAX(maxmax,maxmin);  
     }    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if(maxmax < ftolpl){    if (!m) nrerror("allocation failure 1 in matrix()");
       return prlim;    m += NR_END;
     }    m -= nrl;
   }  
 }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 /*************** transition probabilities ***************/    m[nrl] += NR_END;
     m[nrl] -= ncl;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  
 {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   double s1, s2;    return m;
   /*double t34;*/    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
   int i,j,j1, nc, ii, jj;     */
   }
     for(i=1; i<= nlstate; i++){  
     for(j=1; j<i;j++){  /*************************free matrix ************************/
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         /*s2 += param[i][j][nc]*cov[nc];*/  {
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    free((FREE_ARG)(m+nrl-NR_END));
       }  }
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  /******************* ma3x *******************************/
     }  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     for(j=i+1; j<=nlstate+ndeath;j++){  {
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    double ***m;
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       ps[i][j]=(s2);    if (!m) nrerror("allocation failure 1 in matrix()");
     }    m += NR_END;
   }    m -= nrl;
     /*ps[3][2]=1;*/  
     m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   for(i=1; i<= nlstate; i++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
      s1=0;    m[nrl] += NR_END;
     for(j=1; j<i; j++)    m[nrl] -= ncl;
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       s1+=exp(ps[i][j]);  
     ps[i][i]=1./(s1+1.);    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     for(j=1; j<i; j++)    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       ps[i][j]= exp(ps[i][j])*ps[i][i];    m[nrl][ncl] += NR_END;
     for(j=i+1; j<=nlstate+ndeath; j++)    m[nrl][ncl] -= nll;
       ps[i][j]= exp(ps[i][j])*ps[i][i];    for (j=ncl+1; j<=nch; j++) 
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */      m[nrl][j]=m[nrl][j-1]+nlay;
   } /* end i */    
     for (i=nrl+1; i<=nrh; i++) {
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     for(jj=1; jj<= nlstate+ndeath; jj++){      for (j=ncl+1; j<=nch; j++) 
       ps[ii][jj]=0;        m[i][j]=m[i][j-1]+nlay;
       ps[ii][ii]=1;    }
     }    return m; 
   }    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
              &(m[i][j][k]) <=> *((*(m+i) + j)+k)
     */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /*************************free ma3x ************************/
    }  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     printf("\n ");  {
     }    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     printf("\n ");printf("%lf ",cov[2]);*/    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 /*    free((FREE_ARG)(m+nrl-NR_END));
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  }
   goto end;*/  
     return ps;  /*************** function subdirf ***********/
 }  char *subdirf(char fileres[])
   {
 /**************** Product of 2 matrices ******************/    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    strcat(tmpout,"/"); /* Add to the right */
 {    strcat(tmpout,fileres);
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    return tmpout;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  }
   /* in, b, out are matrice of pointers which should have been initialized  
      before: only the contents of out is modified. The function returns  /*************** function subdirf2 ***********/
      a pointer to pointers identical to out */  char *subdirf2(char fileres[], char *preop)
   long i, j, k;  {
   for(i=nrl; i<= nrh; i++)    
     for(k=ncolol; k<=ncoloh; k++)    /* Caution optionfilefiname is hidden */
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    strcpy(tmpout,optionfilefiname);
         out[i][k] +=in[i][j]*b[j][k];    strcat(tmpout,"/");
     strcat(tmpout,preop);
   return out;    strcat(tmpout,fileres);
 }    return tmpout;
   }
   
 /************* Higher Matrix Product ***************/  /*************** function subdirf3 ***********/
   char *subdirf3(char fileres[], char *preop, char *preop2)
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  {
 {    
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    /* Caution optionfilefiname is hidden */
      duration (i.e. until    strcpy(tmpout,optionfilefiname);
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    strcat(tmpout,"/");
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    strcat(tmpout,preop);
      (typically every 2 years instead of every month which is too big).    strcat(tmpout,preop2);
      Model is determined by parameters x and covariates have to be    strcat(tmpout,fileres);
      included manually here.    return tmpout;
   }
      */  
   /***************** f1dim *************************/
   int i, j, d, h, k;  extern int ncom; 
   double **out, cov[NCOVMAX];  extern double *pcom,*xicom;
   double **newm;  extern double (*nrfunc)(double []); 
    
   /* Hstepm could be zero and should return the unit matrix */  double f1dim(double x) 
   for (i=1;i<=nlstate+ndeath;i++)  { 
     for (j=1;j<=nlstate+ndeath;j++){    int j; 
       oldm[i][j]=(i==j ? 1.0 : 0.0);    double f;
       po[i][j][0]=(i==j ? 1.0 : 0.0);    double *xt; 
     }   
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    xt=vector(1,ncom); 
   for(h=1; h <=nhstepm; h++){    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     for(d=1; d <=hstepm; d++){    f=(*nrfunc)(xt); 
       newm=savm;    free_vector(xt,1,ncom); 
       /* Covariates have to be included here again */    return f; 
       cov[1]=1.;  } 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;  
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  /*****************brent *************************/
       for (k=1; k<=cptcovage;k++)  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  { 
       for (k=1; k<=cptcovprod;k++)    int iter; 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    double a,b,d,etemp;
     double fu,fv,fw,fx;
     double ftemp;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    double p,q,r,tol1,tol2,u,v,w,x,xm; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    double e=0.0; 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,   
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    a=(ax < cx ? ax : cx); 
       savm=oldm;    b=(ax > cx ? ax : cx); 
       oldm=newm;    x=w=v=bx; 
     }    fw=fv=fx=(*f)(x); 
     for(i=1; i<=nlstate+ndeath; i++)    for (iter=1;iter<=ITMAX;iter++) { 
       for(j=1;j<=nlstate+ndeath;j++) {      xm=0.5*(a+b); 
         po[i][j][h]=newm[i][j];      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
          */      printf(".");fflush(stdout);
       }      fprintf(ficlog,".");fflush(ficlog);
   } /* end h */  #ifdef DEBUG
   return po;      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)))) { */
   #endif
 /*************** log-likelihood *************/      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
 double func( double *x)        *xmin=x; 
 {        return fx; 
   int i, ii, j, k, mi, d, kk;      } 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      ftemp=fu;
   double **out;      if (fabs(e) > tol1) { 
   double sw; /* Sum of weights */        r=(x-w)*(fx-fv); 
   double lli; /* Individual log likelihood */        q=(x-v)*(fx-fw); 
   long ipmx;        p=(x-v)*q-(x-w)*r; 
   /*extern weight */        q=2.0*(q-r); 
   /* We are differentiating ll according to initial status */        if (q > 0.0) p = -p; 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/        q=fabs(q); 
   /*for(i=1;i<imx;i++)        etemp=e; 
     printf(" %d\n",s[4][i]);        e=d; 
   */        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
   cov[1]=1.;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         else { 
   for(k=1; k<=nlstate; k++) ll[k]=0.;          d=p/q; 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){          u=x+d; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];          if (u-a < tol2 || b-u < tol2) 
     for(mi=1; mi<= wav[i]-1; mi++){            d=SIGN(tol1,xm-x); 
       for (ii=1;ii<=nlstate+ndeath;ii++)        } 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      } else { 
       for(d=0; d<dh[mi][i]; d++){        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         newm=savm;      } 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
         for (kk=1; kk<=cptcovage;kk++) {      fu=(*f)(u); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];      if (fu <= fx) { 
         }        if (u >= x) a=x; else b=x; 
                SHFT(v,w,x,u) 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,          SHFT(fv,fw,fx,fu) 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));          } else { 
         savm=oldm;            if (u < x) a=u; else b=u; 
         oldm=newm;            if (fu <= fw || w == x) { 
                      v=w; 
                      w=u; 
       } /* end mult */              fv=fw; 
                    fw=fu; 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);            } else if (fu <= fv || v == x || v == w) { 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/              v=u; 
       ipmx +=1;              fv=fu; 
       sw += weight[i];            } 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;          } 
     } /* end of wave */    } 
   } /* end of individual */    nrerror("Too many iterations in brent"); 
     *xmin=x; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    return fx; 
   /* 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;  /****************** mnbrak ***********************/
 }  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
               double (*func)(double)) 
 /*********** Maximum Likelihood Estimation ***************/  { 
     double ulim,u,r,q, dum;
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    double fu; 
 {   
   int i,j, iter;    *fa=(*func)(*ax); 
   double **xi,*delti;    *fb=(*func)(*bx); 
   double fret;    if (*fb > *fa) { 
   xi=matrix(1,npar,1,npar);      SHFT(dum,*ax,*bx,dum) 
   for (i=1;i<=npar;i++)        SHFT(dum,*fb,*fa,dum) 
     for (j=1;j<=npar;j++)        } 
       xi[i][j]=(i==j ? 1.0 : 0.0);    *cx=(*bx)+GOLD*(*bx-*ax); 
   printf("Powell\n");    *fc=(*func)(*cx); 
   powell(p,xi,npar,ftol,&iter,&fret,func);    while (*fb > *fc) { 
       r=(*bx-*ax)*(*fb-*fc); 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));      q=(*bx-*cx)*(*fb-*fa); 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
         (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
 }      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       if ((*bx-u)*(u-*cx) > 0.0) { 
 /**** Computes Hessian and covariance matrix ***/        fu=(*func)(u); 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      } else if ((*cx-u)*(u-ulim) > 0.0) { 
 {        fu=(*func)(u); 
   double  **a,**y,*x,pd;        if (fu < *fc) { 
   double **hess;          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   int i, j,jk;            SHFT(*fb,*fc,fu,(*func)(u)) 
   int *indx;            } 
       } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
   double hessii(double p[], double delta, int theta, double delti[]);        u=ulim; 
   double hessij(double p[], double delti[], int i, int j);        fu=(*func)(u); 
   void lubksb(double **a, int npar, int *indx, double b[]) ;      } else { 
   void ludcmp(double **a, int npar, int *indx, double *d) ;        u=(*cx)+GOLD*(*cx-*bx); 
         fu=(*func)(u); 
   hess=matrix(1,npar,1,npar);      } 
       SHFT(*ax,*bx,*cx,u) 
   printf("\nCalculation of the hessian matrix. Wait...\n");        SHFT(*fa,*fb,*fc,fu) 
   for (i=1;i<=npar;i++){        } 
     printf("%d",i);fflush(stdout);  } 
     hess[i][i]=hessii(p,ftolhess,i,delti);  
     /*printf(" %f ",p[i]);*/  /*************** linmin ************************/
     /*printf(" %lf ",hess[i][i]);*/  
   }  int ncom; 
    double *pcom,*xicom;
   for (i=1;i<=npar;i++) {  double (*nrfunc)(double []); 
     for (j=1;j<=npar;j++)  {   
       if (j>i) {  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
         printf(".%d%d",i,j);fflush(stdout);  { 
         hess[i][j]=hessij(p,delti,i,j);    double brent(double ax, double bx, double cx, 
         hess[j][i]=hess[i][j];                     double (*f)(double), double tol, double *xmin); 
         /*printf(" %lf ",hess[i][j]);*/    double f1dim(double x); 
       }    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     }                double *fc, double (*func)(double)); 
   }    int j; 
   printf("\n");    double xx,xmin,bx,ax; 
     double fx,fb,fa;
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");   
      ncom=n; 
   a=matrix(1,npar,1,npar);    pcom=vector(1,n); 
   y=matrix(1,npar,1,npar);    xicom=vector(1,n); 
   x=vector(1,npar);    nrfunc=func; 
   indx=ivector(1,npar);    for (j=1;j<=n;j++) { 
   for (i=1;i<=npar;i++)      pcom[j]=p[j]; 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      xicom[j]=xi[j]; 
   ludcmp(a,npar,indx,&pd);    } 
     ax=0.0; 
   for (j=1;j<=npar;j++) {    xx=1.0; 
     for (i=1;i<=npar;i++) x[i]=0;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     x[j]=1;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     lubksb(a,npar,indx,x);  #ifdef DEBUG
     for (i=1;i<=npar;i++){    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
       matcov[i][j]=x[i];    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     }  #endif
   }    for (j=1;j<=n;j++) { 
       xi[j] *= xmin; 
   printf("\n#Hessian matrix#\n");      p[j] += xi[j]; 
   for (i=1;i<=npar;i++) {    } 
     for (j=1;j<=npar;j++) {    free_vector(xicom,1,n); 
       printf("%.3e ",hess[i][j]);    free_vector(pcom,1,n); 
     }  } 
     printf("\n");  
   }  char *asc_diff_time(long time_sec, char ascdiff[])
   {
   /* Recompute Inverse */    long sec_left, days, hours, minutes;
   for (i=1;i<=npar;i++)    days = (time_sec) / (60*60*24);
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    sec_left = (time_sec) % (60*60*24);
   ludcmp(a,npar,indx,&pd);    hours = (sec_left) / (60*60) ;
     sec_left = (sec_left) %(60*60);
   /*  printf("\n#Hessian matrix recomputed#\n");    minutes = (sec_left) /60;
     sec_left = (sec_left) % (60);
   for (j=1;j<=npar;j++) {    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
     for (i=1;i<=npar;i++) x[i]=0;    return ascdiff;
     x[j]=1;  }
     lubksb(a,npar,indx,x);  
     for (i=1;i<=npar;i++){  /*************** powell ************************/
       y[i][j]=x[i];  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       printf("%.3e ",y[i][j]);              double (*func)(double [])) 
     }  { 
     printf("\n");    void linmin(double p[], double xi[], int n, double *fret, 
   }                double (*func)(double [])); 
   */    int i,ibig,j; 
     double del,t,*pt,*ptt,*xit;
   free_matrix(a,1,npar,1,npar);    double fp,fptt;
   free_matrix(y,1,npar,1,npar);    double *xits;
   free_vector(x,1,npar);    int niterf, itmp;
   free_ivector(indx,1,npar);  
   free_matrix(hess,1,npar,1,npar);    pt=vector(1,n); 
     ptt=vector(1,n); 
     xit=vector(1,n); 
 }    xits=vector(1,n); 
     *fret=(*func)(p); 
 /*************** hessian matrix ****************/    for (j=1;j<=n;j++) pt[j]=p[j]; 
 double hessii( double x[], double delta, int theta, double delti[])    for (*iter=1;;++(*iter)) { 
 {      fp=(*fret); 
   int i;      ibig=0; 
   int l=1, lmax=20;      del=0.0; 
   double k1,k2;      last_time=curr_time;
   double p2[NPARMAX+1];      (void) gettimeofday(&curr_time,&tzp);
   double res;      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);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;      /*    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);
   double fx;      fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec);
   int k=0,kmax=10;      */
   double l1;     for (i=1;i<=n;i++) {
         printf(" %d %.12f",i, p[i]);
   fx=func(x);        fprintf(ficlog," %d %.12lf",i, p[i]);
   for (i=1;i<=npar;i++) p2[i]=x[i];        fprintf(ficrespow," %.12lf", p[i]);
   for(l=0 ; l <=lmax; l++){      }
     l1=pow(10,l);      printf("\n");
     delts=delt;      fprintf(ficlog,"\n");
     for(k=1 ; k <kmax; k=k+1){      fprintf(ficrespow,"\n");fflush(ficrespow);
       delt = delta*(l1*k);      if(*iter <=3){
       p2[theta]=x[theta] +delt;        tm = *localtime(&curr_time.tv_sec);
       k1=func(p2)-fx;        strcpy(strcurr,asctime(&tm));
       p2[theta]=x[theta]-delt;  /*       asctime_r(&tm,strcurr); */
       k2=func(p2)-fx;        forecast_time=curr_time; 
       /*res= (k1-2.0*fx+k2)/delt/delt; */        itmp = strlen(strcurr);
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
                strcurr[itmp-1]='\0';
 #ifdef DEBUG        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
       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);        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 #endif        for(niterf=10;niterf<=30;niterf+=10){
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){          tmf = *localtime(&forecast_time.tv_sec);
         k=kmax;  /*      asctime_r(&tmf,strfor); */
       }          strcpy(strfor,asctime(&tmf));
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */          itmp = strlen(strfor);
         k=kmax; l=lmax*10.;          if(strfor[itmp-1]=='\n')
       }          strfor[itmp-1]='\0';
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){          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);
         delts=delt;          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);
       }        }
     }      }
   }      for (i=1;i<=n;i++) { 
   delti[theta]=delts;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   return res;        fptt=(*fret); 
    #ifdef DEBUG
 }        printf("fret=%lf \n",*fret);
         fprintf(ficlog,"fret=%lf \n",*fret);
 double hessij( double x[], double delti[], int thetai,int thetaj)  #endif
 {        printf("%d",i);fflush(stdout);
   int i;        fprintf(ficlog,"%d",i);fflush(ficlog);
   int l=1, l1, lmax=20;        linmin(p,xit,n,fret,func); 
   double k1,k2,k3,k4,res,fx;        if (fabs(fptt-(*fret)) > del) { 
   double p2[NPARMAX+1];          del=fabs(fptt-(*fret)); 
   int k;          ibig=i; 
         } 
   fx=func(x);  #ifdef DEBUG
   for (k=1; k<=2; k++) {        printf("%d %.12e",i,(*fret));
     for (i=1;i<=npar;i++) p2[i]=x[i];        fprintf(ficlog,"%d %.12e",i,(*fret));
     p2[thetai]=x[thetai]+delti[thetai]/k;        for (j=1;j<=n;j++) {
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     k1=func(p2)-fx;          printf(" x(%d)=%.12e",j,xit[j]);
            fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     p2[thetai]=x[thetai]+delti[thetai]/k;        }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        for(j=1;j<=n;j++) {
     k2=func(p2)-fx;          printf(" p=%.12e",p[j]);
            fprintf(ficlog," p=%.12e",p[j]);
     p2[thetai]=x[thetai]-delti[thetai]/k;        }
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        printf("\n");
     k3=func(p2)-fx;        fprintf(ficlog,"\n");
    #endif
     p2[thetai]=x[thetai]-delti[thetai]/k;      } 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     k4=func(p2)-fx;  #ifdef DEBUG
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */        int k[2],l;
 #ifdef DEBUG        k[0]=1;
     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);        k[1]=-1;
 #endif        printf("Max: %.12e",(*func)(p));
   }        fprintf(ficlog,"Max: %.12e",(*func)(p));
   return res;        for (j=1;j<=n;j++) {
 }          printf(" %.12e",p[j]);
           fprintf(ficlog," %.12e",p[j]);
 /************** Inverse of matrix **************/        }
 void ludcmp(double **a, int n, int *indx, double *d)        printf("\n");
 {        fprintf(ficlog,"\n");
   int i,imax,j,k;        for(l=0;l<=1;l++) {
   double big,dum,sum,temp;          for (j=1;j<=n;j++) {
   double *vv;            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]);
   vv=vector(1,n);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   *d=1.0;          }
   for (i=1;i<=n;i++) {          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     big=0.0;          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     for (j=1;j<=n;j++)        }
       if ((temp=fabs(a[i][j])) > big) big=temp;  #endif
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  
     vv[i]=1.0/big;  
   }        free_vector(xit,1,n); 
   for (j=1;j<=n;j++) {        free_vector(xits,1,n); 
     for (i=1;i<j;i++) {        free_vector(ptt,1,n); 
       sum=a[i][j];        free_vector(pt,1,n); 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];        return; 
       a[i][j]=sum;      } 
     }      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     big=0.0;      for (j=1;j<=n;j++) { 
     for (i=j;i<=n;i++) {        ptt[j]=2.0*p[j]-pt[j]; 
       sum=a[i][j];        xit[j]=p[j]-pt[j]; 
       for (k=1;k<j;k++)        pt[j]=p[j]; 
         sum -= a[i][k]*a[k][j];      } 
       a[i][j]=sum;      fptt=(*func)(ptt); 
       if ( (dum=vv[i]*fabs(sum)) >= big) {      if (fptt < fp) { 
         big=dum;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
         imax=i;        if (t < 0.0) { 
       }          linmin(p,xit,n,fret,func); 
     }          for (j=1;j<=n;j++) { 
     if (j != imax) {            xi[j][ibig]=xi[j][n]; 
       for (k=1;k<=n;k++) {            xi[j][n]=xit[j]; 
         dum=a[imax][k];          }
         a[imax][k]=a[j][k];  #ifdef DEBUG
         a[j][k]=dum;          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);
       *d = -(*d);          for(j=1;j<=n;j++){
       vv[imax]=vv[j];            printf(" %.12e",xit[j]);
     }            fprintf(ficlog," %.12e",xit[j]);
     indx[j]=imax;          }
     if (a[j][j] == 0.0) a[j][j]=TINY;          printf("\n");
     if (j != n) {          fprintf(ficlog,"\n");
       dum=1.0/(a[j][j]);  #endif
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        }
     }      } 
   }    } 
   free_vector(vv,1,n);  /* Doesn't work */  } 
 ;  
 }  /**** Prevalence limit (stable or period prevalence)  ****************/
   
 void lubksb(double **a, int n, int *indx, double b[])  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
 {  {
   int i,ii=0,ip,j;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   double sum;       matrix by transitions matrix until convergence is reached */
    
   for (i=1;i<=n;i++) {    int i, ii,j,k;
     ip=indx[i];    double min, max, maxmin, maxmax,sumnew=0.;
     sum=b[ip];    double **matprod2();
     b[ip]=b[i];    double **out, cov[NCOVMAX], **pmij();
     if (ii)    double **newm;
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];    double agefin, delaymax=50 ; /* Max number of years to converge */
     else if (sum) ii=i;  
     b[i]=sum;    for (ii=1;ii<=nlstate+ndeath;ii++)
   }      for (j=1;j<=nlstate+ndeath;j++){
   for (i=n;i>=1;i--) {        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     sum=b[i];      }
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];  
     b[i]=sum/a[i][i];     cov[1]=1.;
   }   
 }   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
 /************ Frequencies ********************/      newm=savm;
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)      /* Covariates have to be included here again */
 {  /* Some frequencies */       cov[2]=agefin;
      
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;        for (k=1; k<=cptcovn;k++) {
   double ***freq; /* Frequencies */          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   double *pp;          /*      printf("ij=%d k=%d Tvar[k]=%d nbcode=%d cov=%lf codtab[ij][Tvar[k]]=%d \n",ij,k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], codtab[ij][Tvar[k]]);*/
   double pos;        }
   FILE *ficresp;        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   char fileresp[FILENAMELENGTH];        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]]];
   pp=vector(1,nlstate);  
  probs= ma3x(1,130 ,1,8, 1,8);        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   strcpy(fileresp,"p");        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   strcat(fileresp,fileres);        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   if((ficresp=fopen(fileresp,"w"))==NULL) {      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
     printf("Problem with prevalence resultfile: %s\n", fileresp);  
     exit(0);      savm=oldm;
   }      oldm=newm;
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);      maxmax=0.;
   j1=0;      for(j=1;j<=nlstate;j++){
         min=1.;
   j=cptcoveff;        max=0.;
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for(i=1; i<=nlstate; i++) {
           sumnew=0;
   for(k1=1; k1<=j;k1++){          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
    for(i1=1; i1<=ncodemax[k1];i1++){          prlim[i][j]= newm[i][j]/(1-sumnew);
        j1++;          max=FMAX(max,prlim[i][j]);
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          min=FMIN(min,prlim[i][j]);
          scanf("%d", i);*/        }
         for (i=-1; i<=nlstate+ndeath; i++)          maxmin=max-min;
          for (jk=-1; jk<=nlstate+ndeath; jk++)          maxmax=FMAX(maxmax,maxmin);
            for(m=agemin; m <= agemax+3; m++)      }
              freq[i][jk][m]=0;      if(maxmax < ftolpl){
                return prlim;
        for (i=1; i<=imx; i++) {      }
          bool=1;    }
          if  (cptcovn>0) {  }
            for (z1=1; z1<=cptcoveff; z1++)  
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])  /*************** transition probabilities ***************/ 
                bool=0;  
          }  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
           if (bool==1) {  {
            for(m=firstpass; m<=lastpass-1; m++){    double s1, s2;
              if(agev[m][i]==0) agev[m][i]=agemax+1;    /*double t34;*/
              if(agev[m][i]==1) agev[m][i]=agemax+2;    int i,j,j1, nc, ii, jj;
              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];      for(i=1; i<= nlstate; i++){
            }        for(j=1; j<i;j++){
          }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
        }            /*s2 += param[i][j][nc]*cov[nc];*/
         if  (cptcovn>0) {            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
          fprintf(ficresp, "\n#********** Variable ");  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          }
        fprintf(ficresp, "**********\n#");          ps[i][j]=s2;
         }  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
        for(i=1; i<=nlstate;i++)        }
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        for(j=i+1; j<=nlstate+ndeath;j++){
        fprintf(ficresp, "\n");          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];
   for(i=(int)agemin; i <= (int)agemax+3; i++){  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
     if(i==(int)agemax+3)          }
       printf("Total");          ps[i][j]=s2;
     else        }
       printf("Age %d", i);      }
     for(jk=1; jk <=nlstate ; jk++){      /*ps[3][2]=1;*/
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      
         pp[jk] += freq[jk][m][i];      for(i=1; i<= nlstate; i++){
     }        s1=0;
     for(jk=1; jk <=nlstate ; jk++){        for(j=1; j<i; j++)
       for(m=-1, pos=0; m <=0 ; m++)          s1+=exp(ps[i][j]);
         pos += freq[jk][m][i];        for(j=i+1; j<=nlstate+ndeath; j++)
       if(pp[jk]>=1.e-10)          s1+=exp(ps[i][j]);
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        ps[i][i]=1./(s1+1.);
       else        for(j=1; j<i; j++)
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          ps[i][j]= exp(ps[i][j])*ps[i][i];
     }        for(j=i+1; j<=nlstate+ndeath; j++)
     for(jk=1; jk <=nlstate ; jk++){          ps[i][j]= exp(ps[i][j])*ps[i][i];
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
         pp[jk] += freq[jk][m][i];      } /* end i */
     }      
     for(jk=1,pos=0; jk <=nlstate ; jk++)      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
       pos += pp[jk];        for(jj=1; jj<= nlstate+ndeath; jj++){
     for(jk=1; jk <=nlstate ; jk++){          ps[ii][jj]=0;
       if(pos>=1.e-5)          ps[ii][ii]=1;
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);        }
       else      }
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);      
       if( i <= (int) agemax){  
         if(pos>=1.e-5){  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
           probs[i][jk][j1]= pp[jk]/pos;  /*         printf("ddd %lf ",ps[ii][jj]); */
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/  /*       } */
         }  /*       printf("\n "); */
       else  /*        } */
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);  /*        printf("\n ");printf("%lf ",cov[2]); */
       }         /*
     }        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     for(jk=-1; jk <=nlstate+ndeath; jk++)        goto end;*/
       for(m=-1; m <=nlstate+ndeath; m++)      return ps;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);  }
     if(i <= (int) agemax)  
       fprintf(ficresp,"\n");  /**************** Product of 2 matrices ******************/
     printf("\n");  
     }  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
     }  {
  }    /* 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(...) */
   fclose(ficresp);    /* in, b, out are matrice of pointers which should have been initialized 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);       before: only the contents of out is modified. The function returns
   free_vector(pp,1,nlstate);       a pointer to pointers identical to out */
     long i, j, k;
 }  /* End of Freq */    for(i=nrl; i<= nrh; i++)
       for(k=ncolol; k<=ncoloh; k++)
 /************* Waves Concatenation ***************/        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)  
 {    return out;
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.  }
      Death is a valid wave (if date is known).  
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i  
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]  /************* Higher Matrix Product ***************/
      and mw[mi+1][i]. dh depends on stepm.  
      */  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   {
   int i, mi, m;    /* Computes the transition matrix starting at age 'age' over 
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;       'nhstepm*hstepm*stepm' months (i.e. until
      double sum=0., jmean=0.;*/       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
   int j, k=0,jk, ju, jl;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
   double sum=0.;       (typically every 2 years instead of every month which is too big 
   jmin=1e+5;       for the memory).
   jmax=-1;       Model is determined by parameters x and covariates have to be 
   jmean=0.;       included manually here. 
   for(i=1; i<=imx; i++){  
     mi=0;       */
     m=firstpass;  
     while(s[m][i] <= nlstate){    int i, j, d, h, k;
       if(s[m][i]>=1)    double **out, cov[NCOVMAX];
         mw[++mi][i]=m;    double **newm;
       if(m >=lastpass)  
         break;    /* Hstepm could be zero and should return the unit matrix */
       else    for (i=1;i<=nlstate+ndeath;i++)
         m++;      for (j=1;j<=nlstate+ndeath;j++){
     }/* end while */        oldm[i][j]=(i==j ? 1.0 : 0.0);
     if (s[m][i] > nlstate){        po[i][j][0]=(i==j ? 1.0 : 0.0);
       mi++;     /* Death is another wave */      }
       /* if(mi==0)  never been interviewed correctly before death */    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
          /* Only death is a correct wave */    for(h=1; h <=nhstepm; h++){
       mw[mi][i]=m;      for(d=1; d <=hstepm; d++){
     }        newm=savm;
         /* Covariates have to be included here again */
     wav[i]=mi;        cov[1]=1.;
     if(mi==0)        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   }        for (k=1; k<=cptcovage;k++)
           cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   for(i=1; i<=imx; i++){        for (k=1; k<=cptcovprod;k++)
     for(mi=1; mi<wav[i];mi++){          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
       if (stepm <=0)  
         dh[mi][i]=1;  
       else{        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
         if (s[mw[mi+1][i]][i] > nlstate) {        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
           if (agedc[i] < 2*AGESUP) {        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);                     pmij(pmmij,cov,ncovmodel,x,nlstate));
           if(j==0) j=1;  /* Survives at least one month after exam */        savm=oldm;
           k=k+1;        oldm=newm;
           if (j >= jmax) jmax=j;      }
           if (j <= jmin) jmin=j;      for(i=1; i<=nlstate+ndeath; i++)
           sum=sum+j;        for(j=1;j<=nlstate+ndeath;j++) {
           /* if (j<10) printf("j=%d num=%d ",j,i); */          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]);
         }           */
         else{        }
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));    } /* end h */
           k=k+1;    return po;
           if (j >= jmax) jmax=j;  }
           else if (j <= jmin)jmin=j;  
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */  
           sum=sum+j;  /*************** log-likelihood *************/
         }  double func( double *x)
         jk= j/stepm;  {
         jl= j -jk*stepm;    int i, ii, j, k, mi, d, kk;
         ju= j -(jk+1)*stepm;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
         if(jl <= -ju)    double **out;
           dh[mi][i]=jk;    double sw; /* Sum of weights */
         else    double lli; /* Individual log likelihood */
           dh[mi][i]=jk+1;    int s1, s2;
         if(dh[mi][i]==0)    double bbh, survp;
           dh[mi][i]=1; /* At least one step */    long ipmx;
       }    /*extern weight */
     }    /* We are differentiating ll according to initial status */
   }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   jmean=sum/k;    /*for(i=1;i<imx;i++) 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);      printf(" %d\n",s[4][i]);
  }    */
 /*********** Tricode ****************************/    cov[1]=1.;
 void tricode(int *Tvar, int **nbcode, int imx)  
 {    for(k=1; k<=nlstate; k++) ll[k]=0.;
   int Ndum[20],ij=1, k, j, i;  
   int cptcode=0;    if(mle==1){
   cptcoveff=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   for (k=0; k<19; k++) Ndum[k]=0;        for(mi=1; mi<= wav[i]-1; mi++){
   for (k=1; k<=7; k++) ncodemax[k]=0;          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=1; i<=imx; i++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       ij=(int)(covar[Tvar[j]][i]);            }
       Ndum[ij]++;          for(d=0; d<dh[mi][i]; d++){
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            newm=savm;
       if (ij > cptcode) cptcode=ij;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     }            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for (i=0; i<=cptcode; i++) {            }
       if(Ndum[i]!=0) ncodemax[j]++;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     ij=1;            savm=oldm;
             oldm=newm;
           } /* end mult */
     for (i=1; i<=ncodemax[j]; i++) {        
       for (k=0; k<=19; k++) {          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
         if (Ndum[k] != 0) {          /* But now since version 0.9 we anticipate for bias at large stepm.
           nbcode[Tvar[j]][ij]=k;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
           ij++;           * (in months) between two waves is not a multiple of stepm, we rounded to 
         }           * the nearest (and in case of equal distance, to the lowest) interval but now
         if (ij > ncodemax[j]) break;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
       }             * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
     }           * probability in order to take into account the bias as a fraction of the way
   }             * from savm to out if bh is negative or even beyond if bh is positive. bh varies
            * -stepm/2 to stepm/2 .
  for (k=0; k<19; k++) Ndum[k]=0;           * For stepm=1 the results are the same as for previous versions of Imach.
            * For stepm > 1 the results are less biased than in previous versions. 
  for (i=1; i<=ncovmodel-2; i++) {           */
       ij=Tvar[i];          s1=s[mw[mi][i]][i];
       Ndum[ij]++;          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias bh is positive if real duration
  ij=1;           * is higher than the multiple of stepm and negative otherwise.
  for (i=1; i<=10; i++) {           */
    if((Ndum[i]!=0) && (i<=ncov)){          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
      Tvaraff[ij]=i;          if( s2 > nlstate){ 
      ij++;            /* i.e. if s2 is a death state and if the date of death is known 
    }               then the contribution to the likelihood is the probability to 
  }               die between last step unit time and current  step unit time, 
                 which is also equal to probability to die before dh 
     cptcoveff=ij-1;               minus probability to die before dh-stepm . 
 }               In version up to 0.92 likelihood was computed
           as if date of death was unknown. Death was treated as any other
 /*********** Health Expectancies ****************/          health state: the date of the interview describes the actual state
           and not the date of a change in health state. The former idea was
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)          to consider that at each interview the state was recorded
 {          (healthy, disable or death) and IMaCh was corrected; but when we
   /* Health expectancies */          introduced the exact date of death then we should have modified
   int i, j, nhstepm, hstepm, h;          the contribution of an exact death to the likelihood. This new
   double age, agelim,hf;          contribution is smaller and very dependent of the step unit
   double ***p3mat;          stepm. It is no more the probability to die between last interview
            and month of death but the probability to survive from last
   fprintf(ficreseij,"# Health expectancies\n");          interview up to one month before death multiplied by the
   fprintf(ficreseij,"# Age");          probability to die within a month. Thanks to Chris
   for(i=1; i<=nlstate;i++)          Jackson for correcting this bug.  Former versions increased
     for(j=1; j<=nlstate;j++)          mortality artificially. The bad side is that we add another loop
       fprintf(ficreseij," %1d-%1d",i,j);          which slows down the processing. The difference can be up to 10%
   fprintf(ficreseij,"\n");          lower mortality.
             */
   hstepm=1*YEARM; /*  Every j years of age (in month) */            lli=log(out[s1][s2] - savm[s1][s2]);
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   
   agelim=AGESUP;          } else if  (s2==-2) {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */            for (j=1,survp=0. ; j<=nlstate; j++) 
     /* nhstepm age range expressed in number of stepm */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);            /*survp += out[s1][j]; */
     /* Typically if 20 years = 20*12/6=40 stepm */            lli= log(survp);
     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);          else if  (s2==-4) { 
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            for (j=3,survp=0. ; j<=nlstate; j++)  
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              lli= log(survp); 
           } 
   
     for(i=1; i<=nlstate;i++)          else if  (s2==-5) { 
       for(j=1; j<=nlstate;j++)            for (j=1,survp=0. ; j<=2; j++)  
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           eij[i][j][(int)age] +=p3mat[i][j][h];            lli= log(survp); 
         }          } 
              
     hf=1;          else{
     if (stepm >= YEARM) hf=stepm/YEARM;            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     fprintf(ficreseij,"%.0f",age );            /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
     for(i=1; i<=nlstate;i++)          } 
       for(j=1; j<=nlstate;j++){          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);          /*if(lli ==000.0)*/
       }          /*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); */
     fprintf(ficreseij,"\n");          ipmx +=1;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          sw += weight[i];
   }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
 }        } /* end of wave */
       } /* end of individual */
 /************ Variance ******************/    }  else if(mle==2){
 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)      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 {        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   /* Variance of health expectancies */        for(mi=1; mi<= wav[i]-1; mi++){
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          for (ii=1;ii<=nlstate+ndeath;ii++)
   double **newm;            for (j=1;j<=nlstate+ndeath;j++){
   double **dnewm,**doldm;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, j, nhstepm, hstepm, h;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int k, cptcode;            }
   double *xp;          for(d=0; d<=dh[mi][i]; d++){
   double **gp, **gm;            newm=savm;
   double ***gradg, ***trgradg;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double ***p3mat;            for (kk=1; kk<=cptcovage;kk++) {
   double age,agelim;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   int theta;            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
    fprintf(ficresvij,"# Covariances of life expectancies\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   fprintf(ficresvij,"# Age");            savm=oldm;
   for(i=1; i<=nlstate;i++)            oldm=newm;
     for(j=1; j<=nlstate;j++)          } /* end mult */
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        
   fprintf(ficresvij,"\n");          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
   xp=vector(1,npar);          bbh=(double)bh[mi][i]/(double)stepm; 
   dnewm=matrix(1,nlstate,1,npar);          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
   doldm=matrix(1,nlstate,1,nlstate);          ipmx +=1;
            sw += weight[i];
   hstepm=1*YEARM; /* Every year of age */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        } /* end of wave */
   agelim = AGESUP;      } /* end of individual */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    }  else if(mle==3){  /* exponential inter-extrapolation */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     if (stepm >= YEARM) hstepm=1;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        for(mi=1; mi<= wav[i]-1; mi++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);            for (j=1;j<=nlstate+ndeath;j++){
     gp=matrix(0,nhstepm,1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     gm=matrix(0,nhstepm,1,nlstate);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
     for(theta=1; theta <=npar; theta++){          for(d=0; d<dh[mi][i]; d++){
       for(i=1; i<=npar; i++){ /* Computes gradient */            newm=savm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       }            for (kk=1; kk<=cptcovage;kk++) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);                cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            }
       for(j=1; j<= nlstate; j++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         for(h=0; h<=nhstepm; h++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)            savm=oldm;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];            oldm=newm;
         }          } /* end mult */
       }        
              s1=s[mw[mi][i]][i];
       for(i=1; i<=npar; i++) /* Computes gradient */          s2=s[mw[mi+1][i]][i];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          bbh=(double)bh[mi][i]/(double)stepm; 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            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 */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          ipmx +=1;
       for(j=1; j<= nlstate; j++){          sw += weight[i];
         for(h=0; h<=nhstepm; h++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)        } /* end of wave */
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];      } /* end of individual */
         }    }else if (mle==4){  /* ml=4 no inter-extrapolation */
       }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(j=1; j<= nlstate; j++)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(h=0; h<=nhstepm; h++){        for(mi=1; mi<= wav[i]-1; mi++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          for (ii=1;ii<=nlstate+ndeath;ii++)
         }            for (j=1;j<=nlstate+ndeath;j++){
     } /* End theta */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);            }
           for(d=0; d<dh[mi][i]; d++){
     for(h=0; h<=nhstepm; h++)            newm=savm;
       for(j=1; j<=nlstate;j++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         for(theta=1; theta <=npar; theta++)            for (kk=1; kk<=cptcovage;kk++) {
           trgradg[h][j][theta]=gradg[h][theta][j];              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
     for(i=1;i<=nlstate;i++)          
       for(j=1;j<=nlstate;j++)            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         vareij[i][j][(int)age] =0.;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for(h=0;h<=nhstepm;h++){            savm=oldm;
       for(k=0;k<=nhstepm;k++){            oldm=newm;
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);          } /* end mult */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        
         for(i=1;i<=nlstate;i++)          s1=s[mw[mi][i]][i];
           for(j=1;j<=nlstate;j++)          s2=s[mw[mi+1][i]][i];
             vareij[i][j][(int)age] += doldm[i][j];          if( s2 > nlstate){ 
       }            lli=log(out[s1][s2] - savm[s1][s2]);
     }          }else{
     h=1;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     if (stepm >= YEARM) h=stepm/YEARM;          }
     fprintf(ficresvij,"%.0f ",age );          ipmx +=1;
     for(i=1; i<=nlstate;i++)          sw += weight[i];
       for(j=1; j<=nlstate;j++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
       }        } /* end of wave */
     fprintf(ficresvij,"\n");      } /* end of individual */
     free_matrix(gp,0,nhstepm,1,nlstate);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     free_matrix(gm,0,nhstepm,1,nlstate);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
   } /* End age */            for (j=1;j<=nlstate+ndeath;j++){
                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_vector(xp,1,npar);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_matrix(doldm,1,nlstate,1,npar);            }
   free_matrix(dnewm,1,nlstate,1,nlstate);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
 }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
 /************ Variance of prevlim ******************/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 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)            }
 {          
   /* Variance of prevalence limit */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double **newm;            savm=oldm;
   double **dnewm,**doldm;            oldm=newm;
   int i, j, nhstepm, hstepm;          } /* end mult */
   int k, cptcode;        
   double *xp;          s1=s[mw[mi][i]][i];
   double *gp, *gm;          s2=s[mw[mi+1][i]][i];
   double **gradg, **trgradg;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   double age,agelim;          ipmx +=1;
   int theta;          sw += weight[i];
              ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
   fprintf(ficresvpl,"# Age");        } /* end of wave */
   for(i=1; i<=nlstate;i++)      } /* end of individual */
       fprintf(ficresvpl," %1d-%1d",i,i);    } /* End of if */
   fprintf(ficresvpl,"\n");    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   xp=vector(1,npar);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   dnewm=matrix(1,nlstate,1,npar);    return -l;
   doldm=matrix(1,nlstate,1,nlstate);  }
    
   hstepm=1*YEARM; /* Every year of age */  /*************** log-likelihood *************/
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  double funcone( double *x)
   agelim = AGESUP;  {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    /* Same as likeli but slower because of a lot of printf and if */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    int i, ii, j, k, mi, d, kk;
     if (stepm >= YEARM) hstepm=1;    double l, ll[NLSTATEMAX], cov[NCOVMAX];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    double **out;
     gradg=matrix(1,npar,1,nlstate);    double lli; /* Individual log likelihood */
     gp=vector(1,nlstate);    double llt;
     gm=vector(1,nlstate);    int s1, s2;
     double bbh, survp;
     for(theta=1; theta <=npar; theta++){    /*extern weight */
       for(i=1; i<=npar; i++){ /* Computes gradient */    /* We are differentiating ll according to initial status */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       }    /*for(i=1;i<imx;i++) 
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      printf(" %d\n",s[4][i]);
       for(i=1;i<=nlstate;i++)    */
         gp[i] = prlim[i][i];    cov[1]=1.;
      
       for(i=1; i<=npar; i++) /* Computes gradient */    for(k=1; k<=nlstate; k++) ll[k]=0.;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for(i=1;i<=nlstate;i++)      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         gm[i] = prlim[i][i];      for(mi=1; mi<= wav[i]-1; mi++){
         for (ii=1;ii<=nlstate+ndeath;ii++)
       for(i=1;i<=nlstate;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);
     } /* End theta */            savm[ii][j]=(ii==j ? 1.0 : 0.0);
           }
     trgradg =matrix(1,nlstate,1,npar);        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
     for(j=1; j<=nlstate;j++)          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       for(theta=1; theta <=npar; theta++)          for (kk=1; kk<=cptcovage;kk++) {
         trgradg[j][theta]=gradg[theta][j];            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           }
     for(i=1;i<=nlstate;i++)          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       varpl[i][(int)age] =0.;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);          savm=oldm;
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);          oldm=newm;
     for(i=1;i<=nlstate;i++)        } /* end mult */
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */        
         s1=s[mw[mi][i]][i];
     fprintf(ficresvpl,"%.0f ",age );        s2=s[mw[mi+1][i]][i];
     for(i=1; i<=nlstate;i++)        bbh=(double)bh[mi][i]/(double)stepm; 
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));        /* bias is positive if real duration
     fprintf(ficresvpl,"\n");         * is higher than the multiple of stepm and negative otherwise.
     free_vector(gp,1,nlstate);         */
     free_vector(gm,1,nlstate);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     free_matrix(gradg,1,npar,1,nlstate);          lli=log(out[s1][s2] - savm[s1][s2]);
     free_matrix(trgradg,1,nlstate,1,npar);        } else if  (s2==-2) {
   } /* End age */          for (j=1,survp=0. ; j<=nlstate; j++) 
             survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   free_vector(xp,1,npar);          lli= log(survp);
   free_matrix(doldm,1,nlstate,1,npar);        }else if (mle==1){
   free_matrix(dnewm,1,nlstate,1,nlstate);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
         } 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 */
         } else if(mle==3){  /* exponential inter-extrapolation */
 /************ Variance of one-step probabilities  ******************/          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 */
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)        } else if (mle==4){  /* mle=4 no inter-extrapolation */
 {          lli=log(out[s1][s2]); /* Original formula */
   int i, j;        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
   int k=0, cptcode;          lli=log(out[s1][s2]); /* Original formula */
   double **dnewm,**doldm;        } /* End of if */
   double *xp;        ipmx +=1;
   double *gp, *gm;        sw += weight[i];
   double **gradg, **trgradg;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double age,agelim, cov[NCOVMAX];  /*       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]); */
   int theta;        if(globpr){
   char fileresprob[FILENAMELENGTH];          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
    %11.6f %11.6f %11.6f ", \
   strcpy(fileresprob,"prob");                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
   strcat(fileresprob,fileres);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     printf("Problem with resultfile: %s\n", fileresprob);            llt +=ll[k]*gipmx/gsw;
   }            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);          }
            fprintf(ficresilk," %10.6f\n", -llt);
         }
   xp=vector(1,npar);      } /* end of wave */
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    } /* end of individual */
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   cov[1]=1;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   for (age=bage; age<=fage; age ++){    if(globpr==0){ /* First time we count the contributions and weights */
     cov[2]=age;      gipmx=ipmx;
     gradg=matrix(1,npar,1,9);      gsw=sw;
     trgradg=matrix(1,9,1,npar);    }
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    return -l;
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));  }
      
     for(theta=1; theta <=npar; theta++){  
       for(i=1; i<=npar; i++)  /*************** function likelione ***********/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
        {
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    /* This routine should help understanding what is done with 
           the selection of individuals/waves and
       k=0;       to check the exact contribution to the likelihood.
       for(i=1; i<= (nlstate+ndeath); i++){       Plotting could be done.
         for(j=1; j<=(nlstate+ndeath);j++){     */
            k=k+1;    int k;
           gp[k]=pmmij[i][j];  
         }    if(*globpri !=0){ /* Just counts and sums, no printings */
       }      strcpy(fileresilk,"ilk"); 
       strcat(fileresilk,fileres);
       for(i=1; i<=npar; i++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        printf("Problem with resultfile: %s\n", fileresilk);
            fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       }
       pmij(pmmij,cov,ncovmodel,xp,nlstate);      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");
       k=0;      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       for(i=1; i<=(nlstate+ndeath); 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(j=1; j<=(nlstate+ndeath);j++){      for(k=1; k<=nlstate; k++) 
           k=k+1;        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
           gm[k]=pmmij[i][j];      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
         }    }
       }  
          *fretone=(*funcone)(p);
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)    if(*globpri !=0){
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        fclose(ficresilk);
     }      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       fflush(fichtm); 
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    } 
       for(theta=1; theta <=npar; theta++)    return;
       trgradg[j][theta]=gradg[theta][j];  }
    
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);  
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);  /*********** Maximum Likelihood Estimation ***************/
   
      pmij(pmmij,cov,ncovmodel,x,nlstate);  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   {
      k=0;    int i,j, iter;
      for(i=1; i<=(nlstate+ndeath); i++){    double **xi;
        for(j=1; j<=(nlstate+ndeath);j++){    double fret;
          k=k+1;    double fretone; /* Only one call to likelihood */
          gm[k]=pmmij[i][j];    /*  char filerespow[FILENAMELENGTH];*/
         }    xi=matrix(1,npar,1,npar);
      }    for (i=1;i<=npar;i++)
            for (j=1;j<=npar;j++)
      /*printf("\n%d ",(int)age);        xi[i][j]=(i==j ? 1.0 : 0.0);
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    printf("Powell\n");  fprintf(ficlog,"Powell\n");
            strcpy(filerespow,"pow"); 
     strcat(filerespow,fileres);
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    if((ficrespow=fopen(filerespow,"w"))==NULL) {
      }*/      printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   fprintf(ficresprob,"\n%d ",(int)age);    }
     fprintf(ficrespow,"# Powell\n# iter -2*LL");
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    for (i=1;i<=nlstate;i++)
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      for(j=1;j<=nlstate+ndeath;j++)
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   }    fprintf(ficrespow,"\n");
   
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    powell(p,xi,npar,ftol,&iter,&fret,func);
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));  
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    free_matrix(xi,1,npar,1,npar);
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    fclose(ficrespow);
 }    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
  free_vector(xp,1,npar);    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
 fclose(ficresprob);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
  exit(0);  
 }  }
   
 /***********************************************/  /**** Computes Hessian and covariance matrix ***/
 /**************** Main Program *****************/  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
 /***********************************************/  {
     double  **a,**y,*x,pd;
 /*int main(int argc, char *argv[])*/    double **hess;
 int main()    int i, j,jk;
 {    int *indx;
   
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   double agedeb, agefin,hf;    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   double agemin=1.e20, agemax=-1.e20;    void lubksb(double **a, int npar, int *indx, double b[]) ;
     void ludcmp(double **a, int npar, int *indx, double *d) ;
   double fret;    double gompertz(double p[]);
   double **xi,tmp,delta;    hess=matrix(1,npar,1,npar);
   
   double dum; /* Dummy variable */    printf("\nCalculation of the hessian matrix. Wait...\n");
   double ***p3mat;    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   int *indx;    for (i=1;i<=npar;i++){
   char line[MAXLINE], linepar[MAXLINE];      printf("%d",i);fflush(stdout);
   char title[MAXLINE];      fprintf(ficlog,"%d",i);fflush(ficlog);
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];     
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   char filerest[FILENAMELENGTH];      
   char fileregp[FILENAMELENGTH];      /*  printf(" %f ",p[i]);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   int firstobs=1, lastobs=10;    }
   int sdeb, sfin; /* Status at beginning and end */    
   int c,  h , cpt,l;    for (i=1;i<=npar;i++) {
   int ju,jl, mi;      for (j=1;j<=npar;j++)  {
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;        if (j>i) { 
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          printf(".%d%d",i,j);fflush(stdout);
            fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   int hstepm, nhstepm;          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double bage, fage, age, agelim, agebase;          
   double ftolpl=FTOL;          hess[j][i]=hess[i][j];    
   double **prlim;          /*printf(" %lf ",hess[i][j]);*/
   double *severity;        }
   double ***param; /* Matrix of parameters */      }
   double  *p;    }
   double **matcov; /* Matrix of covariance */    printf("\n");
   double ***delti3; /* Scale */    fprintf(ficlog,"\n");
   double *delti; /* Scale */  
   double ***eij, ***vareij;    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   double **varpl; /* Variances of prevalence limits by age */    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   double *epj, vepp;    
   double kk1;    a=matrix(1,npar,1,npar);
     y=matrix(1,npar,1,npar);
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";    x=vector(1,npar);
   char *alph[]={"a","a","b","c","d","e"}, str[4];    indx=ivector(1,npar);
     for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   char z[1]="c", occ;    ludcmp(a,npar,indx,&pd);
 #include <sys/time.h>  
 #include <time.h>    for (j=1;j<=npar;j++) {
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];      for (i=1;i<=npar;i++) x[i]=0;
   /* long total_usecs;      x[j]=1;
   struct timeval start_time, end_time;      lubksb(a,npar,indx,x);
        for (i=1;i<=npar;i++){ 
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */        matcov[i][j]=x[i];
       }
     }
   printf("\nIMACH, Version 0.64b");  
   printf("\nEnter the parameter file name: ");    printf("\n#Hessian matrix#\n");
     fprintf(ficlog,"\n#Hessian matrix#\n");
 #ifdef windows    for (i=1;i<=npar;i++) { 
   scanf("%s",pathtot);      for (j=1;j<=npar;j++) { 
   getcwd(pathcd, size);        printf("%.3e ",hess[i][j]);
   /*cygwin_split_path(pathtot,path,optionfile);        fprintf(ficlog,"%.3e ",hess[i][j]);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/      }
   /* cutv(path,optionfile,pathtot,'\\');*/      printf("\n");
       fprintf(ficlog,"\n");
 split(pathtot, path,optionfile);    }
   chdir(path);  
   replace(pathc,path);    /* Recompute Inverse */
 #endif    for (i=1;i<=npar;i++)
 #ifdef unix      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   scanf("%s",optionfile);    ludcmp(a,npar,indx,&pd);
 #endif  
     /*  printf("\n#Hessian matrix recomputed#\n");
 /*-------- arguments in the command line --------*/  
     for (j=1;j<=npar;j++) {
   strcpy(fileres,"r");      for (i=1;i<=npar;i++) x[i]=0;
   strcat(fileres, optionfile);      x[j]=1;
       lubksb(a,npar,indx,x);
   /*---------arguments file --------*/      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        printf("%.3e ",y[i][j]);
     printf("Problem with optionfile %s\n",optionfile);        fprintf(ficlog,"%.3e ",y[i][j]);
     goto end;      }
   }      printf("\n");
       fprintf(ficlog,"\n");
   strcpy(filereso,"o");    }
   strcat(filereso,fileres);    */
   if((ficparo=fopen(filereso,"w"))==NULL) {  
     printf("Problem with Output resultfile: %s\n", filereso);goto end;    free_matrix(a,1,npar,1,npar);
   }    free_matrix(y,1,npar,1,npar);
     free_vector(x,1,npar);
   /* Reads comments: lines beginning with '#' */    free_ivector(indx,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){    free_matrix(hess,1,npar,1,npar);
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);  
     puts(line);  }
     fputs(line,ficparo);  
   }  /*************** hessian matrix ****************/
   ungetc(c,ficpar);  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   {
   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);    int i;
   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);    int l=1, lmax=20;
   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);    double k1,k2;
     double p2[NPARMAX+1];
   covar=matrix(0,NCOVMAX,1,n);    double res;
   cptcovn=0;    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    double fx;
     int k=0,kmax=10;
   ncovmodel=2+cptcovn;    double l1;
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */  
      fx=func(x);
   /* Read guess parameters */    for (i=1;i<=npar;i++) p2[i]=x[i];
   /* Reads comments: lines beginning with '#' */    for(l=0 ; l <=lmax; l++){
   while((c=getc(ficpar))=='#' && c!= EOF){      l1=pow(10,l);
     ungetc(c,ficpar);      delts=delt;
     fgets(line, MAXLINE, ficpar);      for(k=1 ; k <kmax; k=k+1){
     puts(line);        delt = delta*(l1*k);
     fputs(line,ficparo);        p2[theta]=x[theta] +delt;
   }        k1=func(p2)-fx;
   ungetc(c,ficpar);        p2[theta]=x[theta]-delt;
          k2=func(p2)-fx;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        /*res= (k1-2.0*fx+k2)/delt/delt; */
     for(i=1; i <=nlstate; i++)        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     for(j=1; j <=nlstate+ndeath-1; j++){        
       fscanf(ficpar,"%1d%1d",&i1,&j1);  #ifdef DEBUG
       fprintf(ficparo,"%1d%1d",i1,j1);        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);
       printf("%1d%1d",i,j);        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);
       for(k=1; k<=ncovmodel;k++){  #endif
         fscanf(ficpar," %lf",&param[i][j][k]);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         printf(" %lf",param[i][j][k]);        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
         fprintf(ficparo," %lf",param[i][j][k]);          k=kmax;
       }        }
       fscanf(ficpar,"\n");        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
       printf("\n");          k=kmax; l=lmax*10.;
       fprintf(ficparo,"\n");        }
     }        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            delts=delt;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        }
       }
   p=param[1][1];    }
      delti[theta]=delts;
   /* Reads comments: lines beginning with '#' */    return res; 
   while((c=getc(ficpar))=='#' && c!= EOF){    
     ungetc(c,ficpar);  }
     fgets(line, MAXLINE, ficpar);  
     puts(line);  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
     fputs(line,ficparo);  {
   }    int i;
   ungetc(c,ficpar);    int l=1, l1, lmax=20;
     double k1,k2,k3,k4,res,fx;
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    double p2[NPARMAX+1];
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */    int k;
   for(i=1; i <=nlstate; i++){  
     for(j=1; j <=nlstate+ndeath-1; j++){    fx=func(x);
       fscanf(ficpar,"%1d%1d",&i1,&j1);    for (k=1; k<=2; k++) {
       printf("%1d%1d",i,j);      for (i=1;i<=npar;i++) p2[i]=x[i];
       fprintf(ficparo,"%1d%1d",i1,j1);      p2[thetai]=x[thetai]+delti[thetai]/k;
       for(k=1; k<=ncovmodel;k++){      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
         fscanf(ficpar,"%le",&delti3[i][j][k]);      k1=func(p2)-fx;
         printf(" %le",delti3[i][j][k]);    
         fprintf(ficparo," %le",delti3[i][j][k]);      p2[thetai]=x[thetai]+delti[thetai]/k;
       }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       fscanf(ficpar,"\n");      k2=func(p2)-fx;
       printf("\n");    
       fprintf(ficparo,"\n");      p2[thetai]=x[thetai]-delti[thetai]/k;
     }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   }      k3=func(p2)-fx;
   delti=delti3[1][1];    
        p2[thetai]=x[thetai]-delti[thetai]/k;
   /* Reads comments: lines beginning with '#' */      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   while((c=getc(ficpar))=='#' && c!= EOF){      k4=func(p2)-fx;
     ungetc(c,ficpar);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     fgets(line, MAXLINE, ficpar);  #ifdef DEBUG
     puts(line);      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);
     fputs(line,ficparo);      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);
   }  #endif
   ungetc(c,ficpar);    }
      return res;
   matcov=matrix(1,npar,1,npar);  }
   for(i=1; i <=npar; i++){  
     fscanf(ficpar,"%s",&str);  /************** Inverse of matrix **************/
     printf("%s",str);  void ludcmp(double **a, int n, int *indx, double *d) 
     fprintf(ficparo,"%s",str);  { 
     for(j=1; j <=i; j++){    int i,imax,j,k; 
       fscanf(ficpar," %le",&matcov[i][j]);    double big,dum,sum,temp; 
       printf(" %.5le",matcov[i][j]);    double *vv; 
       fprintf(ficparo," %.5le",matcov[i][j]);   
     }    vv=vector(1,n); 
     fscanf(ficpar,"\n");    *d=1.0; 
     printf("\n");    for (i=1;i<=n;i++) { 
     fprintf(ficparo,"\n");      big=0.0; 
   }      for (j=1;j<=n;j++) 
   for(i=1; i <=npar; i++)        if ((temp=fabs(a[i][j])) > big) big=temp; 
     for(j=i+1;j<=npar;j++)      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
       matcov[i][j]=matcov[j][i];      vv[i]=1.0/big; 
        } 
   printf("\n");    for (j=1;j<=n;j++) { 
       for (i=1;i<j;i++) { 
         sum=a[i][j]; 
     /*-------- data file ----------*/        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     if((ficres =fopen(fileres,"w"))==NULL) {        a[i][j]=sum; 
       printf("Problem with resultfile: %s\n", fileres);goto end;      } 
     }      big=0.0; 
     fprintf(ficres,"#%s\n",version);      for (i=j;i<=n;i++) { 
            sum=a[i][j]; 
     if((fic=fopen(datafile,"r"))==NULL)    {        for (k=1;k<j;k++) 
       printf("Problem with datafile: %s\n", datafile);goto end;          sum -= a[i][k]*a[k][j]; 
     }        a[i][j]=sum; 
         if ( (dum=vv[i]*fabs(sum)) >= big) { 
     n= lastobs;          big=dum; 
     severity = vector(1,maxwav);          imax=i; 
     outcome=imatrix(1,maxwav+1,1,n);        } 
     num=ivector(1,n);      } 
     moisnais=vector(1,n);      if (j != imax) { 
     annais=vector(1,n);        for (k=1;k<=n;k++) { 
     moisdc=vector(1,n);          dum=a[imax][k]; 
     andc=vector(1,n);          a[imax][k]=a[j][k]; 
     agedc=vector(1,n);          a[j][k]=dum; 
     cod=ivector(1,n);        } 
     weight=vector(1,n);        *d = -(*d); 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */        vv[imax]=vv[j]; 
     mint=matrix(1,maxwav,1,n);      } 
     anint=matrix(1,maxwav,1,n);      indx[j]=imax; 
     s=imatrix(1,maxwav+1,1,n);      if (a[j][j] == 0.0) a[j][j]=TINY; 
     adl=imatrix(1,maxwav+1,1,n);          if (j != n) { 
     tab=ivector(1,NCOVMAX);        dum=1.0/(a[j][j]); 
     ncodemax=ivector(1,8);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
       } 
     i=1;    } 
     while (fgets(line, MAXLINE, fic) != NULL)    {    free_vector(vv,1,n);  /* Doesn't work */
       if ((i >= firstobs) && (i <=lastobs)) {  ;
          } 
         for (j=maxwav;j>=1;j--){  
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  void lubksb(double **a, int n, int *indx, double b[]) 
           strcpy(line,stra);  { 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int i,ii=0,ip,j; 
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    double sum; 
         }   
            for (i=1;i<=n;i++) { 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);      ip=indx[i]; 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);      sum=b[ip]; 
       b[ip]=b[i]; 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      if (ii) 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       else if (sum) ii=i; 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      b[i]=sum; 
         for (j=ncov;j>=1;j--){    } 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    for (i=n;i>=1;i--) { 
         }      sum=b[i]; 
         num[i]=atol(stra);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
              b[i]=sum/a[i][i]; 
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){    } 
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/  } 
   
         i=i+1;  void pstamp(FILE *fichier)
       }  {
     }    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
     /* printf("ii=%d", ij);  }
        scanf("%d",i);*/  
   imx=i-1; /* Number of individuals */  /************ Frequencies ********************/
   void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
   /* for (i=1; i<=imx; i++){  {  /* Some frequencies */
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    int i, m, jk, k1,i1, j1, bool, z1,z2,j;
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    int first;
   }    double ***freq; /* Frequencies */
   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]));*/    double *pp, **prop;
     double pos,posprop, k2, dateintsum=0,k2cpt=0;
   /* Calculation of the number of parameter from char model*/    char fileresp[FILENAMELENGTH];
   Tvar=ivector(1,15);    
   Tprod=ivector(1,15);    pp=vector(1,nlstate);
   Tvaraff=ivector(1,15);    prop=matrix(1,nlstate,iagemin,iagemax+3);
   Tvard=imatrix(1,15,1,2);    strcpy(fileresp,"p");
   Tage=ivector(1,15);          strcat(fileresp,fileres);
        if((ficresp=fopen(fileresp,"w"))==NULL) {
   if (strlen(model) >1){      printf("Problem with prevalence resultfile: %s\n", fileresp);
     j=0, j1=0, k1=1, k2=1;      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
     j=nbocc(model,'+');      exit(0);
     j1=nbocc(model,'*');    }
     cptcovn=j+1;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
     cptcovprod=j1;    j1=0;
        
        j=cptcoveff;
     strcpy(modelsav,model);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);    first=1;
       goto end;  
     }    for(k1=1; k1<=j;k1++){
          for(i1=1; i1<=ncodemax[k1];i1++){
     for(i=(j+1); i>=1;i--){        j1++;
       cutv(stra,strb,modelsav,'+');        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);          scanf("%d", i);*/
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/        for (i=-5; i<=nlstate+ndeath; i++)  
       /*scanf("%d",i);*/          for (jk=-5; jk<=nlstate+ndeath; jk++)  
       if (strchr(strb,'*')) {            for(m=iagemin; m <= iagemax+3; m++)
         cutv(strd,strc,strb,'*');              freq[i][jk][m]=0;
         if (strcmp(strc,"age")==0) {  
           cptcovprod--;      for (i=1; i<=nlstate; i++)  
           cutv(strb,stre,strd,'V');        for(m=iagemin; m <= iagemax+3; m++)
           Tvar[i]=atoi(stre);          prop[i][m]=0;
           cptcovage++;        
             Tage[cptcovage]=i;        dateintsum=0;
             /*printf("stre=%s ", stre);*/        k2cpt=0;
         }        for (i=1; i<=imx; i++) {
         else if (strcmp(strd,"age")==0) {          bool=1;
           cptcovprod--;          if  (cptcovn>0) {
           cutv(strb,stre,strc,'V');            for (z1=1; z1<=cptcoveff; z1++) 
           Tvar[i]=atoi(stre);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
           cptcovage++;                bool=0;
           Tage[cptcovage]=i;          }
         }          if (bool==1){
         else {            for(m=firstpass; m<=lastpass; m++){
           cutv(strb,stre,strc,'V');              k2=anint[m][i]+(mint[m][i]/12.);
           Tvar[i]=ncov+k1;              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
           cutv(strb,strc,strd,'V');                if(agev[m][i]==0) agev[m][i]=iagemax+1;
           Tprod[k1]=i;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
           Tvard[k1][1]=atoi(strc);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
           Tvard[k1][2]=atoi(stre);                if (m<lastpass) {
           Tvar[cptcovn+k2]=Tvard[k1][1];                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
           Tvar[cptcovn+k2+1]=Tvard[k1][2];                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
           for (k=1; k<=lastobs;k++)                }
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];                
           k1++;                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
           k2=k2+2;                  dateintsum=dateintsum+k2;
         }                  k2cpt++;
       }                }
       else {                /*}*/
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/            }
        /*  scanf("%d",i);*/          }
       cutv(strd,strc,strb,'V');        }
       Tvar[i]=atoi(strc);         
       }        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       strcpy(modelsav,stra);          pstamp(ficresp);
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        if  (cptcovn>0) {
         scanf("%d",i);*/          fprintf(ficresp, "\n#********** Variable "); 
     }          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 }          fprintf(ficresp, "**********\n#");
          }
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);        for(i=1; i<=nlstate;i++) 
   printf("cptcovprod=%d ", cptcovprod);          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   scanf("%d ",i);*/        fprintf(ficresp, "\n");
     fclose(fic);        
         for(i=iagemin; i <= iagemax+3; i++){
     /*  if(mle==1){*/          if(i==iagemax+3){
     if (weightopt != 1) { /* Maximisation without weights*/            fprintf(ficlog,"Total");
       for(i=1;i<=n;i++) weight[i]=1.0;          }else{
     }            if(first==1){
     /*-calculation of age at interview from date of interview and age at death -*/              first=0;
     agev=matrix(1,maxwav,1,imx);              printf("See log file for details...\n");
             }
    for (i=1; i<=imx; i++)            fprintf(ficlog,"Age %d", i);
      for(m=2; (m<= maxwav); m++)          }
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){          for(jk=1; jk <=nlstate ; jk++){
          anint[m][i]=9999;            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
          s[m][i]=-1;              pp[jk] += freq[jk][m][i]; 
        }          }
              for(jk=1; jk <=nlstate ; jk++){
     for (i=1; i<=imx; i++)  {            for(m=-1, pos=0; m <=0 ; m++)
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);              pos += freq[jk][m][i];
       for(m=1; (m<= maxwav); m++){            if(pp[jk]>=1.e-10){
         if(s[m][i] >0){              if(first==1){
           if (s[m][i] == nlstate+1) {              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             if(agedc[i]>0)              }
               if(moisdc[i]!=99 && andc[i]!=9999)              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               agev[m][i]=agedc[i];            }else{
             else {              if(first==1)
               if (andc[i]!=9999){                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               printf("Warning negative age at death: %d line:%d\n",num[i],i);              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               agev[m][i]=-1;            }
               }          }
             }  
           }          for(jk=1; jk <=nlstate ; jk++){
           else if(s[m][i] !=9){ /* Should no more exist */            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);              pp[jk] += freq[jk][m][i];
             if(mint[m][i]==99 || anint[m][i]==9999)          }       
               agev[m][i]=1;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
             else if(agev[m][i] <agemin){            pos += pp[jk];
               agemin=agev[m][i];            posprop += prop[jk][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/          }
             }          for(jk=1; jk <=nlstate ; jk++){
             else if(agev[m][i] >agemax){            if(pos>=1.e-5){
               agemax=agev[m][i];              if(first==1)
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             /*agev[m][i]=anint[m][i]-annais[i];*/            }else{
             /*   agev[m][i] = age[i]+2*m;*/              if(first==1)
           }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
           else { /* =9 */              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             agev[m][i]=1;            }
             s[m][i]=-1;            if( i <= iagemax){
           }              if(pos>=1.e-5){
         }                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
         else /*= 0 Unknown */                /*probs[i][jk][j1]= pp[jk]/pos;*/
           agev[m][i]=1;                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
       }              }
                  else
     }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     for (i=1; i<=imx; i++)  {            }
       for(m=1; (m<= maxwav); m++){          }
         if (s[m][i] > (nlstate+ndeath)) {          
           printf("Error: Wrong value in nlstate or ndeath\n");            for(jk=-1; jk <=nlstate+ndeath; jk++)
           goto end;            for(m=-1; m <=nlstate+ndeath; m++)
         }              if(freq[jk][m][i] !=0 ) {
       }              if(first==1)
     }                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                 fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);              }
           if(i <= iagemax)
     free_vector(severity,1,maxwav);            fprintf(ficresp,"\n");
     free_imatrix(outcome,1,maxwav+1,1,n);          if(first==1)
     free_vector(moisnais,1,n);            printf("Others in log...\n");
     free_vector(annais,1,n);          fprintf(ficlog,"\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);    dateintmean=dateintsum/k2cpt; 
    
        fclose(ficresp);
     wav=ivector(1,imx);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    free_vector(pp,1,nlstate);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
        /* End of Freq */
     /* Concatenates waves */  }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  
   /************ Prevalence ********************/
   void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
       Tcode=ivector(1,100);  {  
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
       ncodemax[1]=1;       in each health status at the date of interview (if between dateprev1 and dateprev2).
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);       We still use firstpass and lastpass as another selection.
          */
    codtab=imatrix(1,100,1,10);   
    h=0;    int i, m, jk, k1, i1, j1, bool, z1,z2,j;
    m=pow(2,cptcoveff);    double ***freq; /* Frequencies */
      double *pp, **prop;
    for(k=1;k<=cptcoveff; k++){    double pos,posprop; 
      for(i=1; i <=(m/pow(2,k));i++){    double  y2; /* in fractional years */
        for(j=1; j <= ncodemax[k]; j++){    int iagemin, iagemax;
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  
            h++;    iagemin= (int) agemin;
            if (h>m) h=1;codtab[h][k]=j;    iagemax= (int) agemax;
          }    /*pp=vector(1,nlstate);*/
        }    prop=matrix(1,nlstate,iagemin,iagemax+3); 
      }    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
    }    j1=0;
     
     j=cptcoveff;
    /*for(i=1; i <=m ;i++){    if (cptcovn<1) {j=1;ncodemax[1]=1;}
      for(k=1; k <=cptcovn; k++){    
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);    for(k1=1; k1<=j;k1++){
      }      for(i1=1; i1<=ncodemax[k1];i1++){
      printf("\n");        j1++;
    }        
    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]=0.0;
        and prints on file fileres'p'. */       
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);        for (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          if  (cptcovn>0) {
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */            for (z1=1; z1<=cptcoveff; z1++) 
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */                bool=0;
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */          } 
                if (bool==1) { 
     /* For Powell, parameters are in a vector p[] starting at p[1]            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
     if(mle==1){                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);                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) { 
                      /*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]]);*/
     /*--------- results files --------------*/                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     fprintf(ficres,"\ntitle=%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);                  prop[s[m][i]][iagemax+3] += weight[i]; 
                    } 
    jk=1;              }
    fprintf(ficres,"# Parameters\n");            } /* end selection of waves */
    printf("# Parameters\n");          }
    for(i=1,jk=1; i <=nlstate; i++){        }
      for(k=1; k <=(nlstate+ndeath); k++){        for(i=iagemin; i <= iagemax+3; i++){  
        if (k != i)          
          {          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
            printf("%d%d ",i,k);            posprop += prop[jk][i]; 
            fprintf(ficres,"%1d%1d ",i,k);          } 
            for(j=1; j <=ncovmodel; j++){  
              printf("%f ",p[jk]);          for(jk=1; jk <=nlstate ; jk++){     
              fprintf(ficres,"%f ",p[jk]);            if( i <=  iagemax){ 
              jk++;              if(posprop>=1.e-5){ 
            }                probs[i][jk][j1]= prop[jk][i]/posprop;
            printf("\n");              } 
            fprintf(ficres,"\n");            } 
          }          }/* end jk */ 
      }        }/* end i */ 
    }      } /* end i1 */
  if(mle==1){    } /* end k1 */
     /* Computing hessian and covariance matrix */    
     ftolhess=ftol; /* Usually correct */    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     hesscov(matcov, p, npar, delti, ftolhess, func);    /*free_vector(pp,1,nlstate);*/
  }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
     fprintf(ficres,"# Scales\n");  }  /* End of prevalence */
     printf("# Scales\n");  
      for(i=1,jk=1; i <=nlstate; i++){  /************* Waves Concatenation ***************/
       for(j=1; j <=nlstate+ndeath; j++){  
         if (j!=i) {  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
           fprintf(ficres,"%1d%1d",i,j);  {
           printf("%1d%1d",i,j);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           for(k=1; k<=ncovmodel;k++){       Death is a valid wave (if date is known).
             printf(" %.5e",delti[jk]);       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
             fprintf(ficres," %.5e",delti[jk]);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
             jk++;       and mw[mi+1][i]. dh depends on stepm.
           }       */
           printf("\n");  
           fprintf(ficres,"\n");    int i, mi, m;
         }    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       }       double sum=0., jmean=0.;*/
       }    int first;
        int j, k=0,jk, ju, jl;
     k=1;    double sum=0.;
     fprintf(ficres,"# Covariance\n");    first=0;
     printf("# Covariance\n");    jmin=1e+5;
     for(i=1;i<=npar;i++){    jmax=-1;
       /*  if (k>nlstate) k=1;    jmean=0.;
       i1=(i-1)/(ncovmodel*nlstate)+1;    for(i=1; i<=imx; i++){
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);      mi=0;
       printf("%s%d%d",alph[k],i1,tab[i]);*/      m=firstpass;
       fprintf(ficres,"%3d",i);      while(s[m][i] <= nlstate){
       printf("%3d",i);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
       for(j=1; j<=i;j++){          mw[++mi][i]=m;
         fprintf(ficres," %.5e",matcov[i][j]);        if(m >=lastpass)
         printf(" %.5e",matcov[i][j]);          break;
       }        else
       fprintf(ficres,"\n");          m++;
       printf("\n");      }/* end while */
       k++;      if (s[m][i] > nlstate){
     }        mi++;     /* Death is another wave */
            /* if(mi==0)  never been interviewed correctly before death */
     while((c=getc(ficpar))=='#' && c!= EOF){           /* Only death is a correct wave */
       ungetc(c,ficpar);        mw[mi][i]=m;
       fgets(line, MAXLINE, ficpar);      }
       puts(line);  
       fputs(line,ficparo);      wav[i]=mi;
     }      if(mi==0){
     ungetc(c,ficpar);        nbwarn++;
          if(first==0){
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
              first=1;
     if (fage <= 2) {        }
       bage = agemin;        if(first==1){
       fage = agemax;          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
     }        }
       } /* end mi==0 */
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");    } /* End individuals */
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  
     for(i=1; i<=imx; i++){
          for(mi=1; mi<wav[i];mi++){
 /*------------ gnuplot -------------*/        if (stepm <=0)
 chdir(pathcd);          dh[mi][i]=1;
   if((ficgp=fopen("graph.plt","w"))==NULL) {        else{
     printf("Problem with file graph.gp");goto end;          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
   }            if (agedc[i] < 2*AGESUP) {
 #ifdef windows              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   fprintf(ficgp,"cd \"%s\" \n",pathc);              if(j==0) j=1;  /* Survives at least one month after exam */
 #endif              else if(j<0){
 m=pow(2,cptcoveff);                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]);
  /* 1eme*/                j=1; /* Temporary Dangerous patch */
   for (cpt=1; cpt<= nlstate ; cpt ++) {                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);
    for (k1=1; k1<= m ; k1 ++) {                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                 fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
 #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);              k=k+1;
 #endif              if (j >= jmax){
 #ifdef unix                jmax=j;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);                ijmax=i;
 #endif              }
               if (j <= jmin){
 for (i=1; i<= nlstate ; i ++) {                jmin=j;
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");                ijmin=i;
   else fprintf(ficgp," \%%*lf (\%%*lf)");              }
 }              sum=sum+j;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
     for (i=1; i<= nlstate ; i ++) {              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          }
 }          else{
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
      for (i=1; i<= nlstate ; i ++) {  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");            k=k+1;
 }              if (j >= jmax) {
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));              jmax=j;
 #ifdef unix              ijmax=i;
 fprintf(ficgp,"\nset ter gif small size 400,300");            }
 #endif            else if (j <= jmin){
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);              jmin=j;
    }              ijmin=i;
   }            }
   /*2 eme*/            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
   for (k1=1; k1<= m ; k1 ++) {            if(j<0){
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);              nberr++;
                  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]);
     for (i=1; i<= nlstate+1 ; i ++) {              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       k=2*i;            }
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);            sum=sum+j;
       for (j=1; j<= nlstate+1 ; j ++) {          }
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          jk= j/stepm;
   else fprintf(ficgp," \%%*lf (\%%*lf)");          jl= j -jk*stepm;
 }            ju= j -(jk+1)*stepm;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);            if(jl==0){
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);              dh[mi][i]=jk;
       for (j=1; j<= nlstate+1 ; j ++) {              bh[mi][i]=0;
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");            }else{ /* We want a negative bias in order to only have interpolation ie
         else fprintf(ficgp," \%%*lf (\%%*lf)");                    * at the price of an extra matrix product in likelihood */
 }                dh[mi][i]=jk+1;
       fprintf(ficgp,"\" t\"\" w l 0,");              bh[mi][i]=ju;
      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 ++) {          }else{
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");            if(jl <= -ju){
   else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=jk;
 }                bh[mi][i]=jl;       /* bias is positive if real duration
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");                                   * is higher than the multiple of stepm and negative otherwise.
       else fprintf(ficgp,"\" t\"\" w l 0,");                                   */
     }            }
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);            else{
   }              dh[mi][i]=jk+1;
                bh[mi][i]=ju;
   /*3eme*/            }
             if(dh[mi][i]==0){
   for (k1=1; k1<= m ; k1 ++) {              dh[mi][i]=1; /* At least one step */
     for (cpt=1; cpt<= nlstate ; cpt ++) {              bh[mi][i]=ju; /* At least one step */
       k=2+nlstate*(cpt-1);              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);            }
       for (i=1; i< nlstate ; i ++) {          } /* end if mle */
         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);        }
       }      } /* end wave */
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    }
     }    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);
      fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
   /* CV preval stat */   }
   for (k1=1; k1<= m ; k1 ++) {  
     for (cpt=1; cpt<nlstate ; cpt ++) {  /*********** Tricode ****************************/
       k=3;  void tricode(int *Tvar, int **nbcode, int imx)
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);  {
       for (i=1; i< nlstate ; i ++)    
         fprintf(ficgp,"+$%d",k+i+1);    int Ndum[20],ij=1, k, j, i, maxncov=19;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    int cptcode=0;
          cptcoveff=0; 
       l=3+(nlstate+ndeath)*cpt;   
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    for (k=0; k<maxncov; k++) Ndum[k]=0;
       for (i=1; i< nlstate ; i ++) {    for (k=1; k<=7; k++) ncodemax[k]=0;
         l=3+(nlstate+ndeath)*cpt;  
         fprintf(ficgp,"+$%d",l+i+1);    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       }      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);                                   modality*/ 
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
     }        Ndum[ij]++; /*store the modality */
   }          /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
   /* proba elementaires */                                         Tvar[j]. If V=sex and male is 0 and 
    for(i=1,jk=1; i <=nlstate; i++){                                         female is 1, then  cptcode=1.*/
     for(k=1; k <=(nlstate+ndeath); k++){      }
       if (k != i) {  
         for(j=1; j <=ncovmodel; j++){      for (i=0; i<=cptcode; i++) {
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
           /*fprintf(ficgp,"%s",alph[1]);*/      }
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);  
           jk++;      ij=1; 
           fprintf(ficgp,"\n");      for (i=1; i<=ncodemax[j]; i++) {
         }        for (k=0; k<= maxncov; k++) {
       }          if (Ndum[k] != 0) {
     }            nbcode[Tvar[j]][ij]=k; 
     }            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
             
   for(jk=1; jk <=m; jk++) {            ij++;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);          }
    i=1;          if (ij > ncodemax[j]) break; 
    for(k2=1; k2<=nlstate; k2++) {        }  
      k3=i;      } 
      for(k=1; k<=(nlstate+ndeath); k++) {    }  
        if (k != k2){  
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);   for (k=0; k< maxncov; k++) Ndum[k]=0;
 ij=1;  
         for(j=3; j <=ncovmodel; j++) {   for (i=1; i<=ncovmodel-2; i++) { 
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);     ij=Tvar[i];
             ij++;     Ndum[ij]++;
           }   }
           else  
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);   ij=1;
         }   for (i=1; i<= maxncov; i++) {
           fprintf(ficgp,")/(1");     if((Ndum[i]!=0) && (i<=ncovcol)){
               Tvaraff[ij]=i; /*For printing */
         for(k1=1; k1 <=nlstate; k1++){         ij++;
           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)) {   cptcoveff=ij-1; /*Number of simple covariates*/
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);  }
             ij++;  
           }  /*********** Health Expectancies ****************/
           else  
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
           }  
           fprintf(ficgp,")");  {
         }    /* Health expectancies, no variances */
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    double age, agelim, hf;
         i=i+ncovmodel;    double ***p3mat;
        }    double eip;
      }  
    }    pstamp(ficreseij);
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
   }    fprintf(ficreseij,"# Age");
        for(i=1; i<=nlstate;i++){
   fclose(ficgp);      for(j=1; j<=nlstate;j++){
            fprintf(ficreseij," e%1d%1d ",i,j);
 chdir(path);      }
     free_matrix(agev,1,maxwav,1,imx);      fprintf(ficreseij," e%1d. ",i);
     free_ivector(wav,1,imx);    }
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    fprintf(ficreseij,"\n");
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);  
        
     free_imatrix(s,1,maxwav+1,1,n);    if(estepm < stepm){
          printf ("Problem %d lower than %d\n",estepm, stepm);
        }
     free_ivector(num,1,n);    else  hstepm=estepm;   
     free_vector(agedc,1,n);    /* We compute the life expectancy from trapezoids spaced every estepm months
     free_vector(weight,1,n);     * This is mainly to measure the difference between two models: for example
     /*free_matrix(covar,1,NCOVMAX,1,n);*/     * if stepm=24 months pijx are given only every 2 years and by summing them
     fclose(ficparo);     * we are calculating an estimate of the Life Expectancy assuming a linear 
     fclose(ficres);     * progression in between and thus overestimating or underestimating according
     /*  }*/     * to the curvature of the survival function. If, for the same date, we 
         * estimate the model with stepm=1 month, we can keep estepm to 24 months
    /*________fin mle=1_________*/     * to compare the new estimate of Life expectancy with the same linear 
         * hypothesis. A more precise result, taking into account a more precise
      * curvature will be obtained if estepm is as small as stepm. */
    
     /* No more information from the sample is required now */    /* For example we decided to compute the life expectancy with the smallest unit */
   /* Reads comments: lines beginning with '#' */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   while((c=getc(ficpar))=='#' && c!= EOF){       nhstepm is the number of hstepm from age to agelim 
     ungetc(c,ficpar);       nstepm is the number of stepm from age to agelin. 
     fgets(line, MAXLINE, ficpar);       Look at hpijx to understand the reason of that which relies in memory size
     puts(line);       and note for a fixed period like estepm months */
     fputs(line,ficparo);    /* 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
   ungetc(c,ficpar);       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 
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);       results. So we changed our mind and took the option of the best precision.
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    */
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
 /*--------- index.htm --------*/  
     agelim=AGESUP;
   strcpy(optionfilehtm,optionfile);    /* nhstepm age range expressed in number of stepm */
   strcat(optionfilehtm,".htm");    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     printf("Problem with %s \n",optionfilehtm);goto end;    /* if (stepm >= YEARM) hstepm=1;*/
   }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.64b </font> <hr size=\"2\" color=\"#EC5E5E\">  
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
 Total number of observations=%d <br>      /* Computed by stepm unit matrices, product of hstepm matrices, stored
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
 <hr  size=\"2\" color=\"#EC5E5E\">      
 <li>Outputs files<br><br>\n      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
         - 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>      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      printf("%d|",(int)age);fflush(stdout);
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>      
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>      /* Computing expectancies */
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>      for(i=1; i<=nlstate;i++)
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><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);        for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
  fprintf(fichtm," <li>Graphs</li><p>");            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
  m=cptcoveff;            /* 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]);*/
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  
           }
  j1=0;  
  for(k1=1; k1<=m;k1++){      fprintf(ficreseij,"%3.0f",age );
    for(i1=1; i1<=ncodemax[k1];i1++){      for(i=1; i<=nlstate;i++){
        j1++;        eip=0;
        if (cptcovn > 0) {        for(j=1; j<=nlstate;j++){
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");          eip +=eij[i][j][(int)age];
          for (cpt=1; cpt<=cptcoveff;cpt++)          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[j1][cpt]]);        }
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");        fprintf(ficreseij,"%9.4f", eip );
        }      }
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      fprintf(ficreseij,"\n");
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);          
        for(cpt=1; cpt<nlstate;cpt++){    }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    printf("\n");
        }    fprintf(ficlog,"\n");
     for(cpt=1; cpt<=nlstate;cpt++) {    
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  }
 interval) in state (%d): v%s%d%d.gif <br>  
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    void cvevsij(char fileres[], 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[] )
      }  
      for(cpt=1; cpt<=nlstate;cpt++) {  {
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    /* Covariances of health expectancies eij and of total life expectancies according
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);     to initial status i, ei. .
      }    */
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
 health expectancies in states (1) and (2): e%s%d.gif<br>    double age, agelim, hf;
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);    double ***p3matp, ***p3matm, ***varhe;
 fprintf(fichtm,"\n</body>");    double **dnewm,**doldm;
    }    double *xp, *xm;
  }    double **gp, **gm;
 fclose(fichtm);    double ***gradg, ***trgradg;
     int theta;
   /*--------------- Prevalence limit --------------*/  
      double eip, vip;
   strcpy(filerespl,"pl");  
   strcat(filerespl,fileres);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    xp=vector(1,npar);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    xm=vector(1,npar);
   }    dnewm=matrix(1,nlstate*nlstate,1,npar);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   fprintf(ficrespl,"#Prevalence limit\n");    
   fprintf(ficrespl,"#Age ");    pstamp(ficresstdeij);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   fprintf(ficrespl,"\n");    fprintf(ficresstdeij,"# Age");
      for(i=1; i<=nlstate;i++){
   prlim=matrix(1,nlstate,1,nlstate);      for(j=1; j<=nlstate;j++)
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresstdeij," e%1d. ",i);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    }
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresstdeij,"\n");
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  
   k=0;    pstamp(ficrescveij);
   agebase=agemin;    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
   agelim=agemax;    fprintf(ficrescveij,"# Age");
   ftolpl=1.e-10;    for(i=1; i<=nlstate;i++)
   i1=cptcoveff;      for(j=1; j<=nlstate;j++){
   if (cptcovn < 1){i1=1;}        cptj= (j-1)*nlstate+i;
         for(i2=1; i2<=nlstate;i2++)
   for(cptcov=1;cptcov<=i1;cptcov++){          for(j2=1; j2<=nlstate;j2++){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){            cptj2= (j2-1)*nlstate+i2;
         k=k+1;            if(cptj2 <= cptj)
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
         fprintf(ficrespl,"\n#******");          }
         for(j=1;j<=cptcoveff;j++)      }
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficrescveij,"\n");
         fprintf(ficrespl,"******\n");    
            if(estepm < stepm){
         for (age=agebase; age<=agelim; age++){      printf ("Problem %d lower than %d\n",estepm, stepm);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    }
           fprintf(ficrespl,"%.0f",age );    else  hstepm=estepm;   
           for(i=1; i<=nlstate;i++)    /* We compute the life expectancy from trapezoids spaced every estepm months
           fprintf(ficrespl," %.5f", prlim[i][i]);     * This is mainly to measure the difference between two models: for example
           fprintf(ficrespl,"\n");     * if stepm=24 months pijx are given only every 2 years and by summing them
         }     * we are calculating an estimate of the Life Expectancy assuming a linear 
       }     * progression in between and thus overestimating or underestimating according
     }     * to the curvature of the survival function. If, for the same date, we 
   fclose(ficrespl);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
      * to compare the new estimate of Life expectancy with the same linear 
   /*------------- h Pij x at various ages ------------*/     * hypothesis. A more precise result, taking into account a more precise
       * curvature will be obtained if estepm is as small as stepm. */
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    /* For example we decided to compute the life expectancy with the smallest unit */
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   }       nhstepm is the number of hstepm from age to agelim 
   printf("Computing pij: result on file '%s' \n", filerespij);       nstepm is the number of stepm from age to agelin. 
         Look at hpijx to understand the reason of that which relies in memory size
   stepsize=(int) (stepm+YEARM-1)/YEARM;       and note for a fixed period like estepm months */
   /*if (stepm<=24) stepsize=2;*/    /* 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
   agelim=AGESUP;       means that if the survival funtion is printed only each two years of age and if
   hstepm=stepsize*YEARM; /* Every year of age */       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */       results. So we changed our mind and took the option of the best precision.
      */
   k=0;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    /* If stepm=6 months */
       k=k+1;    /* nhstepm age range expressed in number of stepm */
         fprintf(ficrespij,"\n#****** ");    agelim=AGESUP;
         for(j=1;j<=cptcoveff;j++)    nstepm=(int) rint((agelim-age)*YEARM/stepm); 
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
         fprintf(ficrespij,"******\n");    /* if (stepm >= YEARM) hstepm=1;*/
            nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */    
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
           oldm=oldms;savm=savms;    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      gp=matrix(0,nhstepm,1,nlstate*nlstate);
           fprintf(ficrespij,"# Age");    gm=matrix(0,nhstepm,1,nlstate*nlstate);
           for(i=1; i<=nlstate;i++)  
             for(j=1; j<=nlstate+ndeath;j++)    for (age=bage; age<=fage; age ++){ 
               fprintf(ficrespij," %1d-%1d",i,j);  
           fprintf(ficrespij,"\n");      /* Computed by stepm unit matrices, product of hstepm matrices, stored
           for (h=0; h<=nhstepm; h++){         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );   
             for(i=1; i<=nlstate;i++)      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
               for(j=1; j<=nlstate+ndeath;j++)  
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);      /* Computing  Variances of health expectancies */
             fprintf(ficrespij,"\n");      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
           }         decrease memory allocation */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      for(theta=1; theta <=npar; theta++){
           fprintf(ficrespij,"\n");        for(i=1; i<=npar; i++){ 
         }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
     }          xm[i] = x[i] - (i==theta ?delti[theta]:0);
   }        }
         hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     
   fclose(ficrespij);        for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate; i++){
   exit(0);            for(h=0; h<=nhstepm-1; h++){
   /*---------- Forecasting ------------------*/              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
               gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   strcpy(fileresf,"f");            }
   strcat(fileresf,fileres);          }
   if((ficresf=fopen(fileresf,"w"))==NULL) {        }
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;       
   }        for(ij=1; ij<= nlstate*nlstate; ij++)
   printf("Computing forecasting: result on file '%s' \n", fileresf);          for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   /* Mobile average */          }
       }/* End theta */
   /* for (agedeb=bage; agedeb<=fage; agedeb++)      
     for (i=1; i<=nlstate;i++)      
       for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++)      for(h=0; h<=nhstepm-1; h++)
       printf("%f %d i=%d j1=%d\n", probs[(int)agedeb][i][cptcod],(int) agedeb,i,cptcod);*/        for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
   if (cptcoveff==0) ncodemax[cptcoveff]=1;            trgradg[h][j][theta]=gradg[h][theta][j];
       
   mobaverage= ma3x(1,130 ,1,8, 1,8);  
   for (agedeb=bage+3; agedeb<=fage-2; agedeb++)       for(ij=1;ij<=nlstate*nlstate;ij++)
     for (i=1; i<=nlstate;i++)        for(ji=1;ji<=nlstate*nlstate;ji++)
       for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)          varhe[ij][ji][(int)age] =0.;
         mobaverage[(int)agedeb][i][cptcod]=0.;  
         printf("%d|",(int)age);fflush(stdout);
   for (agedeb=bage+4; agedeb<=fage; agedeb++){       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
     for (i=1; i<=nlstate;i++){       for(h=0;h<=nhstepm-1;h++){
       for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        for(k=0;k<=nhstepm-1;k++){
         for (cpt=0;cpt<=4;cpt++){          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           }          for(ij=1;ij<=nlstate*nlstate;ij++)
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;            for(ji=1;ji<=nlstate*nlstate;ji++)
       }              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
     }        }
   }      }
       /* Computing expectancies */
 /* if (cptcod==2) printf("m=%f p=%f %d age=%d ",mobaverage[(int)agedeb-2][i][cptcod],probs[(int)agedeb-cpt][i][cptcod],cpt,(int)agedeb-2);*/      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   stepsize=(int) (stepm+YEARM-1)/YEARM;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   if (stepm<=24) stepsize=2;            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
   agelim=AGESUP;            /* 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]);*/
   hstepm=stepsize*YEARM; /* Every year of age */  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */          }
   hstepm=12;  
    k=0;      fprintf(ficresstdeij,"%3.0f",age );
   for(cptcov=1;cptcov<=i1;cptcov++){      for(i=1; i<=nlstate;i++){
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        eip=0.;
       k=k+1;        vip=0.;
       fprintf(ficresf,"\n#****** ");        for(j=1; j<=nlstate;j++){
       for(j=1;j<=cptcoveff;j++) {          eip += eij[i][j][(int)age];
         fprintf(ficresf,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
       }            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
                fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
       fprintf(ficresf,"******\n");        }
         fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       fprintf(ficresf,"# StartingAge FinalAge Horizon(in years)");      }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);      fprintf(ficresstdeij,"\n");
   
       for (agedeb=fage; agedeb>=bage; agedeb--){      fprintf(ficrescveij,"%3.0f",age );
         fprintf(ficresf,"\n%d %.f %.f 0 ",k,agedeb, agedeb);      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)        for(j=1; j<=nlstate;j++){
           fprintf(ficresf,"%.3f ",mobaverage[(int)agedeb][j][cptcod]);          cptj= (j-1)*nlstate+i;
       }          for(i2=1; i2<=nlstate;i2++)
       for(j=1; j<=ndeath;j++) fprintf(ficresf,"0.");            for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
       for (cpt=1; cpt<=8;cpt++)                if(cptj2 <= cptj)
       for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
                    }
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        }
         nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      fprintf(ficrescveij,"\n");
         /*printf("stepm=%d hstepm=%d nhstepm=%d \n",stepm,hstepm,nhstepm);*/     
     }
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
         oldm=oldms;savm=savms;    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
                    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
         for (h=0; h<=nhstepm; h++){    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
            free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           if (h*hstepm/YEARM*stepm==cpt)    printf("\n");
  fprintf(ficresf,"\n%d %.f %.f %.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm, h*hstepm/YEARM*stepm);    fprintf(ficlog,"\n");
            
           for(j=1; j<=nlstate+ndeath;j++) {    free_vector(xm,1,npar);
             kk1=0.;    free_vector(xp,1,npar);
             for(i=1; i<=nlstate;i++) {            free_matrix(dnewm,1,nlstate*nlstate,1,npar);
               /*   kk1=kk1+p3mat[i][j][h]*probs[(int)agedeb][i][cptcod];*/    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
                 kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb][i][cptcod];    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
             }  }
              
             if (h*hstepm/YEARM*stepm==cpt)  /************ Variance ******************/
               fprintf(ficresf," %.5f ", kk1);  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 */
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
         }    /* double **newm;*/
       }    double **dnewm,**doldm;
     }    double **dnewmp,**doldmp;
   fclose(ficresf);    int i, j, nhstepm, hstepm, h, nstepm ;
     int k, cptcode;
   /*---------- Health expectancies and variances ------------*/    double *xp;
     double **gp, **gm;  /* for var eij */
   strcpy(filerest,"t");    double ***gradg, ***trgradg; /*for var eij */
   strcat(filerest,fileres);    double **gradgp, **trgradgp; /* for var p point j */
   if((ficrest=fopen(filerest,"w"))==NULL) {    double *gpp, *gmp; /* for var p point j */
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   }    double ***p3mat;
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    double age,agelim, hf;
     double ***mobaverage;
     int theta;
   strcpy(filerese,"e");    char digit[4];
   strcat(filerese,fileres);    char digitp[25];
   if((ficreseij=fopen(filerese,"w"))==NULL) {  
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    char fileresprobmorprev[FILENAMELENGTH];
   }  
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    if(popbased==1){
       if(mobilav!=0)
  strcpy(fileresv,"v");        strcpy(digitp,"-populbased-mobilav-");
   strcat(fileresv,fileres);      else strcpy(digitp,"-populbased-nomobil-");
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    }
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    else 
   }      strcpy(digitp,"-stablbased-");
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);  
     if (mobilav!=0) {
   k=0;      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   for(cptcov=1;cptcov<=i1;cptcov++){      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
       k=k+1;        printf(" Error in movingaverage mobilav=%d\n",mobilav);
       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");    strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
       fprintf(ficreseij,"\n#****** ");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
       for(j=1;j<=cptcoveff;j++)    strcat(fileresprobmorprev,digit); /* Tvar to be done */
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
       fprintf(ficreseij,"******\n");    strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       fprintf(ficresvij,"\n#****** ");      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       for(j=1;j<=cptcoveff;j++)      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    }
       fprintf(ficresvij,"******\n");    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       oldm=oldms;savm=savms;    pstamp(ficresprobmorprev);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);      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);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
       oldm=oldms;savm=savms;    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      fprintf(ficresprobmorprev," p.%-d SE",j);
            for(i=1; i<=nlstate;i++)
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    }  
       fprintf(ficrest,"\n");    fprintf(ficresprobmorprev,"\n");
            fprintf(ficgp,"\n# Routine varevsij");
       hf=1;    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
       if (stepm >= YEARM) hf=stepm/YEARM;    fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
       epj=vector(1,nlstate+1);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       for(age=bage; age <=fage ;age++){  /*   } */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         fprintf(ficrest," %.0f",age);    pstamp(ficresvij);
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    if(popbased==1)
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];      fprintf(ficresvij,"the age specific prevalence observed in the population i.e cross-sectionally\n in each health state (popbased=1)");
           }    else
           epj[nlstate+1] +=epj[j];      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
         }    fprintf(ficresvij,"# Age");
         for(i=1, vepp=0.;i <=nlstate;i++)    for(i=1; i<=nlstate;i++)
           for(j=1;j <=nlstate;j++)      for(j=1; j<=nlstate;j++)
             vepp += vareij[i][j][(int)age];        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    fprintf(ficresvij,"\n");
         for(j=1;j <=nlstate;j++){  
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    xp=vector(1,npar);
         }    dnewm=matrix(1,nlstate,1,npar);
         fprintf(ficrest,"\n");    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*/
  fclose(ficreseij);    
  fclose(ficresvij);    if(estepm < stepm){
   fclose(ficrest);      printf ("Problem %d lower than %d\n",estepm, stepm);
   fclose(ficpar);    }
   free_vector(epj,1,nlstate+1);    else  hstepm=estepm;   
   /*  scanf("%d ",i); */    /* 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. 
   /*------- Variance limit prevalence------*/         nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
 strcpy(fileresvpl,"vpl");       Look at hpijx to understand the reason of that which relies in memory size
   strcat(fileresvpl,fileres);       and note for a fixed period like k years */
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);       survival function given by stepm (the optimization length). Unfortunately it
     exit(0);       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 
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);       results. So we changed our mind and took the option of the best precision.
     */
  k=0;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
  for(cptcov=1;cptcov<=i1;cptcov++){    agelim = AGESUP;
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      k=k+1;      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
      fprintf(ficresvpl,"\n#****** ");      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
      for(j=1;j<=cptcoveff;j++)      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
      fprintf(ficresvpl,"******\n");      gp=matrix(0,nhstepm,1,nlstate);
            gm=matrix(0,nhstepm,1,nlstate);
      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(theta=1; theta <=npar; theta++){
    }        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
  }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
   fclose(ficresvpl);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   /*---------- End : free ----------------*/  
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        if (popbased==1) {
            if(mobilav ==0){
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);            for(i=1; i<=nlstate;i++)
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);              prlim[i][i]=probs[(int)age][i][ij];
            }else{ /* mobilav */ 
              for(i=1; i<=nlstate;i++)
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);              prlim[i][i]=mobaverage[(int)age][i][ij];
   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);    
          for(j=1; j<= nlstate; j++){
   free_matrix(matcov,1,npar,1,npar);          for(h=0; h<=nhstepm; h++){
   free_vector(delti,1,npar);            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
                gp[h][j] += prlim[i][i]*p3mat[i][j][h];
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);          }
         }
   printf("End of Imach\n");        /* This for computing probability of death (h=1 means
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */           computed over hstepm matrices product = hstepm*stepm months) 
             as a weighted average of prlim.
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/        */
   /*printf("Total time was %d uSec.\n", total_usecs);*/        for(j=nlstate+1;j<=nlstate+ndeath;j++){
   /*------ End -----------*/          for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
  end:        /* end probability of death */
 #ifdef windows  
  chdir(pathcd);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
 #endif          xp[i] = x[i] - (i==theta ?delti[theta]:0);
          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
  system("..\\gp37mgw\\wgnuplot graph.plt");        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    
 #ifdef windows        if (popbased==1) {
   while (z[0] != 'q') {          if(mobilav ==0){
     chdir(pathcd);            for(i=1; i<=nlstate;i++)
     printf("\nType e to edit output files, c to start again, and q for exiting: ");              prlim[i][i]=probs[(int)age][i][ij];
     scanf("%s",z);          }else{ /* mobilav */ 
     if (z[0] == 'c') system("./imach");            for(i=1; i<=nlstate;i++)
     else if (z[0] == 'e') {              prlim[i][i]=mobaverage[(int)age][i][ij];
       chdir(path);          }
       system(optionfilehtm);        }
     }  
     else if (z[0] == 'q') exit(0);        for(j=1; j<= nlstate; j++){
   }          for(h=0; h<=nhstepm; h++){
 #endif            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,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; set nolog 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 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 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;
     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];
     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;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       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#");    
         }
         
         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]]];
           }
           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]]];
           
           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(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);
           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);
   
           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=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++){
                 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 */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nset noparametric;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;
         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.;
                     /* 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\nset size 0.65,0.65");
                       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, (b) health expectancies by health status at initial age:  ei., eij . If one or more covariate 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</li>",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
   
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=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%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.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%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.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>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",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 : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,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), eij 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: <a href=\"%s\">%s</a> <br>\n",
            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=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): %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 m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   /*   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*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        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\n\
   set size 0.65,0.65\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 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 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     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\nset size 0.65,0.65\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 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 0");
         else fprintf(ficgp,"\" t\"\" w l 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\n\
   set size 0.65,0.65\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 (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         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\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* 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");
           }
         }
       }
      }
   
      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\nset size 0.65,0.65\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;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    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 */
      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;
   }
   
   /******************* 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\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);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     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;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  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, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*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 *severity;
     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];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char  *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     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\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     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++;
       puts(line);
       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++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     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 guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         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);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         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);
   
       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++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       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 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     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);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     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;
       }
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         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 '%d' at line number %d %s 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);
           exit(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.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           exit(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 %ld %s for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         exit(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.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line,j);
         exit(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 %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         exit(1);
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld 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);
           exit(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 */
     fclose(fic);
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       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;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        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]));}*/
     
     /* for (i=1; i<=imx; i++) */
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; 
       cptcovprod=j1; /*Number of products */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
   
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */ 
         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 */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/
             cptcovage++;
               Tage[cptcovage]=i;
               /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/
             Tvar[i]=ncovcol+k1;
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  
         /*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);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     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(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\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);     
           goto end;
         }
       }
     }
   
     /*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); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     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 */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/
           } 
         }
       }
     } 
     /* 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);*/
       
     /*------------ 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");
     }
     /*  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);
       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]);*/
       
       
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
       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);
       }
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
       /*  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");
       
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       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);
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
     
       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("%f ",p[jk]);
               fprintf(ficlog,"%f ",p[jk]);
               fprintf(ficres,"%f ",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);
         puts(line);
         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);
         puts(line);
         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);
         puts(line);
         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);
         puts(line);
         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) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       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); */
         /*      } */
       }
     
   
       /*---------- 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(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);
   
       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);
   
       /* 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);
         }
       }
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           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(ficreseij,"\n#****** ");
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][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(ficreseij,"******\n");
           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;
           evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
           cvevsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0, mobilav, strstart);
           if(popbased==1){
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased,mobilav, strstart);
           }
   
           pstamp(ficrest);
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n# 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 (popbased==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,1,15,1,2);
       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(ficreseij);
       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++){
           k=k+1;
           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 */
     free_matrix(prlim,1,nlstate,1,nlstate);
       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,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
       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 %d 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 %d 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("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       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);
     }
   }
   
   
   

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  Added in v.1.123


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