Diff for /imach/src/imach.c between versions 1.25 and 1.130

version 1.25, 2002/02/26 17:11:54 version 1.130, 2009/05/26 06:44:34
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.130  2009/05/26 06:44:34  brouard
      (Module): Max Covariate is now set to 20 instead of 8. A
   This program computes Healthy Life Expectancies from    lot of cleaning with variables initialized to 0. Trying to make
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   first survey ("cross") where individuals from different ages are  
   interviewed on their health status or degree of disability (in the    Revision 1.129  2007/08/31 13:49:27  lievre
   case of a health survey which is our main interest) -2- at least a    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   second wave of interviews ("longitudinal") which measure each change  
   (if any) in individual health status.  Health expectancies are    Revision 1.128  2006/06/30 13:02:05  brouard
   computed from the time spent in each health state according to a    (Module): Clarifications on computing e.j
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.127  2006/04/28 18:11:50  brouard
   simplest model is the multinomial logistic model where pij is the    (Module): Yes the sum of survivors was wrong since
   probabibility to be observed in state j at the second wave    imach-114 because nhstepm was no more computed in the age
   conditional to be observed in state i at the first wave. Therefore    loop. Now we define nhstepma in the age loop.
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    (Module): In order to speed up (in case of numerous covariates) we
   'age' is age and 'sex' is a covariate. If you want to have a more    compute health expectancies (without variances) in a first step
   complex model than "constant and age", you should modify the program    and then all the health expectancies with variances or standard
   where the markup *Covariates have to be included here again* invites    deviation (needs data from the Hessian matrices) which slows the
   you to do it.  More covariates you add, slower the    computation.
   convergence.    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.126  2006/04/28 17:23:28  brouard
   identical for each individual. Also, if a individual missed an    (Module): Yes the sum of survivors was wrong since
   intermediate interview, the information is lost, but taken into    imach-114 because nhstepm was no more computed in the age
   account using an interpolation or extrapolation.      loop. Now we define nhstepma in the age loop.
     Version 0.98h
   hPijx is the probability to be observed in state i at age x+h  
   conditional to the observed state i at age x. The delay 'h' can be    Revision 1.125  2006/04/04 15:20:31  lievre
   split into an exact number (nh*stepm) of unobserved intermediate    Errors in calculation of health expectancies. Age was not initialized.
   states. This elementary transition (by month or quarter trimester,    Forecasting file added.
   semester or year) is model as a multinomial logistic.  The hPx  
   matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.124  2006/03/22 17:13:53  lievre
   and the contribution of each individual to the likelihood is simply    Parameters are printed with %lf instead of %f (more numbers after the comma).
   hPijx.    The log-likelihood is printed in the log file
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.123  2006/03/20 10:52:43  brouard
   of the life expectancies. It also computes the prevalence limits.    * imach.c (Module): <title> changed, corresponds to .htm file
      name. <head> headers where missing.
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).  
            Institut national d'études démographiques, Paris.    * imach.c (Module): Weights can have a decimal point as for
   This software have been partly granted by Euro-REVES, a concerted action    English (a comma might work with a correct LC_NUMERIC environment,
   from the European Union.    otherwise the weight is truncated).
   It is copyrighted identically to a GNU software product, ie programme and    Modification of warning when the covariates values are not 0 or
   software can be distributed freely for non commercial use. Latest version    1.
   can be accessed at http://euroreves.ined.fr/imach .    Version 0.98g
   **********************************************************************/  
      Revision 1.122  2006/03/20 09:45:41  brouard
 #include <math.h>    (Module): Weights can have a decimal point as for
 #include <stdio.h>    English (a comma might work with a correct LC_NUMERIC environment,
 #include <stdlib.h>    otherwise the weight is truncated).
 #include <unistd.h>    Modification of warning when the covariates values are not 0 or
     1.
 #define MAXLINE 256    Version 0.98g
 #define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"  
 #define FILENAMELENGTH 80    Revision 1.121  2006/03/16 17:45:01  lievre
 /*#define DEBUG*/    * imach.c (Module): Comments concerning covariates added
 #define windows  
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    * imach.c (Module): refinements in the computation of lli if
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */  
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Revision 1.120  2006/03/16 15:10:38  lievre
     (Module): refinements in the computation of lli if
 #define NINTERVMAX 8    status=-2 in order to have more reliable computation if stepm is
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    not 1 month. Version 0.98f
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  
 #define NCOVMAX 8 /* Maximum number of covariates */    Revision 1.119  2006/03/15 17:42:26  brouard
 #define MAXN 20000    (Module): Bug if status = -2, the loglikelihood was
 #define YEARM 12. /* Number of months per year */    computed as likelihood omitting the logarithm. Version O.98e
 #define AGESUP 130  
 #define AGEBASE 40    Revision 1.118  2006/03/14 18:20:07  brouard
     (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 int erreur; /* Error number */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 int nvar;    (Module): Function pstamp added
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    (Module): Version 0.98d
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.117  2006/03/14 17:16:22  brouard
 int ndeath=1; /* Number of dead states */    (Module): varevsij Comments added explaining the second
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    table of variances if popbased=1 .
 int popbased=0;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): Version 0.98d
 int maxwav; /* Maxim number of waves */  
 int jmin, jmax; /* min, max spacing between 2 waves */    Revision 1.116  2006/03/06 10:29:27  brouard
 int mle, weightopt;    (Module): Variance-covariance wrong links and
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    varian-covariance of ej. is needed (Saito).
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.115  2006/02/27 12:17:45  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): One freematrix added in mlikeli! 0.98c
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    Revision 1.114  2006/02/26 12:57:58  brouard
 FILE *ficgp,*ficresprob,*ficpop;    (Module): Some improvements in processing parameter
 FILE *ficreseij;    filename with strsep.
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.113  2006/02/24 14:20:24  brouard
   char fileresv[FILENAMELENGTH];    (Module): Memory leaks checks with valgrind and:
  FILE  *ficresvpl;    datafile was not closed, some imatrix were not freed and on matrix
   char fileresvpl[FILENAMELENGTH];    allocation too.
   
 #define NR_END 1    Revision 1.112  2006/01/30 09:55:26  brouard
 #define FREE_ARG char*    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define FTOL 1.0e-10  
     Revision 1.111  2006/01/25 20:38:18  brouard
 #define NRANSI    (Module): Lots of cleaning and bugs added (Gompertz)
 #define ITMAX 200    (Module): Comments can be added in data file. Missing date values
     can be a simple dot '.'.
 #define TOL 2.0e-4  
     Revision 1.110  2006/01/25 00:51:50  brouard
 #define CGOLD 0.3819660    (Module): Lots of cleaning and bugs added (Gompertz)
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.109  2006/01/24 19:37:15  brouard
     (Module): Comments (lines starting with a #) are allowed in data.
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.108  2006/01/19 18:05:42  lievre
 #define TINY 1.0e-20    Gnuplot problem appeared...
     To be fixed
 static double maxarg1,maxarg2;  
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Revision 1.107  2006/01/19 16:20:37  brouard
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Test existence of gnuplot in imach path
    
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Revision 1.106  2006/01/19 13:24:36  brouard
 #define rint(a) floor(a+0.5)    Some cleaning and links added in html output
   
 static double sqrarg;    Revision 1.105  2006/01/05 20:23:19  lievre
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    *** empty log message ***
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}  
     Revision 1.104  2005/09/30 16:11:43  lievre
 int imx;    (Module): sump fixed, loop imx fixed, and simplifications.
 int stepm;    (Module): If the status is missing at the last wave but we know
 /* Stepm, step in month: minimum step interpolation*/    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
 int m,nb;    contributions to the likelihood is 1 - Prob of dying from last
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    health status (= 1-p13= p11+p12 in the easiest case of somebody in
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    the healthy state at last known wave). Version is 0.98
 double **pmmij, ***probs, ***mobaverage;  
 double dateintmean=0;    Revision 1.103  2005/09/30 15:54:49  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 double *weight;  
 int **s; /* Status */    Revision 1.102  2004/09/15 17:31:30  brouard
 double *agedc, **covar, idx;    Add the possibility to read data file including tab characters.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.101  2004/09/15 10:38:38  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Fix on curr_time
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.100  2004/07/12 18:29:06  brouard
 /**************** split *************************/    Add version for Mac OS X. Just define UNIX in Makefile
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.99  2004/06/05 08:57:40  brouard
    char *s;                             /* pointer */    *** empty log message ***
    int  l1, l2;                         /* length counters */  
     Revision 1.98  2004/05/16 15:05:56  brouard
    l1 = strlen( path );                 /* length of path */    New version 0.97 . First attempt to estimate force of mortality
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    directly from the data i.e. without the need of knowing the health
 #ifdef windows    state at each age, but using a Gompertz model: log u =a + b*age .
    s = strrchr( path, '\\' );           /* find last / */    This is the basic analysis of mortality and should be done before any
 #else    other analysis, in order to test if the mortality estimated from the
    s = strrchr( path, '/' );            /* find last / */    cross-longitudinal survey is different from the mortality estimated
 #endif    from other sources like vital statistic data.
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    The same imach parameter file can be used but the option for mle should be -3.
       extern char       *getwd( );  
     Agnès, who wrote this part of the code, tried to keep most of the
       if ( getwd( dirc ) == NULL ) {    former routines in order to include the new code within the former code.
 #else  
       extern char       *getcwd( );    The output is very simple: only an estimate of the intercept and of
     the slope with 95% confident intervals.
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    Current limitations:
          return( GLOCK_ERROR_GETCWD );    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.
       strcpy( name, path );             /* we've got it */    B) There is no computation of Life Expectancy nor Life Table.
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */    Revision 1.97  2004/02/20 13:25:42  lievre
       l2 = strlen( s );                 /* length of filename */    Version 0.96d. Population forecasting command line is (temporarily)
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    suppressed.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    Revision 1.96  2003/07/15 15:38:55  brouard
       dirc[l1-l2] = 0;                  /* add zero */    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
    }    rewritten within the same printf. Workaround: many printfs.
    l1 = strlen( dirc );                 /* length of directory */  
 #ifdef windows    Revision 1.95  2003/07/08 07:54:34  brouard
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    * imach.c (Repository):
 #else    (Repository): Using imachwizard code to output a more meaningful covariance
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    matrix (cov(a12,c31) instead of numbers.
 #endif  
    s = strrchr( name, '.' );            /* find last / */    Revision 1.94  2003/06/27 13:00:02  brouard
    s++;    Just cleaning
    strcpy(ext,s);                       /* save extension */  
    l1= strlen( name);    Revision 1.93  2003/06/25 16:33:55  brouard
    l2= strlen( s)+1;    (Module): On windows (cygwin) function asctime_r doesn't
    strncpy( finame, name, l1-l2);    exist so I changed back to asctime which exists.
    finame[l1-l2]= 0;    (Module): Version 0.96b
    return( 0 );                         /* we're done */  
 }    Revision 1.92  2003/06/25 16:30:45  brouard
     (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
 /******************************************/  
     Revision 1.91  2003/06/25 15:30:29  brouard
 void replace(char *s, char*t)    * imach.c (Repository): Duplicated warning errors corrected.
 {    (Repository): Elapsed time after each iteration is now output. It
   int i;    helps to forecast when convergence will be reached. Elapsed time
   int lg=20;    is stamped in powell.  We created a new html file for the graphs
   i=0;    concerning matrix of covariance. It has extension -cov.htm.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.90  2003/06/24 12:34:15  brouard
     (s[i] = t[i]);    (Module): Some bugs corrected for windows. Also, when
     if (t[i]== '\\') s[i]='/';    mle=-1 a template is output in file "or"mypar.txt with the design
   }    of the covariance matrix to be input.
 }  
     Revision 1.89  2003/06/24 12:30:52  brouard
 int nbocc(char *s, char occ)    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   int i,j=0;    of the covariance matrix to be input.
   int lg=20;  
   i=0;    Revision 1.88  2003/06/23 17:54:56  brouard
   lg=strlen(s);    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Revision 1.87  2003/06/18 12:26:01  brouard
   }    Version 0.96
   return j;  
 }    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 void cutv(char *u,char *v, char*t, char occ)    routine fileappend.
 {  
   int i,lg,j,p=0;    Revision 1.85  2003/06/17 13:12:43  brouard
   i=0;    * imach.c (Repository): Check when date of death was earlier that
   for(j=0; j<=strlen(t)-1; j++) {    current date of interview. It may happen when the death was just
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    prior to the death. In this case, dh was negative and likelihood
   }    was wrong (infinity). We still send an "Error" but patch by
     assuming that the date of death was just one stepm after the
   lg=strlen(t);    interview.
   for(j=0; j<p; j++) {    (Repository): Because some people have very long ID (first column)
     (u[j] = t[j]);    we changed int to long in num[] and we added a new lvector for
   }    memory allocation. But we also truncated to 8 characters (left
      u[p]='\0';    truncation)
     (Repository): No more line truncation errors.
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);    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
     many times. Probs is memory consuming and must be used with
 /********************** nrerror ********************/    parcimony.
     Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 void nrerror(char error_text[])  
 {    Revision 1.83  2003/06/10 13:39:11  lievre
   fprintf(stderr,"ERREUR ...\n");    *** empty log message ***
   fprintf(stderr,"%s\n",error_text);  
   exit(1);    Revision 1.82  2003/06/05 15:57:20  brouard
 }    Add log in  imach.c and  fullversion number is now printed.
 /*********************** vector *******************/  
 double *vector(int nl, int nh)  */
 {  /*
   double *v;     Interpolated Markov Chain
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Short summary of the programme:
   return v-nl+NR_END;    
 }    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /************************ free vector ******************/    first survey ("cross") where individuals from different ages are
 void free_vector(double*v, int nl, int nh)    interviewed on their health status or degree of disability (in the
 {    case of a health survey which is our main interest) -2- at least a
   free((FREE_ARG)(v+nl-NR_END));    second wave of interviews ("longitudinal") which measure each change
 }    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
 /************************ivector *******************************/    model. More health states you consider, more time is necessary to reach the
 int *ivector(long nl,long nh)    Maximum Likelihood of the parameters involved in the model.  The
 {    simplest model is the multinomial logistic model where pij is the
   int *v;    probability to be observed in state j at the second wave
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    conditional to be observed in state i at the first wave. Therefore
   if (!v) nrerror("allocation failure in ivector");    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   return v-nl+NR_END;    'age' is age and 'sex' is a covariate. If you want to have a more
 }    complex model than "constant and age", you should modify the program
     where the markup *Covariates have to be included here again* invites
 /******************free ivector **************************/    you to do it.  More covariates you add, slower the
 void free_ivector(int *v, long nl, long nh)    convergence.
 {  
   free((FREE_ARG)(v+nl-NR_END));    The advantage of this computer programme, compared to a simple
 }    multinomial logistic model, is clear when the delay between waves is not
     identical for each individual. Also, if a individual missed an
 /******************* imatrix *******************************/    intermediate interview, the information is lost, but taken into
 int **imatrix(long nrl, long nrh, long ncl, long nch)    account using an interpolation or extrapolation.  
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {    hPijx is the probability to be observed in state i at age x+h
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    conditional to the observed state i at age x. The delay 'h' can be
   int **m;    split into an exact number (nh*stepm) of unobserved intermediate
      states. This elementary transition (by month, quarter,
   /* allocate pointers to rows */    semester or year) is modelled as a multinomial logistic.  The hPx
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    matrix is simply the matrix product of nh*stepm elementary matrices
   if (!m) nrerror("allocation failure 1 in matrix()");    and the contribution of each individual to the likelihood is simply
   m += NR_END;    hPijx.
   m -= nrl;  
      Also this programme outputs the covariance matrix of the parameters but also
      of the life expectancies. It also computes the period (stable) prevalence. 
   /* allocate rows and set pointers to them */    
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");             Institut national d'études démographiques, Paris.
   m[nrl] += NR_END;    This software have been partly granted by Euro-REVES, a concerted action
   m[nrl] -= ncl;    from the European Union.
      It is copyrighted identically to a GNU software product, ie programme and
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    software can be distributed freely for non commercial use. Latest version
      can be accessed at http://euroreves.ined.fr/imach .
   /* return pointer to array of pointers to rows */  
   return m;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     
 /****************** free_imatrix *************************/    **********************************************************************/
 void free_imatrix(m,nrl,nrh,ncl,nch)  /*
       int **m;    main
       long nch,ncl,nrh,nrl;    read parameterfile
      /* free an int matrix allocated by imatrix() */    read datafile
 {    concatwav
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    freqsummary
   free((FREE_ARG) (m+nrl-NR_END));    if (mle >= 1)
 }      mlikeli
     print results files
 /******************* matrix *******************************/    if mle==1 
 double **matrix(long nrl, long nrh, long ncl, long nch)       computes hessian
 {    read end of parameter file: agemin, agemax, bage, fage, estepm
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;        begin-prev-date,...
   double **m;    open gnuplot file
     open html file
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    period (stable) prevalence
   if (!m) nrerror("allocation failure 1 in matrix()");     for age prevalim()
   m += NR_END;    h Pij x
   m -= nrl;    variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    health expectancies
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    Variance-covariance of DFLE
   m[nrl] += NR_END;    prevalence()
   m[nrl] -= ncl;     movingaverage()
     varevsij() 
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    if popbased==1 varevsij(,popbased)
   return m;    total life expectancies
 }    Variance of period (stable) prevalence
    end
 /*************************free matrix ************************/  */
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));   
 }  #include <math.h>
   #include <stdio.h>
 /******************* ma3x *******************************/  #include <stdlib.h>
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #include <string.h>
 {  #include <unistd.h>
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  
   double ***m;  #include <limits.h>
   #include <sys/types.h>
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #include <sys/stat.h>
   if (!m) nrerror("allocation failure 1 in matrix()");  #include <errno.h>
   m += NR_END;  extern int errno;
   m -= nrl;  
   /* #include <sys/time.h> */
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #include <time.h>
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #include "timeval.h"
   m[nrl] += NR_END;  
   m[nrl] -= ncl;  /* #include <libintl.h> */
   /* #define _(String) gettext (String) */
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   #define MAXLINE 256
   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 GNUPLOTPROGRAM "gnuplot"
   m[nrl][ncl] += NR_END;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   m[nrl][ncl] -= nll;  #define FILENAMELENGTH 132
   for (j=ncl+1; j<=nch; j++)  
     m[nrl][j]=m[nrl][j-1]+nlay;  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
    #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   for (i=nrl+1; i<=nrh; i++) {  
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
     for (j=ncl+1; j<=nch; j++)  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
       m[i][j]=m[i][j-1]+nlay;  
   }  #define NINTERVMAX 8
   return m;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
 }  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   #define NCOVMAX 20 /* Maximum number of covariates */
 /*************************free ma3x ************************/  #define MAXN 20000
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #define YEARM 12. /* Number of months per year */
 {  #define AGESUP 130
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  #define AGEBASE 40
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   free((FREE_ARG)(m+nrl-NR_END));  #ifdef UNIX
 }  #define DIRSEPARATOR '/'
   #define CHARSEPARATOR "/"
 /***************** f1dim *************************/  #define ODIRSEPARATOR '\\'
 extern int ncom;  #else
 extern double *pcom,*xicom;  #define DIRSEPARATOR '\\'
 extern double (*nrfunc)(double []);  #define CHARSEPARATOR "\\"
    #define ODIRSEPARATOR '/'
 double f1dim(double x)  #endif
 {  
   int j;  /* $Id$ */
   double f;  /* $State$ */
   double *xt;  
    char version[]="Imach version 0.98i, June 2006, INED-EUROREVES-Institut de longevite ";
   xt=vector(1,ncom);  char fullversion[]="$Revision$ $Date$"; 
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  char strstart[80];
   f=(*nrfunc)(xt);  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   free_vector(xt,1,ncom);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   return f;  int nvar=0;
 }  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
   int npar=NPARMAX;
 /*****************brent *************************/  int nlstate=2; /* Number of live states */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  int ndeath=1; /* Number of dead states */
 {  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   int iter;  int popbased=0;
   double a,b,d,etemp;  
   double fu,fv,fw,fx;  int *wav; /* Number of waves for this individuual 0 is possible */
   double ftemp;  int maxwav=0; /* Maxim number of waves */
   double p,q,r,tol1,tol2,u,v,w,x,xm;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
   double e=0.0;  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
    int gipmx=0, gsw=0; /* Global variables on the number of contributions 
   a=(ax < cx ? ax : cx);                     to the likelihood and the sum of weights (done by funcone)*/
   b=(ax > cx ? ax : cx);  int mle=1, weightopt=0;
   x=w=v=bx;  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
   fw=fv=fx=(*f)(x);  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
   for (iter=1;iter<=ITMAX;iter++) {  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
     xm=0.5*(a+b);             * wave mi and wave mi+1 is not an exact multiple of stepm. */
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  double jmean=1; /* Mean space between 2 waves */
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  double **oldm, **newm, **savm; /* Working pointers to matrices */
     printf(".");fflush(stdout);  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
 #ifdef DEBUG  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     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 *ficlog, *ficrespow;
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int globpr=0; /* Global variable for printing or not */
 #endif  double fretone; /* Only one call to likelihood */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  long ipmx=0; /* Number of contributions */
       *xmin=x;  double sw; /* Sum of weights */
       return fx;  char filerespow[FILENAMELENGTH];
     }  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     ftemp=fu;  FILE *ficresilk;
     if (fabs(e) > tol1) {  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       r=(x-w)*(fx-fv);  FILE *ficresprobmorprev;
       q=(x-v)*(fx-fw);  FILE *fichtm, *fichtmcov; /* Html File */
       p=(x-v)*q-(x-w)*r;  FILE *ficreseij;
       q=2.0*(q-r);  char filerese[FILENAMELENGTH];
       if (q > 0.0) p = -p;  FILE *ficresstdeij;
       q=fabs(q);  char fileresstde[FILENAMELENGTH];
       etemp=e;  FILE *ficrescveij;
       e=d;  char filerescve[FILENAMELENGTH];
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  FILE  *ficresvij;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  char fileresv[FILENAMELENGTH];
       else {  FILE  *ficresvpl;
         d=p/q;  char fileresvpl[FILENAMELENGTH];
         u=x+d;  char title[MAXLINE];
         if (u-a < tol2 || b-u < tol2)  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
           d=SIGN(tol1,xm-x);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       }  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
     } else {  char command[FILENAMELENGTH];
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  int  outcmd=0;
     }  
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     fu=(*f)(u);  
     if (fu <= fx) {  char filelog[FILENAMELENGTH]; /* Log file */
       if (u >= x) a=x; else b=x;  char filerest[FILENAMELENGTH];
       SHFT(v,w,x,u)  char fileregp[FILENAMELENGTH];
         SHFT(fv,fw,fx,fu)  char popfile[FILENAMELENGTH];
         } else {  
           if (u < x) a=u; else b=u;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
           if (fu <= fw || w == x) {  
             v=w;  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
             w=u;  struct timezone tzp;
             fv=fw;  extern int gettimeofday();
             fw=fu;  struct tm tmg, tm, tmf, *gmtime(), *localtime();
           } else if (fu <= fv || v == x || v == w) {  long time_value;
             v=u;  extern long time();
             fv=fu;  char strcurr[80], strfor[80];
           }  
         }  char *endptr;
   }  long lval;
   nrerror("Too many iterations in brent");  double dval;
   *xmin=x;  
   return fx;  #define NR_END 1
 }  #define FREE_ARG char*
   #define FTOL 1.0e-10
 /****************** mnbrak ***********************/  
   #define NRANSI 
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  #define ITMAX 200 
             double (*func)(double))  
 {  #define TOL 2.0e-4 
   double ulim,u,r,q, dum;  
   double fu;  #define CGOLD 0.3819660 
    #define ZEPS 1.0e-10 
   *fa=(*func)(*ax);  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   *fb=(*func)(*bx);  
   if (*fb > *fa) {  #define GOLD 1.618034 
     SHFT(dum,*ax,*bx,dum)  #define GLIMIT 100.0 
       SHFT(dum,*fb,*fa,dum)  #define TINY 1.0e-20 
       }  
   *cx=(*bx)+GOLD*(*bx-*ax);  static double maxarg1,maxarg2;
   *fc=(*func)(*cx);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   while (*fb > *fc) {  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     r=(*bx-*ax)*(*fb-*fc);    
     q=(*bx-*cx)*(*fb-*fa);  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  #define rint(a) floor(a+0.5)
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  
     ulim=(*bx)+GLIMIT*(*cx-*bx);  static double sqrarg;
     if ((*bx-u)*(u-*cx) > 0.0) {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       fu=(*func)(u);  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
     } else if ((*cx-u)*(u-ulim) > 0.0) {  int agegomp= AGEGOMP;
       fu=(*func)(u);  
       if (fu < *fc) {  int imx; 
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  int stepm=1;
           SHFT(*fb,*fc,fu,(*func)(u))  /* Stepm, step in month: minimum step interpolation*/
           }  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  int estepm;
       u=ulim;  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
       fu=(*func)(u);  
     } else {  int m,nb;
       u=(*cx)+GOLD*(*cx-*bx);  long *num;
       fu=(*func)(u);  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     SHFT(*ax,*bx,*cx,u)  double **pmmij, ***probs;
       SHFT(*fa,*fb,*fc,fu)  double *ageexmed,*agecens;
       }  double dateintmean=0;
 }  
   double *weight;
 /*************** linmin ************************/  int **s; /* Status */
   double *agedc, **covar, idx;
 int ncom;  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
 double *pcom,*xicom;  double *lsurv, *lpop, *tpop;
 double (*nrfunc)(double []);  
    double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  double ftolhess; /* Tolerance for computing hessian */
 {  
   double brent(double ax, double bx, double cx,  /**************** split *************************/
                double (*f)(double), double tol, double *xmin);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
   double f1dim(double x);  {
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
               double *fc, double (*func)(double));       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   int j;    */ 
   double xx,xmin,bx,ax;    char  *ss;                            /* pointer */
   double fx,fb,fa;    int   l1, l2;                         /* length counters */
    
   ncom=n;    l1 = strlen(path );                   /* length of path */
   pcom=vector(1,n);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
   xicom=vector(1,n);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
   nrfunc=func;    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   for (j=1;j<=n;j++) {      strcpy( name, path );               /* we got the fullname name because no directory */
     pcom[j]=p[j];      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     xicom[j]=xi[j];        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   }      /* get current working directory */
   ax=0.0;      /*    extern  char* getcwd ( char *buf , int len);*/
   xx=1.0;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);        return( GLOCK_ERROR_GETCWD );
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);      }
 #ifdef DEBUG      /* got dirc from getcwd*/
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);      printf(" DIRC = %s \n",dirc);
 #endif    } else {                              /* strip direcotry from path */
   for (j=1;j<=n;j++) {      ss++;                               /* after this, the filename */
     xi[j] *= xmin;      l2 = strlen( ss );                  /* length of filename */
     p[j] += xi[j];      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   }      strcpy( name, ss );         /* save file name */
   free_vector(xicom,1,n);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
   free_vector(pcom,1,n);      dirc[l1-l2] = 0;                    /* add zero */
 }      printf(" DIRC2 = %s \n",dirc);
     }
 /*************** powell ************************/    /* We add a separator at the end of dirc if not exists */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    l1 = strlen( dirc );                  /* length of directory */
             double (*func)(double []))    if( dirc[l1-1] != DIRSEPARATOR ){
 {      dirc[l1] =  DIRSEPARATOR;
   void linmin(double p[], double xi[], int n, double *fret,      dirc[l1+1] = 0; 
               double (*func)(double []));      printf(" DIRC3 = %s \n",dirc);
   int i,ibig,j;    }
   double del,t,*pt,*ptt,*xit;    ss = strrchr( name, '.' );            /* find last / */
   double fp,fptt;    if (ss >0){
   double *xits;      ss++;
   pt=vector(1,n);      strcpy(ext,ss);                     /* save extension */
   ptt=vector(1,n);      l1= strlen( name);
   xit=vector(1,n);      l2= strlen(ss)+1;
   xits=vector(1,n);      strncpy( finame, name, l1-l2);
   *fret=(*func)(p);      finame[l1-l2]= 0;
   for (j=1;j<=n;j++) pt[j]=p[j];    }
   for (*iter=1;;++(*iter)) {  
     fp=(*fret);    return( 0 );                          /* we're done */
     ibig=0;  }
     del=0.0;  
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)  /******************************************/
       printf(" %d %.12f",i, p[i]);  
     printf("\n");  void replace_back_to_slash(char *s, char*t)
     for (i=1;i<=n;i++) {  {
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    int i;
       fptt=(*fret);    int lg=0;
 #ifdef DEBUG    i=0;
       printf("fret=%lf \n",*fret);    lg=strlen(t);
 #endif    for(i=0; i<= lg; i++) {
       printf("%d",i);fflush(stdout);      (s[i] = t[i]);
       linmin(p,xit,n,fret,func);      if (t[i]== '\\') s[i]='/';
       if (fabs(fptt-(*fret)) > del) {    }
         del=fabs(fptt-(*fret));  }
         ibig=i;  
       }  int nbocc(char *s, char occ)
 #ifdef DEBUG  {
       printf("%d %.12e",i,(*fret));    int i,j=0;
       for (j=1;j<=n;j++) {    int lg=20;
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    i=0;
         printf(" x(%d)=%.12e",j,xit[j]);    lg=strlen(s);
       }    for(i=0; i<= lg; i++) {
       for(j=1;j<=n;j++)    if  (s[i] == occ ) j++;
         printf(" p=%.12e",p[j]);    }
       printf("\n");    return j;
 #endif  }
     }  
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  void cutv(char *u,char *v, char*t, char occ)
 #ifdef DEBUG  {
       int k[2],l;    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
       k[0]=1;       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
       k[1]=-1;       gives u="abcedf" and v="ghi2j" */
       printf("Max: %.12e",(*func)(p));    int i,lg,j,p=0;
       for (j=1;j<=n;j++)    i=0;
         printf(" %.12e",p[j]);    for(j=0; j<=strlen(t)-1; j++) {
       printf("\n");      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
       for(l=0;l<=1;l++) {    }
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];    lg=strlen(t);
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);    for(j=0; j<p; j++) {
         }      (u[j] = t[j]);
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    }
       }       u[p]='\0';
 #endif  
      for(j=0; j<= lg; j++) {
       if (j>=(p+1))(v[j-p-1] = t[j]);
       free_vector(xit,1,n);    }
       free_vector(xits,1,n);  }
       free_vector(ptt,1,n);  
       free_vector(pt,1,n);  /********************** nrerror ********************/
       return;  
     }  void nrerror(char error_text[])
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  {
     for (j=1;j<=n;j++) {    fprintf(stderr,"ERREUR ...\n");
       ptt[j]=2.0*p[j]-pt[j];    fprintf(stderr,"%s\n",error_text);
       xit[j]=p[j]-pt[j];    exit(EXIT_FAILURE);
       pt[j]=p[j];  }
     }  /*********************** vector *******************/
     fptt=(*func)(ptt);  double *vector(int nl, int nh)
     if (fptt < fp) {  {
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    double *v;
       if (t < 0.0) {    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
         linmin(p,xit,n,fret,func);    if (!v) nrerror("allocation failure in vector");
         for (j=1;j<=n;j++) {    return v-nl+NR_END;
           xi[j][ibig]=xi[j][n];  }
           xi[j][n]=xit[j];  
         }  /************************ free vector ******************/
 #ifdef DEBUG  void free_vector(double*v, int nl, int nh)
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  {
         for(j=1;j<=n;j++)    free((FREE_ARG)(v+nl-NR_END));
           printf(" %.12e",xit[j]);  }
         printf("\n");  
 #endif  /************************ivector *******************************/
       }  int *ivector(long nl,long nh)
     }  {
   }    int *v;
 }    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
 /**** Prevalence limit ****************/    return v-nl+NR_END;
   }
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  
 {  /******************free ivector **************************/
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  void free_ivector(int *v, long nl, long nh)
      matrix by transitions matrix until convergence is reached */  {
     free((FREE_ARG)(v+nl-NR_END));
   int i, ii,j,k;  }
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();  /************************lvector *******************************/
   double **out, cov[NCOVMAX], **pmij();  long *lvector(long nl,long nh)
   double **newm;  {
   double agefin, delaymax=50 ; /* Max number of years to converge */    long *v;
     v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
   for (ii=1;ii<=nlstate+ndeath;ii++)    if (!v) nrerror("allocation failure in ivector");
     for (j=1;j<=nlstate+ndeath;j++){    return v-nl+NR_END;
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  }
     }  
   /******************free lvector **************************/
    cov[1]=1.;  void free_lvector(long *v, long nl, long nh)
    {
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    free((FREE_ARG)(v+nl-NR_END));
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  }
     newm=savm;  
     /* Covariates have to be included here again */  /******************* imatrix *******************************/
      cov[2]=agefin;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
         /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       for (k=1; k<=cptcovn;k++) {  { 
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    int **m; 
       }    
       for (k=1; k<=cptcovage;k++)    /* allocate pointers to rows */ 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       for (k=1; k<=cptcovprod;k++)    if (!m) nrerror("allocation failure 1 in matrix()"); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    m += NR_END; 
     m -= nrl; 
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    
     /* allocate rows and set pointers to them */ 
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     savm=oldm;    m[nrl] += NR_END; 
     oldm=newm;    m[nrl] -= ncl; 
     maxmax=0.;    
     for(j=1;j<=nlstate;j++){    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
       min=1.;    
       max=0.;    /* return pointer to array of pointers to rows */ 
       for(i=1; i<=nlstate; i++) {    return m; 
         sumnew=0;  } 
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  
         prlim[i][j]= newm[i][j]/(1-sumnew);  /****************** free_imatrix *************************/
         max=FMAX(max,prlim[i][j]);  void free_imatrix(m,nrl,nrh,ncl,nch)
         min=FMIN(min,prlim[i][j]);        int **m;
       }        long nch,ncl,nrh,nrl; 
       maxmin=max-min;       /* free an int matrix allocated by imatrix() */ 
       maxmax=FMAX(maxmax,maxmin);  { 
     }    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     if(maxmax < ftolpl){    free((FREE_ARG) (m+nrl-NR_END)); 
       return prlim;  } 
     }  
   }  /******************* matrix *******************************/
 }  double **matrix(long nrl, long nrh, long ncl, long nch)
   {
 /*************** transition probabilities ***************/    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     double **m;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  
 {    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   double s1, s2;    if (!m) nrerror("allocation failure 1 in matrix()");
   /*double t34;*/    m += NR_END;
   int i,j,j1, nc, ii, jj;    m -= nrl;
   
     for(i=1; i<= nlstate; i++){    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     for(j=1; j<i;j++){    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    m[nrl] += NR_END;
         /*s2 += param[i][j][nc]*cov[nc];*/    m[nrl] -= ncl;
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       }    return m;
       ps[i][j]=s2;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/     */
     }  }
     for(j=i+1; j<=nlstate+ndeath;j++){  
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  /*************************free matrix ************************/
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  {
       }    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       ps[i][j]=s2;    free((FREE_ARG)(m+nrl-NR_END));
     }  }
   }  
     /*ps[3][2]=1;*/  /******************* ma3x *******************************/
   double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   for(i=1; i<= nlstate; i++){  {
      s1=0;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     for(j=1; j<i; j++)    double ***m;
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       s1+=exp(ps[i][j]);    if (!m) nrerror("allocation failure 1 in matrix()");
     ps[i][i]=1./(s1+1.);    m += NR_END;
     for(j=1; j<i; j++)    m -= nrl;
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     for(j=i+1; j<=nlstate+ndeath; j++)    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       ps[i][j]= exp(ps[i][j])*ps[i][i];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    m[nrl] += NR_END;
   } /* end i */    m[nrl] -= ncl;
   
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     for(jj=1; jj<= nlstate+ndeath; jj++){  
       ps[ii][jj]=0;    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       ps[ii][ii]=1;    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
     }    m[nrl][ncl] += NR_END;
   }    m[nrl][ncl] -= nll;
     for (j=ncl+1; j<=nch; j++) 
       m[nrl][j]=m[nrl][j-1]+nlay;
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    
     for(jj=1; jj<= nlstate+ndeath; jj++){    for (i=nrl+1; i<=nrh; i++) {
      printf("%lf ",ps[ii][jj]);      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
    }      for (j=ncl+1; j<=nch; j++) 
     printf("\n ");        m[i][j]=m[i][j-1]+nlay;
     }    }
     printf("\n ");printf("%lf ",cov[2]);*/    return m; 
 /*    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   for(i=1; i<= npar; i++) printf("%f ",x[i]);             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   goto end;*/    */
     return ps;  }
 }  
   /*************************free ma3x ************************/
 /**************** Product of 2 matrices ******************/  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   {
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
 {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    free((FREE_ARG)(m+nrl-NR_END));
      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 subdirf ***********/
      a pointer to pointers identical to out */  char *subdirf(char fileres[])
   long i, j, k;  {
   for(i=nrl; i<= nrh; i++)    /* Caution optionfilefiname is hidden */
     for(k=ncolol; k<=ncoloh; k++)    strcpy(tmpout,optionfilefiname);
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    strcat(tmpout,"/"); /* Add to the right */
         out[i][k] +=in[i][j]*b[j][k];    strcat(tmpout,fileres);
     return tmpout;
   return out;  }
 }  
   /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
 /************* Higher Matrix Product ***************/  {
     
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    /* Caution optionfilefiname is hidden */
 {    strcpy(tmpout,optionfilefiname);
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    strcat(tmpout,"/");
      duration (i.e. until    strcat(tmpout,preop);
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    strcat(tmpout,fileres);
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    return tmpout;
      (typically every 2 years instead of every month which is too big).  }
      Model is determined by parameters x and covariates have to be  
      included manually here.  /*************** function subdirf3 ***********/
   char *subdirf3(char fileres[], char *preop, char *preop2)
      */  {
     
   int i, j, d, h, k;    /* Caution optionfilefiname is hidden */
   double **out, cov[NCOVMAX];    strcpy(tmpout,optionfilefiname);
   double **newm;    strcat(tmpout,"/");
     strcat(tmpout,preop);
   /* Hstepm could be zero and should return the unit matrix */    strcat(tmpout,preop2);
   for (i=1;i<=nlstate+ndeath;i++)    strcat(tmpout,fileres);
     for (j=1;j<=nlstate+ndeath;j++){    return tmpout;
       oldm[i][j]=(i==j ? 1.0 : 0.0);  }
       po[i][j][0]=(i==j ? 1.0 : 0.0);  
     }  /***************** f1dim *************************/
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  extern int ncom; 
   for(h=1; h <=nhstepm; h++){  extern double *pcom,*xicom;
     for(d=1; d <=hstepm; d++){  extern double (*nrfunc)(double []); 
       newm=savm;   
       /* Covariates have to be included here again */  double f1dim(double x) 
       cov[1]=1.;  { 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    int j; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    double f;
       for (k=1; k<=cptcovage;k++)    double *xt; 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];   
       for (k=1; k<=cptcovprod;k++)    xt=vector(1,ncom); 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
     free_vector(xt,1,ncom); 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    return f; 
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/  } 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,  
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  /*****************brent *************************/
       savm=oldm;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
       oldm=newm;  { 
     }    int iter; 
     for(i=1; i<=nlstate+ndeath; i++)    double a,b,d,etemp;
       for(j=1;j<=nlstate+ndeath;j++) {    double fu,fv,fw,fx;
         po[i][j][h]=newm[i][j];    double ftemp;
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
          */    double e=0.0; 
       }   
   } /* end h */    a=(ax < cx ? ax : cx); 
   return po;    b=(ax > cx ? ax : cx); 
 }    x=w=v=bx; 
     fw=fv=fx=(*f)(x); 
     for (iter=1;iter<=ITMAX;iter++) { 
 /*************** log-likelihood *************/      xm=0.5*(a+b); 
 double func( double *x)      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
 {      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   int i, ii, j, k, mi, d, kk;      printf(".");fflush(stdout);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];      fprintf(ficlog,".");fflush(ficlog);
   double **out;  #ifdef DEBUG
   double sw; /* Sum of weights */      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);
   double lli; /* Individual log likelihood */      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);
   long ipmx;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   /*extern weight */  #endif
   /* We are differentiating ll according to initial status */      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/        *xmin=x; 
   /*for(i=1;i<imx;i++)        return fx; 
     printf(" %d\n",s[4][i]);      } 
   */      ftemp=fu;
   cov[1]=1.;      if (fabs(e) > tol1) { 
         r=(x-w)*(fx-fv); 
   for(k=1; k<=nlstate; k++) ll[k]=0.;        q=(x-v)*(fx-fw); 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){        p=(x-v)*q-(x-w)*r; 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];        q=2.0*(q-r); 
     for(mi=1; mi<= wav[i]-1; mi++){        if (q > 0.0) p = -p; 
       for (ii=1;ii<=nlstate+ndeath;ii++)        q=fabs(q); 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);        etemp=e; 
       for(d=0; d<dh[mi][i]; d++){        e=d; 
         newm=savm;        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
         for (kk=1; kk<=cptcovage;kk++) {        else { 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];          d=p/q; 
         }          u=x+d; 
                  if (u-a < tol2 || b-u < tol2) 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,            d=SIGN(tol1,xm-x); 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        } 
         savm=oldm;      } else { 
         oldm=newm;        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
              } 
              u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       } /* end mult */      fu=(*f)(u); 
            if (fu <= fx) { 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);        if (u >= x) a=x; else b=x; 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/        SHFT(v,w,x,u) 
       ipmx +=1;          SHFT(fv,fw,fx,fu) 
       sw += weight[i];          } else { 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;            if (u < x) a=u; else b=u; 
     } /* end of wave */            if (fu <= fw || w == x) { 
   } /* end of individual */              v=w; 
               w=u; 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];              fv=fw; 
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */              fw=fu; 
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */            } else if (fu <= fv || v == x || v == w) { 
   return -l;              v=u; 
 }              fv=fu; 
             } 
           } 
 /*********** Maximum Likelihood Estimation ***************/    } 
     nrerror("Too many iterations in brent"); 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    *xmin=x; 
 {    return fx; 
   int i,j, iter;  } 
   double **xi,*delti;  
   double fret;  /****************** mnbrak ***********************/
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
     for (j=1;j<=npar;j++)              double (*func)(double)) 
       xi[i][j]=(i==j ? 1.0 : 0.0);  { 
   printf("Powell\n");    double ulim,u,r,q, dum;
   powell(p,xi,npar,ftol,&iter,&fret,func);    double fu; 
    
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    *fa=(*func)(*ax); 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    *fb=(*func)(*bx); 
     if (*fb > *fa) { 
 }      SHFT(dum,*ax,*bx,dum) 
         SHFT(dum,*fb,*fa,dum) 
 /**** Computes Hessian and covariance matrix ***/        } 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    *cx=(*bx)+GOLD*(*bx-*ax); 
 {    *fc=(*func)(*cx); 
   double  **a,**y,*x,pd;    while (*fb > *fc) { 
   double **hess;      r=(*bx-*ax)*(*fb-*fc); 
   int i, j,jk;      q=(*bx-*cx)*(*fb-*fa); 
   int *indx;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
         (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
   double hessii(double p[], double delta, int theta, double delti[]);      ulim=(*bx)+GLIMIT*(*cx-*bx); 
   double hessij(double p[], double delti[], int i, int j);      if ((*bx-u)*(u-*cx) > 0.0) { 
   void lubksb(double **a, int npar, int *indx, double b[]) ;        fu=(*func)(u); 
   void ludcmp(double **a, int npar, int *indx, double *d) ;      } else if ((*cx-u)*(u-ulim) > 0.0) { 
         fu=(*func)(u); 
   hess=matrix(1,npar,1,npar);        if (fu < *fc) { 
           SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
   printf("\nCalculation of the hessian matrix. Wait...\n");            SHFT(*fb,*fc,fu,(*func)(u)) 
   for (i=1;i<=npar;i++){            } 
     printf("%d",i);fflush(stdout);      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     hess[i][i]=hessii(p,ftolhess,i,delti);        u=ulim; 
     /*printf(" %f ",p[i]);*/        fu=(*func)(u); 
     /*printf(" %lf ",hess[i][i]);*/      } else { 
   }        u=(*cx)+GOLD*(*cx-*bx); 
          fu=(*func)(u); 
   for (i=1;i<=npar;i++) {      } 
     for (j=1;j<=npar;j++)  {      SHFT(*ax,*bx,*cx,u) 
       if (j>i) {        SHFT(*fa,*fb,*fc,fu) 
         printf(".%d%d",i,j);fflush(stdout);        } 
         hess[i][j]=hessij(p,delti,i,j);  } 
         hess[j][i]=hess[i][j];      
         /*printf(" %lf ",hess[i][j]);*/  /*************** linmin ************************/
       }  
     }  int ncom; 
   }  double *pcom,*xicom;
   printf("\n");  double (*nrfunc)(double []); 
    
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
    { 
   a=matrix(1,npar,1,npar);    double brent(double ax, double bx, double cx, 
   y=matrix(1,npar,1,npar);                 double (*f)(double), double tol, double *xmin); 
   x=vector(1,npar);    double f1dim(double x); 
   indx=ivector(1,npar);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   for (i=1;i<=npar;i++)                double *fc, double (*func)(double)); 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    int j; 
   ludcmp(a,npar,indx,&pd);    double xx,xmin,bx,ax; 
     double fx,fb,fa;
   for (j=1;j<=npar;j++) {   
     for (i=1;i<=npar;i++) x[i]=0;    ncom=n; 
     x[j]=1;    pcom=vector(1,n); 
     lubksb(a,npar,indx,x);    xicom=vector(1,n); 
     for (i=1;i<=npar;i++){    nrfunc=func; 
       matcov[i][j]=x[i];    for (j=1;j<=n;j++) { 
     }      pcom[j]=p[j]; 
   }      xicom[j]=xi[j]; 
     } 
   printf("\n#Hessian matrix#\n");    ax=0.0; 
   for (i=1;i<=npar;i++) {    xx=1.0; 
     for (j=1;j<=npar;j++) {    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
       printf("%.3e ",hess[i][j]);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
     }  #ifdef DEBUG
     printf("\n");    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   }    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
   /* Recompute Inverse */    for (j=1;j<=n;j++) { 
   for (i=1;i<=npar;i++)      xi[j] *= xmin; 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];      p[j] += xi[j]; 
   ludcmp(a,npar,indx,&pd);    } 
     free_vector(xicom,1,n); 
   /*  printf("\n#Hessian matrix recomputed#\n");    free_vector(pcom,1,n); 
   } 
   for (j=1;j<=npar;j++) {  
     for (i=1;i<=npar;i++) x[i]=0;  char *asc_diff_time(long time_sec, char ascdiff[])
     x[j]=1;  {
     lubksb(a,npar,indx,x);    long sec_left, days, hours, minutes;
     for (i=1;i<=npar;i++){    days = (time_sec) / (60*60*24);
       y[i][j]=x[i];    sec_left = (time_sec) % (60*60*24);
       printf("%.3e ",y[i][j]);    hours = (sec_left) / (60*60) ;
     }    sec_left = (sec_left) %(60*60);
     printf("\n");    minutes = (sec_left) /60;
   }    sec_left = (sec_left) % (60);
   */    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
     return ascdiff;
   free_matrix(a,1,npar,1,npar);  }
   free_matrix(y,1,npar,1,npar);  
   free_vector(x,1,npar);  /*************** powell ************************/
   free_ivector(indx,1,npar);  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   free_matrix(hess,1,npar,1,npar);              double (*func)(double [])) 
   { 
     void linmin(double p[], double xi[], int n, double *fret, 
 }                double (*func)(double [])); 
     int i,ibig,j; 
 /*************** hessian matrix ****************/    double del,t,*pt,*ptt,*xit;
 double hessii( double x[], double delta, int theta, double delti[])    double fp,fptt;
 {    double *xits;
   int i;    int niterf, itmp;
   int l=1, lmax=20;  
   double k1,k2;    pt=vector(1,n); 
   double p2[NPARMAX+1];    ptt=vector(1,n); 
   double res;    xit=vector(1,n); 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    xits=vector(1,n); 
   double fx;    *fret=(*func)(p); 
   int k=0,kmax=10;    for (j=1;j<=n;j++) pt[j]=p[j]; 
   double l1;    for (*iter=1;;++(*iter)) { 
       fp=(*fret); 
   fx=func(x);      ibig=0; 
   for (i=1;i<=npar;i++) p2[i]=x[i];      del=0.0; 
   for(l=0 ; l <=lmax; l++){      last_time=curr_time;
     l1=pow(10,l);      (void) gettimeofday(&curr_time,&tzp);
     delts=delt;      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);
     for(k=1 ; k <kmax; k=k+1){      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
       delt = delta*(l1*k);  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       p2[theta]=x[theta] +delt;     for (i=1;i<=n;i++) {
       k1=func(p2)-fx;        printf(" %d %.12f",i, p[i]);
       p2[theta]=x[theta]-delt;        fprintf(ficlog," %d %.12lf",i, p[i]);
       k2=func(p2)-fx;        fprintf(ficrespow," %.12lf", p[i]);
       /*res= (k1-2.0*fx+k2)/delt/delt; */      }
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      printf("\n");
            fprintf(ficlog,"\n");
 #ifdef DEBUG      fprintf(ficrespow,"\n");fflush(ficrespow);
       printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);      if(*iter <=3){
 #endif        tm = *localtime(&curr_time.tv_sec);
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        strcpy(strcurr,asctime(&tm));
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  /*       asctime_r(&tm,strcurr); */
         k=kmax;        forecast_time=curr_time; 
       }        itmp = strlen(strcurr);
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
         k=kmax; l=lmax*10.;          strcurr[itmp-1]='\0';
       }        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
         delts=delt;        for(niterf=10;niterf<=30;niterf+=10){
       }          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     }          tmf = *localtime(&forecast_time.tv_sec);
   }  /*      asctime_r(&tmf,strfor); */
   delti[theta]=delts;          strcpy(strfor,asctime(&tmf));
   return res;          itmp = strlen(strfor);
            if(strfor[itmp-1]=='\n')
 }          strfor[itmp-1]='\0';
           printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
 double hessij( double x[], double delti[], int thetai,int thetaj)          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);
 {        }
   int i;      }
   int l=1, l1, lmax=20;      for (i=1;i<=n;i++) { 
   double k1,k2,k3,k4,res,fx;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   double p2[NPARMAX+1];        fptt=(*fret); 
   int k;  #ifdef DEBUG
         printf("fret=%lf \n",*fret);
   fx=func(x);        fprintf(ficlog,"fret=%lf \n",*fret);
   for (k=1; k<=2; k++) {  #endif
     for (i=1;i<=npar;i++) p2[i]=x[i];        printf("%d",i);fflush(stdout);
     p2[thetai]=x[thetai]+delti[thetai]/k;        fprintf(ficlog,"%d",i);fflush(ficlog);
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        linmin(p,xit,n,fret,func); 
     k1=func(p2)-fx;        if (fabs(fptt-(*fret)) > del) { 
            del=fabs(fptt-(*fret)); 
     p2[thetai]=x[thetai]+delti[thetai]/k;          ibig=i; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        } 
     k2=func(p2)-fx;  #ifdef DEBUG
          printf("%d %.12e",i,(*fret));
     p2[thetai]=x[thetai]-delti[thetai]/k;        fprintf(ficlog,"%d %.12e",i,(*fret));
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        for (j=1;j<=n;j++) {
     k3=func(p2)-fx;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
            printf(" x(%d)=%.12e",j,xit[j]);
     p2[thetai]=x[thetai]-delti[thetai]/k;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        }
     k4=func(p2)-fx;        for(j=1;j<=n;j++) {
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */          printf(" p=%.12e",p[j]);
 #ifdef DEBUG          fprintf(ficlog," p=%.12e",p[j]);
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);        }
 #endif        printf("\n");
   }        fprintf(ficlog,"\n");
   return res;  #endif
 }      } 
       if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
 /************** Inverse of matrix **************/  #ifdef DEBUG
 void ludcmp(double **a, int n, int *indx, double *d)        int k[2],l;
 {        k[0]=1;
   int i,imax,j,k;        k[1]=-1;
   double big,dum,sum,temp;        printf("Max: %.12e",(*func)(p));
   double *vv;        fprintf(ficlog,"Max: %.12e",(*func)(p));
          for (j=1;j<=n;j++) {
   vv=vector(1,n);          printf(" %.12e",p[j]);
   *d=1.0;          fprintf(ficlog," %.12e",p[j]);
   for (i=1;i<=n;i++) {        }
     big=0.0;        printf("\n");
     for (j=1;j<=n;j++)        fprintf(ficlog,"\n");
       if ((temp=fabs(a[i][j])) > big) big=temp;        for(l=0;l<=1;l++) {
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");          for (j=1;j<=n;j++) {
     vv[i]=1.0/big;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
   }            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   for (j=1;j<=n;j++) {            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     for (i=1;i<j;i++) {          }
       sum=a[i][j];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
       a[i][j]=sum;        }
     }  #endif
     big=0.0;  
     for (i=j;i<=n;i++) {  
       sum=a[i][j];        free_vector(xit,1,n); 
       for (k=1;k<j;k++)        free_vector(xits,1,n); 
         sum -= a[i][k]*a[k][j];        free_vector(ptt,1,n); 
       a[i][j]=sum;        free_vector(pt,1,n); 
       if ( (dum=vv[i]*fabs(sum)) >= big) {        return; 
         big=dum;      } 
         imax=i;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
       }      for (j=1;j<=n;j++) { 
     }        ptt[j]=2.0*p[j]-pt[j]; 
     if (j != imax) {        xit[j]=p[j]-pt[j]; 
       for (k=1;k<=n;k++) {        pt[j]=p[j]; 
         dum=a[imax][k];      } 
         a[imax][k]=a[j][k];      fptt=(*func)(ptt); 
         a[j][k]=dum;      if (fptt < fp) { 
       }        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
       *d = -(*d);        if (t < 0.0) { 
       vv[imax]=vv[j];          linmin(p,xit,n,fret,func); 
     }          for (j=1;j<=n;j++) { 
     indx[j]=imax;            xi[j][ibig]=xi[j][n]; 
     if (a[j][j] == 0.0) a[j][j]=TINY;            xi[j][n]=xit[j]; 
     if (j != n) {          }
       dum=1.0/(a[j][j]);  #ifdef DEBUG
       for (i=j+1;i<=n;i++) a[i][j] *= 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);
   }          for(j=1;j<=n;j++){
   free_vector(vv,1,n);  /* Doesn't work */            printf(" %.12e",xit[j]);
 ;            fprintf(ficlog," %.12e",xit[j]);
 }          }
           printf("\n");
 void lubksb(double **a, int n, int *indx, double b[])          fprintf(ficlog,"\n");
 {  #endif
   int i,ii=0,ip,j;        }
   double sum;      } 
      } 
   for (i=1;i<=n;i++) {  } 
     ip=indx[i];  
     sum=b[ip];  /**** Prevalence limit (stable or period prevalence)  ****************/
     b[ip]=b[i];  
     if (ii)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  {
     else if (sum) ii=i;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     b[i]=sum;       matrix by transitions matrix until convergence is reached */
   }  
   for (i=n;i>=1;i--) {    int i, ii,j,k;
     sum=b[i];    double min, max, maxmin, maxmax,sumnew=0.;
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];    double **matprod2();
     b[i]=sum/a[i][i];    double **out, cov[NCOVMAX], **pmij();
   }    double **newm;
 }    double agefin, delaymax=50 ; /* Max number of years to converge */
   
 /************ Frequencies ********************/    for (ii=1;ii<=nlstate+ndeath;ii++)
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2)      for (j=1;j<=nlstate+ndeath;j++){
 {  /* Some frequencies */        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
        }
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  
   double ***freq; /* Frequencies */     cov[1]=1.;
   double *pp;   
   double pos, k2, dateintsum=0,k2cpt=0;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   FILE *ficresp;    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
   char fileresp[FILENAMELENGTH];      newm=savm;
       /* Covariates have to be included here again */
   pp=vector(1,nlstate);       cov[2]=agefin;
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);    
   strcpy(fileresp,"p");        for (k=1; k<=cptcovn;k++) {
   strcat(fileresp,fileres);          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   if((ficresp=fopen(fileresp,"w"))==NULL) {          /*      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]]);*/
     printf("Problem with prevalence resultfile: %s\n", fileresp);        }
     exit(0);        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   }        for (k=1; k<=cptcovprod;k++)
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   j1=0;  
         /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
   j=cptcoveff;        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
   for(k1=1; k1<=j;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){      savm=oldm;
        j1++;      oldm=newm;
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);      maxmax=0.;
          scanf("%d", i);*/      for(j=1;j<=nlstate;j++){
         for (i=-1; i<=nlstate+ndeath; i++)          min=1.;
          for (jk=-1; jk<=nlstate+ndeath; jk++)          max=0.;
            for(m=agemin; m <= agemax+3; m++)        for(i=1; i<=nlstate; i++) {
              freq[i][jk][m]=0;          sumnew=0;
           for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
         dateintsum=0;          prlim[i][j]= newm[i][j]/(1-sumnew);
         k2cpt=0;          max=FMAX(max,prlim[i][j]);
        for (i=1; i<=imx; i++) {          min=FMIN(min,prlim[i][j]);
          bool=1;        }
          if  (cptcovn>0) {        maxmin=max-min;
            for (z1=1; z1<=cptcoveff; z1++)        maxmax=FMAX(maxmax,maxmin);
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      }
                bool=0;      if(maxmax < ftolpl){
          }        return prlim;
          if (bool==1) {      }
            for(m=firstpass; m<=lastpass; m++){    }
              k2=anint[m][i]+(mint[m][i]/12.);  }
              if ((k2>=dateprev1) && (k2<=dateprev2)) {  
                if(agev[m][i]==0) agev[m][i]=agemax+1;  /*************** transition probabilities ***************/ 
                if(agev[m][i]==1) agev[m][i]=agemax+2;  
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
                freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];  {
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {    double s1, s2;
                  dateintsum=dateintsum+k2;    /*double t34;*/
                  k2cpt++;    int i,j,j1, nc, ii, jj;
                }  
       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];*/
        }            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
         if  (cptcovn>0) {  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
          fprintf(ficresp, "\n#********** Variable ");          }
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);          ps[i][j]=s2;
        fprintf(ficresp, "**********\n#");  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
         }        }
        for(i=1; i<=nlstate;i++)        for(j=i+1; j<=nlstate+ndeath;j++){
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
        fprintf(ficresp, "\n");            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
          /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
   for(i=(int)agemin; i <= (int)agemax+3; i++){          }
     if(i==(int)agemax+3)          ps[i][j]=s2;
       printf("Total");        }
     else      }
       printf("Age %d", i);      /*ps[3][2]=1;*/
     for(jk=1; jk <=nlstate ; jk++){      
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for(i=1; i<= nlstate; i++){
         pp[jk] += freq[jk][m][i];        s1=0;
     }        for(j=1; j<i; j++)
     for(jk=1; jk <=nlstate ; jk++){          s1+=exp(ps[i][j]);
       for(m=-1, pos=0; m <=0 ; m++)        for(j=i+1; j<=nlstate+ndeath; j++)
         pos += freq[jk][m][i];          s1+=exp(ps[i][j]);
       if(pp[jk]>=1.e-10)        ps[i][i]=1./(s1+1.);
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        for(j=1; j<i; j++)
       else          ps[i][j]= exp(ps[i][j])*ps[i][i];
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        for(j=i+1; j<=nlstate+ndeath; j++)
     }          ps[i][j]= exp(ps[i][j])*ps[i][i];
         /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
      for(jk=1; jk <=nlstate ; jk++){      } /* end i */
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      
         pp[jk] += freq[jk][m][i];      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
      }        for(jj=1; jj<= nlstate+ndeath; jj++){
           ps[ii][jj]=0;
     for(jk=1,pos=0; jk <=nlstate ; jk++)          ps[ii][ii]=1;
       pos += pp[jk];        }
     for(jk=1; jk <=nlstate ; jk++){      }
       if(pos>=1.e-5)      
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);  
       else  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       if( i <= (int) agemax){  /*         printf("ddd %lf ",ps[ii][jj]); */
         if(pos>=1.e-5){  /*       } */
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  /*       printf("\n "); */
           probs[i][jk][j1]= pp[jk]/pos;  /*        } */
           /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/  /*        printf("\n ");printf("%lf ",cov[2]); */
         }         /*
       else        for(i=1; i<= npar; i++) printf("%f ",x[i]);
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);        goto end;*/
       }      return ps;
     }  }
     for(jk=-1; jk <=nlstate+ndeath; jk++)  
       for(m=-1; m <=nlstate+ndeath; m++)  /**************** Product of 2 matrices ******************/
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);  
     if(i <= (int) agemax)  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       fprintf(ficresp,"\n");  {
     printf("\n");    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     }       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     }    /* in, b, out are matrice of pointers which should have been initialized 
  }       before: only the contents of out is modified. The function returns
   dateintmean=dateintsum/k2cpt;       a pointer to pointers identical to out */
      long i, j, k;
   fclose(ficresp);    for(i=nrl; i<= nrh; i++)
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      for(k=ncolol; k<=ncoloh; k++)
   free_vector(pp,1,nlstate);        for(j=ncl,out[i][k]=0.; j<=nch; j++)
           out[i][k] +=in[i][j]*b[j][k];
   /* End of Freq */  
 }    return out;
   }
 /************ Prevalence ********************/  
 void prevalence(int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)  
 {  /* Some frequencies */  /************* Higher Matrix Product ***************/
    
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   double ***freq; /* Frequencies */  {
   double *pp;    /* Computes the transition matrix starting at age 'age' over 
   double pos, k2;       'nhstepm*hstepm*stepm' months (i.e. until
        age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
   pp=vector(1,nlstate);       nhstepm*hstepm matrices. 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
         (typically every 2 years instead of every month which is too big 
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);       for the memory).
   j1=0;       Model is determined by parameters x and covariates have to be 
         included manually here. 
   j=cptcoveff;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}       */
    
  for(k1=1; k1<=j;k1++){    int i, j, d, h, k;
     for(i1=1; i1<=ncodemax[k1];i1++){    double **out, cov[NCOVMAX];
       j1++;    double **newm;
    
       for (i=-1; i<=nlstate+ndeath; i++)      /* Hstepm could be zero and should return the unit matrix */
         for (jk=-1; jk<=nlstate+ndeath; jk++)      for (i=1;i<=nlstate+ndeath;i++)
           for(m=agemin; m <= agemax+3; m++)      for (j=1;j<=nlstate+ndeath;j++){
             freq[i][jk][m]=0;        oldm[i][j]=(i==j ? 1.0 : 0.0);
              po[i][j][0]=(i==j ? 1.0 : 0.0);
       for (i=1; i<=imx; i++) {      }
         bool=1;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         if  (cptcovn>0) {    for(h=1; h <=nhstepm; h++){
           for (z1=1; z1<=cptcoveff; z1++)      for(d=1; d <=hstepm; d++){
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        newm=savm;
               bool=0;        /* Covariates have to be included here again */
         }        cov[1]=1.;
         if (bool==1) {        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
           for(m=firstpass; m<=lastpass; m++){        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
             k2=anint[m][i]+(mint[m][i]/12.);        for (k=1; k<=cptcovage;k++)
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
               if(agev[m][i]==0) agev[m][i]=agemax+1;        for (k=1; k<=cptcovprod;k++)
               if(agev[m][i]==1) agev[m][i]=agemax+2;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];  
               freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];    
             }        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
           }        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         }        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
       }                     pmij(pmmij,cov,ncovmodel,x,nlstate));
              savm=oldm;
         for(i=(int)agemin; i <= (int)agemax+3; i++){        oldm=newm;
           for(jk=1; jk <=nlstate ; jk++){      }
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)      for(i=1; i<=nlstate+ndeath; i++)
               pp[jk] += freq[jk][m][i];        for(j=1;j<=nlstate+ndeath;j++) {
           }          po[i][j][h]=newm[i][j];
           for(jk=1; jk <=nlstate ; jk++){          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
             for(m=-1, pos=0; m <=0 ; m++)        }
             pos += freq[jk][m][i];      /*printf("h=%d ",h);*/
         }    } /* end h */
          /*     printf("\n H=%d \n",h); */
          for(jk=1; jk <=nlstate ; jk++){    return po;
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)  }
              pp[jk] += freq[jk][m][i];  
          }  
            /*************** log-likelihood *************/
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];  double func( double *x)
   {
          for(jk=1; jk <=nlstate ; jk++){              int i, ii, j, k, mi, d, kk;
            if( i <= (int) agemax){    double l, ll[NLSTATEMAX], cov[NCOVMAX];
              if(pos>=1.e-5){    double **out;
                probs[i][jk][j1]= pp[jk]/pos;    double sw; /* Sum of weights */
              }    double lli; /* Individual log likelihood */
            }    int s1, s2;
          }    double bbh, survp;
              long ipmx;
         }    /*extern weight */
     }    /* We are differentiating ll according to initial status */
   }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
      /*for(i=1;i<imx;i++) 
        printf(" %d\n",s[4][i]);
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    */
   free_vector(pp,1,nlstate);    cov[1]=1.;
    
 }  /* End of Freq */    for(k=1; k<=nlstate; k++) ll[k]=0.;
   
 /************* Waves Concatenation ***************/    if(mle==1){
       for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 {        for(mi=1; mi<= wav[i]-1; mi++){
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.          for (ii=1;ii<=nlstate+ndeath;ii++)
      Death is a valid wave (if date is known).            for (j=1;j<=nlstate+ndeath;j++){
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]              savm[ii][j]=(ii==j ? 1.0 : 0.0);
      and mw[mi+1][i]. dh depends on stepm.            }
      */          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
   int i, mi, m;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;            for (kk=1; kk<=cptcovage;kk++) {
      double sum=0., jmean=0.;*/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
   int j, k=0,jk, ju, jl;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double sum=0.;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   jmin=1e+5;            savm=oldm;
   jmax=-1;            oldm=newm;
   jmean=0.;          } /* end mult */
   for(i=1; i<=imx; i++){        
     mi=0;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     m=firstpass;          /* But now since version 0.9 we anticipate for bias at large stepm.
     while(s[m][i] <= nlstate){           * If stepm is larger than one month (smallest stepm) and if the exact delay 
       if(s[m][i]>=1)           * (in months) between two waves is not a multiple of stepm, we rounded to 
         mw[++mi][i]=m;           * the nearest (and in case of equal distance, to the lowest) interval but now
       if(m >=lastpass)           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         break;           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
       else           * probability in order to take into account the bias as a fraction of the way
         m++;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
     }/* end while */           * -stepm/2 to stepm/2 .
     if (s[m][i] > nlstate){           * For stepm=1 the results are the same as for previous versions of Imach.
       mi++;     /* Death is another wave */           * For stepm > 1 the results are less biased than in previous versions. 
       /* if(mi==0)  never been interviewed correctly before death */           */
          /* Only death is a correct wave */          s1=s[mw[mi][i]][i];
       mw[mi][i]=m;          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
           /* bias bh is positive if real duration
     wav[i]=mi;           * is higher than the multiple of stepm and negative otherwise.
     if(mi==0)           */
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   }          if( s2 > nlstate){ 
             /* i.e. if s2 is a death state and if the date of death is known 
   for(i=1; i<=imx; i++){               then the contribution to the likelihood is the probability to 
     for(mi=1; mi<wav[i];mi++){               die between last step unit time and current  step unit time, 
       if (stepm <=0)               which is also equal to probability to die before dh 
         dh[mi][i]=1;               minus probability to die before dh-stepm . 
       else{               In version up to 0.92 likelihood was computed
         if (s[mw[mi+1][i]][i] > nlstate) {          as if date of death was unknown. Death was treated as any other
           if (agedc[i] < 2*AGESUP) {          health state: the date of the interview describes the actual state
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          and not the date of a change in health state. The former idea was
           if(j==0) j=1;  /* Survives at least one month after exam */          to consider that at each interview the state was recorded
           k=k+1;          (healthy, disable or death) and IMaCh was corrected; but when we
           if (j >= jmax) jmax=j;          introduced the exact date of death then we should have modified
           if (j <= jmin) jmin=j;          the contribution of an exact death to the likelihood. This new
           sum=sum+j;          contribution is smaller and very dependent of the step unit
           /* if (j<10) printf("j=%d num=%d ",j,i); */          stepm. It is no more the probability to die between last interview
           }          and month of death but the probability to survive from last
         }          interview up to one month before death multiplied by the
         else{          probability to die within a month. Thanks to Chris
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));          Jackson for correcting this bug.  Former versions increased
           k=k+1;          mortality artificially. The bad side is that we add another loop
           if (j >= jmax) jmax=j;          which slows down the processing. The difference can be up to 10%
           else if (j <= jmin)jmin=j;          lower mortality.
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */            */
           sum=sum+j;            lli=log(out[s1][s2] - savm[s1][s2]);
         }  
         jk= j/stepm;  
         jl= j -jk*stepm;          } else if  (s2==-2) {
         ju= j -(jk+1)*stepm;            for (j=1,survp=0. ; j<=nlstate; j++) 
         if(jl <= -ju)              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           dh[mi][i]=jk;            /*survp += out[s1][j]; */
         else            lli= log(survp);
           dh[mi][i]=jk+1;          }
         if(dh[mi][i]==0)          
           dh[mi][i]=1; /* At least one step */          else if  (s2==-4) { 
       }            for (j=3,survp=0. ; j<=nlstate; j++)  
     }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   }            lli= log(survp); 
   jmean=sum/k;          } 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);  
  }          else if  (s2==-5) { 
 /*********** Tricode ****************************/            for (j=1,survp=0. ; j<=2; j++)  
 void tricode(int *Tvar, int **nbcode, int imx)              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
 {            lli= log(survp); 
   int Ndum[20],ij=1, k, j, i;          } 
   int cptcode=0;          
   cptcoveff=0;          else{
              lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   for (k=0; k<19; k++) Ndum[k]=0;            /*  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 (k=1; k<=7; k++) ncodemax[k]=0;          } 
           /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          /*if(lli ==000.0)*/
     for (i=1; i<=imx; i++) {          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       ij=(int)(covar[Tvar[j]][i]);          ipmx +=1;
       Ndum[ij]++;          sw += weight[i];
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       if (ij > cptcode) cptcode=ij;        } /* end of wave */
     }      } /* end of individual */
     }  else if(mle==2){
     for (i=0; i<=cptcode; i++) {      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       if(Ndum[i]!=0) ncodemax[j]++;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     }        for(mi=1; mi<= wav[i]-1; mi++){
     ij=1;          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     for (i=1; i<=ncodemax[j]; i++) {              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for (k=0; k<=19; k++) {            }
         if (Ndum[k] != 0) {          for(d=0; d<=dh[mi][i]; d++){
           nbcode[Tvar[j]][ij]=k;            newm=savm;
           ij++;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         }            for (kk=1; kk<=cptcovage;kk++) {
         if (ij > ncodemax[j]) break;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }              }
     }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   }                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
  for (k=0; k<19; k++) Ndum[k]=0;            oldm=newm;
           } /* end mult */
  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; 
           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 */
  ij=1;          ipmx +=1;
  for (i=1; i<=10; i++) {          sw += weight[i];
    if((Ndum[i]!=0) && (i<=ncov)){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      Tvaraff[ij]=i;        } /* end of wave */
      ij++;      } /* end of individual */
    }    }  else if(mle==3){  /* exponential inter-extrapolation */
  }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     cptcoveff=ij-1;        for(mi=1; mi<= wav[i]-1; mi++){
 }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
 /*********** Health Expectancies ****************/              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)            }
 {          for(d=0; d<dh[mi][i]; d++){
   /* Health expectancies */            newm=savm;
   int i, j, nhstepm, hstepm, h;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double age, agelim,hf;            for (kk=1; kk<=cptcovage;kk++) {
   double ***p3mat;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              }
   fprintf(ficreseij,"# Health expectancies\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   fprintf(ficreseij,"# Age");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   for(i=1; i<=nlstate;i++)            savm=oldm;
     for(j=1; j<=nlstate;j++)            oldm=newm;
       fprintf(ficreseij," %1d-%1d",i,j);          } /* end mult */
   fprintf(ficreseij,"\n");        
           s1=s[mw[mi][i]][i];
   hstepm=1*YEARM; /*  Every j years of age (in month) */          s2=s[mw[mi+1][i]][i];
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          bbh=(double)bh[mi][i]/(double)stepm; 
           lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
   agelim=AGESUP;          ipmx +=1;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          sw += weight[i];
     /* nhstepm age range expressed in number of stepm */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);        } /* end of wave */
     /* Typically if 20 years = 20*12/6=40 stepm */      } /* end of individual */
     if (stepm >= YEARM) hstepm=1;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        for(mi=1; mi<= wav[i]-1; mi++){
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */          for (ii=1;ii<=nlstate+ndeath;ii++)
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
     for(i=1; i<=nlstate;i++)            }
       for(j=1; j<=nlstate;j++)          for(d=0; d<dh[mi][i]; d++){
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){            newm=savm;
           eij[i][j][(int)age] +=p3mat[i][j][h];            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];
     hf=1;            }
     if (stepm >= YEARM) hf=stepm/YEARM;          
     fprintf(ficreseij,"%.0f",age );            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     for(i=1; i<=nlstate;i++)                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       for(j=1; j<=nlstate;j++){            savm=oldm;
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);            oldm=newm;
       }          } /* end mult */
     fprintf(ficreseij,"\n");        
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          s1=s[mw[mi][i]][i];
   }          s2=s[mw[mi+1][i]][i];
 }          if( s2 > nlstate){ 
             lli=log(out[s1][s2] - savm[s1][s2]);
 /************ Variance ******************/          }else{
 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)            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
 {          }
   /* Variance of health expectancies */          ipmx +=1;
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          sw += weight[i];
   double **newm;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   double **dnewm,**doldm;  /*      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 i, j, nhstepm, hstepm, h;        } /* end of wave */
   int k, cptcode;      } /* end of individual */
   double *xp;    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   double **gp, **gm;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***gradg, ***trgradg;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   double ***p3mat;        for(mi=1; mi<= wav[i]-1; mi++){
   double age,agelim;          for (ii=1;ii<=nlstate+ndeath;ii++)
   int theta;            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
    fprintf(ficresvij,"# Covariances of life expectancies\n");              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   fprintf(ficresvij,"# Age");            }
   for(i=1; i<=nlstate;i++)          for(d=0; d<dh[mi][i]; d++){
     for(j=1; j<=nlstate;j++)            newm=savm;
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   fprintf(ficresvij,"\n");            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   xp=vector(1,npar);            }
   dnewm=matrix(1,nlstate,1,npar);          
   doldm=matrix(1,nlstate,1,nlstate);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   hstepm=1*YEARM; /* Every year of age */            savm=oldm;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            oldm=newm;
   agelim = AGESUP;          } /* end mult */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          s1=s[mw[mi][i]][i];
     if (stepm >= YEARM) hstepm=1;          s2=s[mw[mi+1][i]][i];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          ipmx +=1;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);          sw += weight[i];
     gp=matrix(0,nhstepm,1,nlstate);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     gm=matrix(0,nhstepm,1,nlstate);          /*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 */
     for(theta=1; theta <=npar; theta++){      } /* end of individual */
       for(i=1; i<=npar; i++){ /* Computes gradient */    } /* End of if */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    return -l;
   }
       if (popbased==1) {  
         for(i=1; i<=nlstate;i++)  /*************** log-likelihood *************/
           prlim[i][i]=probs[(int)age][i][ij];  double funcone( double *x)
       }  {
          /* Same as likeli but slower because of a lot of printf and if */
       for(j=1; j<= nlstate; j++){    int i, ii, j, k, mi, d, kk;
         for(h=0; h<=nhstepm; h++){    double l, ll[NLSTATEMAX], cov[NCOVMAX];
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    double **out;
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    double lli; /* Individual log likelihood */
         }    double llt;
       }    int s1, s2;
        double bbh, survp;
       for(i=1; i<=npar; i++) /* Computes gradient */    /*extern weight */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    /* We are differentiating ll according to initial status */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    /*for(i=1;i<imx;i++) 
       printf(" %d\n",s[4][i]);
       if (popbased==1) {    */
         for(i=1; i<=nlstate;i++)    cov[1]=1.;
           prlim[i][i]=probs[(int)age][i][ij];  
       }    for(k=1; k<=nlstate; k++) ll[k]=0.;
   
       for(j=1; j<= nlstate; j++){    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for(h=0; h<=nhstepm; h++){      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)      for(mi=1; mi<= wav[i]-1; mi++){
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];        for (ii=1;ii<=nlstate+ndeath;ii++)
         }          for (j=1;j<=nlstate+ndeath;j++){
       }            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<= nlstate; j++)          }
         for(h=0; h<=nhstepm; h++){        for(d=0; d<dh[mi][i]; d++){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];          newm=savm;
         }          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     } /* End theta */          for (kk=1; kk<=cptcovage;kk++) {
             cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          }
           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(j=1; j<=nlstate;j++)          savm=oldm;
         for(theta=1; theta <=npar; theta++)          oldm=newm;
           trgradg[h][j][theta]=gradg[h][theta][j];        } /* end mult */
         
     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] =0.;        bbh=(double)bh[mi][i]/(double)stepm; 
     for(h=0;h<=nhstepm;h++){        /* bias is positive if real duration
       for(k=0;k<=nhstepm;k++){         * is higher than the multiple of stepm and negative otherwise.
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);         */
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
         for(i=1;i<=nlstate;i++)          lli=log(out[s1][s2] - savm[s1][s2]);
           for(j=1;j<=nlstate;j++)        } else if  (s2==-2) {
             vareij[i][j][(int)age] += doldm[i][j];          for (j=1,survp=0. ; j<=nlstate; j++) 
       }            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     }          lli= log(survp);
     h=1;        }else if (mle==1){
     if (stepm >= YEARM) h=stepm/YEARM;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     fprintf(ficresvij,"%.0f ",age );        } else if(mle==2){
     for(i=1; i<=nlstate;i++)          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       for(j=1; j<=nlstate;j++){        } else if(mle==3){  /* exponential inter-extrapolation */
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);          lli= (savm[s1][s2]>(double)1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
       }        } else if (mle==4){  /* mle=4 no inter-extrapolation */
     fprintf(ficresvij,"\n");          lli=log(out[s1][s2]); /* Original formula */
     free_matrix(gp,0,nhstepm,1,nlstate);        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
     free_matrix(gm,0,nhstepm,1,nlstate);          lli=log(out[s1][s2]); /* Original formula */
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        } /* End of if */
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        ipmx +=1;
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        sw += weight[i];
   } /* End age */        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    /*       printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
   free_vector(xp,1,npar);        if(globpr){
   free_matrix(doldm,1,nlstate,1,npar);          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
   free_matrix(dnewm,1,nlstate,1,nlstate);   %11.6f %11.6f %11.6f ", \
                   num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
 }                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
           for(k=1,llt=0.,l=0.; k<=nlstate; k++){
 /************ Variance of prevlim ******************/            llt +=ll[k]*gipmx/gsw;
 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)            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
 {          }
   /* Variance of prevalence limit */          fprintf(ficresilk," %10.6f\n", -llt);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        }
   double **newm;      } /* end of wave */
   double **dnewm,**doldm;    } /* end of individual */
   int i, j, nhstepm, hstepm;    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
   int k, cptcode;    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
   double *xp;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   double *gp, *gm;    if(globpr==0){ /* First time we count the contributions and weights */
   double **gradg, **trgradg;      gipmx=ipmx;
   double age,agelim;      gsw=sw;
   int theta;    }
        return -l;
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");  }
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)  
       fprintf(ficresvpl," %1d-%1d",i,i);  /*************** function likelione ***********/
   fprintf(ficresvpl,"\n");  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
   xp=vector(1,npar);    /* This routine should help understanding what is done with 
   dnewm=matrix(1,nlstate,1,npar);       the selection of individuals/waves and
   doldm=matrix(1,nlstate,1,nlstate);       to check the exact contribution to the likelihood.
         Plotting could be done.
   hstepm=1*YEARM; /* Every year of age */     */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    int k;
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    if(*globpri !=0){ /* Just counts and sums, no printings */
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      strcpy(fileresilk,"ilk"); 
     if (stepm >= YEARM) hstepm=1;      strcat(fileresilk,fileres);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
     gradg=matrix(1,npar,1,nlstate);        printf("Problem with resultfile: %s\n", fileresilk);
     gp=vector(1,nlstate);        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
     gm=vector(1,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");
     for(theta=1; theta <=npar; theta++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       for(i=1; i<=npar; i++){ /* Computes gradient */      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      for(k=1; k<=nlstate; k++) 
       }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       for(i=1;i<=nlstate;i++)    }
         gp[i] = prlim[i][i];  
        *fretone=(*funcone)(p);
       for(i=1; i<=npar; i++) /* Computes gradient */    if(*globpri !=0){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      fclose(ficresilk);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       for(i=1;i<=nlstate;i++)      fflush(fichtm); 
         gm[i] = prlim[i][i];    } 
     return;
       for(i=1;i<=nlstate;i++)  }
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];  
     } /* End theta */  
   /*********** Maximum Likelihood Estimation ***************/
     trgradg =matrix(1,nlstate,1,npar);  
   void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     for(j=1; j<=nlstate;j++)  {
       for(theta=1; theta <=npar; theta++)    int i,j, iter;
         trgradg[j][theta]=gradg[theta][j];    double **xi;
     double fret;
     for(i=1;i<=nlstate;i++)    double fretone; /* Only one call to likelihood */
       varpl[i][(int)age] =0.;    /*  char filerespow[FILENAMELENGTH];*/
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    xi=matrix(1,npar,1,npar);
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    for (i=1;i<=npar;i++)
     for(i=1;i<=nlstate;i++)      for (j=1;j<=npar;j++)
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     fprintf(ficresvpl,"%.0f ",age );    strcpy(filerespow,"pow"); 
     for(i=1; i<=nlstate;i++)    strcat(filerespow,fileres);
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    if((ficrespow=fopen(filerespow,"w"))==NULL) {
     fprintf(ficresvpl,"\n");      printf("Problem with resultfile: %s\n", filerespow);
     free_vector(gp,1,nlstate);      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     free_vector(gm,1,nlstate);    }
     free_matrix(gradg,1,npar,1,nlstate);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     free_matrix(trgradg,1,nlstate,1,npar);    for (i=1;i<=nlstate;i++)
   } /* End age */      for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   free_vector(xp,1,npar);    fprintf(ficrespow,"\n");
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    powell(p,xi,npar,ftol,&iter,&fret,func);
   
 }    free_matrix(xi,1,npar,1,npar);
     fclose(ficrespow);
 /************ Variance of one-step probabilities  ******************/    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
 {    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   int i, j;  
   int k=0, cptcode;  }
   double **dnewm,**doldm;  
   double *xp;  /**** Computes Hessian and covariance matrix ***/
   double *gp, *gm;  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   double **gradg, **trgradg;  {
   double age,agelim, cov[NCOVMAX];    double  **a,**y,*x,pd;
   int theta;    double **hess;
   char fileresprob[FILENAMELENGTH];    int i, j,jk;
     int *indx;
   strcpy(fileresprob,"prob");  
   strcat(fileresprob,fileres);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
     printf("Problem with resultfile: %s\n", fileresprob);    void lubksb(double **a, int npar, int *indx, double b[]) ;
   }    void ludcmp(double **a, int npar, int *indx, double *d) ;
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);    double gompertz(double p[]);
      hess=matrix(1,npar,1,npar);
   
   xp=vector(1,npar);    printf("\nCalculation of the hessian matrix. Wait...\n");
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));    for (i=1;i<=npar;i++){
        printf("%d",i);fflush(stdout);
   cov[1]=1;      fprintf(ficlog,"%d",i);fflush(ficlog);
   for (age=bage; age<=fage; age ++){     
     cov[2]=age;       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
     gradg=matrix(1,npar,1,9);      
     trgradg=matrix(1,9,1,npar);      /*  printf(" %f ",p[i]);
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    }
        
     for(theta=1; theta <=npar; theta++){    for (i=1;i<=npar;i++) {
       for(i=1; i<=npar; i++)      for (j=1;j<=npar;j++)  {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);        if (j>i) { 
                printf(".%d%d",i,j);fflush(stdout);
       pmij(pmmij,cov,ncovmodel,xp,nlstate);          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
              hess[i][j]=hessij(p,delti,i,j,func,npar);
       k=0;          
       for(i=1; i<= (nlstate+ndeath); i++){          hess[j][i]=hess[i][j];    
         for(j=1; j<=(nlstate+ndeath);j++){          /*printf(" %lf ",hess[i][j]);*/
            k=k+1;        }
           gp[k]=pmmij[i][j];      }
         }    }
       }    printf("\n");
     fprintf(ficlog,"\n");
       for(i=1; i<=npar; i++)  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
        fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     
       pmij(pmmij,cov,ncovmodel,xp,nlstate);    a=matrix(1,npar,1,npar);
       k=0;    y=matrix(1,npar,1,npar);
       for(i=1; i<=(nlstate+ndeath); i++){    x=vector(1,npar);
         for(j=1; j<=(nlstate+ndeath);j++){    indx=ivector(1,npar);
           k=k+1;    for (i=1;i<=npar;i++)
           gm[k]=pmmij[i][j];      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
         }    ludcmp(a,npar,indx,&pd);
       }  
          for (j=1;j<=npar;j++) {
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)      for (i=1;i<=npar;i++) x[i]=0;
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];        x[j]=1;
     }      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)        matcov[i][j]=x[i];
       for(theta=1; theta <=npar; theta++)      }
       trgradg[j][theta]=gradg[theta][j];    }
    
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);    printf("\n#Hessian matrix#\n");
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);    fprintf(ficlog,"\n#Hessian matrix#\n");
     for (i=1;i<=npar;i++) { 
      pmij(pmmij,cov,ncovmodel,x,nlstate);      for (j=1;j<=npar;j++) { 
         printf("%.3e ",hess[i][j]);
      k=0;        fprintf(ficlog,"%.3e ",hess[i][j]);
      for(i=1; i<=(nlstate+ndeath); i++){      }
        for(j=1; j<=(nlstate+ndeath);j++){      printf("\n");
          k=k+1;      fprintf(ficlog,"\n");
          gm[k]=pmmij[i][j];    }
         }  
      }    /* Recompute Inverse */
          for (i=1;i<=npar;i++)
      /*printf("\n%d ",(int)age);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){    ludcmp(a,npar,indx,&pd);
          
     /*  printf("\n#Hessian matrix recomputed#\n");
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));  
      }*/    for (j=1;j<=npar;j++) {
       for (i=1;i<=npar;i++) x[i]=0;
   fprintf(ficresprob,"\n%d ",(int)age);      x[j]=1;
       lubksb(a,npar,indx,x);
   for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      for (i=1;i<=npar;i++){ 
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        y[i][j]=x[i];
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        printf("%.3e ",y[i][j]);
   }        fprintf(ficlog,"%.3e ",y[i][j]);
       }
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));      printf("\n");
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));      fprintf(ficlog,"\n");
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    }
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);    */
 }  
  free_vector(xp,1,npar);    free_matrix(a,1,npar,1,npar);
 fclose(ficresprob);    free_matrix(y,1,npar,1,npar);
  exit(0);    free_vector(x,1,npar);
 }    free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
 /******************* 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 optionfile[],char optionfilehtm[] ){  
   int jj1, k1, i1, cpt;  }
   FILE *fichtm;  
   /*char optionfilehtm[FILENAMELENGTH];*/  /*************** hessian matrix ****************/
   double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   strcpy(optionfilehtm,optionfile);  {
   strcat(optionfilehtm,".htm");    int i;
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {    int l=1, lmax=20;
     printf("Problem with %s \n",optionfilehtm), exit(0);    double k1,k2;
   }    double p2[NPARMAX+1];
     double res;
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    double fx;
     int k=0,kmax=10;
 Total number of observations=%d <br>    double l1;
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>  
 <hr  size=\"2\" color=\"#EC5E5E\">    fx=func(x);
 <li>Outputs files<br><br>\n    for (i=1;i<=npar;i++) p2[i]=x[i];
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n    for(l=0 ; l <=lmax; l++){
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>      l1=pow(10,l);
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      delts=delt;
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      for(k=1 ; k <kmax; k=k+1){
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>        delt = delta*(l1*k);
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>        p2[theta]=x[theta] +delt;
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>        k1=func(p2)-fx;
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>        p2[theta]=x[theta]-delt;
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>        k2=func(p2)-fx;
         - Prevalences and population forecasting: <a href=\"f%s\">f%s</a> <br>        /*res= (k1-2.0*fx+k2)/delt/delt; */
         <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
          
 fprintf(fichtm," <li>Graphs</li><p>");  #ifdef DEBUG
         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);
  m=cptcoveff;        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);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}  #endif
         /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
  jj1=0;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
  for(k1=1; k1<=m;k1++){          k=kmax;
    for(i1=1; i1<=ncodemax[k1];i1++){        }
        jj1++;        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
        if (cptcovn > 0) {          k=kmax; l=lmax*10.;
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");        }
          for (cpt=1; cpt<=cptcoveff;cpt++)        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);          delts=delt;
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");        }
        }      }
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>    }
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        delti[theta]=delts;
        for(cpt=1; cpt<nlstate;cpt++){    return res; 
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  }
        }  
     for(cpt=1; cpt<=nlstate;cpt++) {  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  {
 interval) in state (%d): v%s%d%d.gif <br>    int i;
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);      int l=1, l1, lmax=20;
      }    double k1,k2,k3,k4,res,fx;
      for(cpt=1; cpt<=nlstate;cpt++) {    double p2[NPARMAX+1];
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    int k;
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);  
      }    fx=func(x);
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    for (k=1; k<=2; k++) {
 health expectancies in states (1) and (2): e%s%d.gif<br>      for (i=1;i<=npar;i++) p2[i]=x[i];
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      p2[thetai]=x[thetai]+delti[thetai]/k;
 fprintf(fichtm,"\n</body>");      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
    }      k1=func(p2)-fx;
    }    
 fclose(fichtm);      p2[thetai]=x[thetai]+delti[thetai]/k;
 }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k2=func(p2)-fx;
 /******************* Gnuplot file **************/    
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double agemin, double agemax, double fage , char pathc[], double p[]){      p2[thetai]=x[thetai]-delti[thetai]/k;
       p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;      k3=func(p2)-fx;
     
   strcpy(optionfilegnuplot,optionfilefiname);      p2[thetai]=x[thetai]-delti[thetai]/k;
   strcat(optionfilegnuplot,".plt");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {      k4=func(p2)-fx;
     printf("Problem with file %s",optionfilegnuplot);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   }  #ifdef DEBUG
       printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
 #ifdef windows      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
     fprintf(ficgp,"cd \"%s\" \n",pathc);  #endif
 #endif    }
 m=pow(2,cptcoveff);    return res;
    }
  /* 1eme*/  
   for (cpt=1; cpt<= nlstate ; cpt ++) {  /************** Inverse of matrix **************/
    for (k1=1; k1<= m ; k1 ++) {  void ludcmp(double **a, int n, int *indx, double *d) 
   { 
 #ifdef windows    int i,imax,j,k; 
     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);    double big,dum,sum,temp; 
 #endif    double *vv; 
 #ifdef unix   
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);    vv=vector(1,n); 
 #endif    *d=1.0; 
     for (i=1;i<=n;i++) { 
 for (i=1; i<= nlstate ; i ++) {      big=0.0; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      for (j=1;j<=n;j++) 
   else fprintf(ficgp," \%%*lf (\%%*lf)");        if ((temp=fabs(a[i][j])) > big) big=temp; 
 }      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);      vv[i]=1.0/big; 
     for (i=1; i<= nlstate ; i ++) {    } 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    for (j=1;j<=n;j++) { 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      for (i=1;i<j;i++) { 
 }        sum=a[i][j]; 
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
      for (i=1; i<= nlstate ; i ++) {        a[i][j]=sum; 
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      } 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      big=0.0; 
 }        for (i=j;i<=n;i++) { 
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));        sum=a[i][j]; 
 #ifdef unix        for (k=1;k<j;k++) 
 fprintf(ficgp,"\nset ter gif small size 400,300");          sum -= a[i][k]*a[k][j]; 
 #endif        a[i][j]=sum; 
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        if ( (dum=vv[i]*fabs(sum)) >= big) { 
    }          big=dum; 
   }          imax=i; 
   /*2 eme*/        } 
       } 
   for (k1=1; k1<= m ; k1 ++) {      if (j != imax) { 
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);        for (k=1;k<=n;k++) { 
              dum=a[imax][k]; 
     for (i=1; i<= nlstate+1 ; i ++) {          a[imax][k]=a[j][k]; 
       k=2*i;          a[j][k]=dum; 
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);        } 
       for (j=1; j<= nlstate+1 ; j ++) {        *d = -(*d); 
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        vv[imax]=vv[j]; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");      } 
 }        indx[j]=imax; 
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");      if (a[j][j] == 0.0) a[j][j]=TINY; 
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);      if (j != n) { 
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);        dum=1.0/(a[j][j]); 
       for (j=1; j<= nlstate+1 ; j ++) {        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      } 
         else fprintf(ficgp," \%%*lf (\%%*lf)");    } 
 }      free_vector(vv,1,n);  /* Doesn't work */
       fprintf(ficgp,"\" t\"\" w l 0,");  ;
      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 ++) {  
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  void lubksb(double **a, int n, int *indx, double b[]) 
   else fprintf(ficgp," \%%*lf (\%%*lf)");  { 
 }      int i,ii=0,ip,j; 
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    double sum; 
       else fprintf(ficgp,"\" t\"\" w l 0,");   
     }    for (i=1;i<=n;i++) { 
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);      ip=indx[i]; 
   }      sum=b[ip]; 
        b[ip]=b[i]; 
   /*3eme*/      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   for (k1=1; k1<= m ; k1 ++) {      else if (sum) ii=i; 
     for (cpt=1; cpt<= nlstate ; cpt ++) {      b[i]=sum; 
       k=2+nlstate*(cpt-1);    } 
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);    for (i=n;i>=1;i--) { 
       for (i=1; i< nlstate ; i ++) {      sum=b[i]; 
         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);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
       }      b[i]=sum/a[i][i]; 
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    } 
     }  } 
     }  
    void pstamp(FILE *fichier)
   /* CV preval stat */  {
     for (k1=1; k1<= m ; k1 ++) {    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
     for (cpt=1; cpt<nlstate ; cpt ++) {  }
       k=3;  
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);  /************ Frequencies ********************/
   void  freqsummary(char fileres[], int iagemin, int iagemax, int **s, double **agev, int nlstate, int imx, int *Tvaraff, int **nbcode, int *ncodemax,double **mint,double **anint, char strstart[])
       for (i=1; i< nlstate ; i ++)  {  /* Some frequencies */
         fprintf(ficgp,"+$%d",k+i+1);    
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    int i, m, jk, k1,i1, j1, bool, z1,j;
          int first;
       l=3+(nlstate+ndeath)*cpt;    double ***freq; /* Frequencies */
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    double *pp, **prop;
       for (i=1; i< nlstate ; i ++) {    double pos,posprop, k2, dateintsum=0,k2cpt=0;
         l=3+(nlstate+ndeath)*cpt;    char fileresp[FILENAMELENGTH];
         fprintf(ficgp,"+$%d",l+i+1);    
       }    pp=vector(1,nlstate);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      prop=matrix(1,nlstate,iagemin,iagemax+3);
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    strcpy(fileresp,"p");
     }    strcat(fileresp,fileres);
   }      if((ficresp=fopen(fileresp,"w"))==NULL) {
        printf("Problem with prevalence resultfile: %s\n", fileresp);
   /* proba elementaires */      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
    for(i=1,jk=1; i <=nlstate; i++){      exit(0);
     for(k=1; k <=(nlstate+ndeath); k++){    }
       if (k != i) {    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
         for(j=1; j <=ncovmodel; j++){    j1=0;
            
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    j=cptcoveff;
           jk++;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           fprintf(ficgp,"\n");  
         }    first=1;
       }  
     }    for(k1=1; k1<=j;k1++){
     }      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
     for(jk=1; jk <=m; jk++) {        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);          scanf("%d", i);*/
    i=1;        for (i=-5; i<=nlstate+ndeath; i++)  
    for(k2=1; k2<=nlstate; k2++) {          for (jk=-5; jk<=nlstate+ndeath; jk++)  
      k3=i;            for(m=iagemin; m <= iagemax+3; m++)
      for(k=1; k<=(nlstate+ndeath); k++) {              freq[i][jk][m]=0;
        if (k != k2){  
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);      for (i=1; i<=nlstate; i++)  
 ij=1;        for(m=iagemin; m <= iagemax+3; m++)
         for(j=3; j <=ncovmodel; j++) {          prop[i][m]=0;
           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]]]);        dateintsum=0;
             ij++;        k2cpt=0;
           }        for (i=1; i<=imx; i++) {
           else          bool=1;
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          if  (cptcovn>0) {
         }            for (z1=1; z1<=cptcoveff; z1++) 
           fprintf(ficgp,")/(1");              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                        bool=0;
         for(k1=1; k1 <=nlstate; k1++){            }
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);          if (bool==1){
 ij=1;            for(m=firstpass; m<=lastpass; m++){
           for(j=3; j <=ncovmodel; j++){              k2=anint[m][i]+(mint[m][i]/12.);
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
             fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
             ij++;                if(agev[m][i]==1) agev[m][i]=iagemax+2;
           }                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
           else                if (m<lastpass) {
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
           }                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
           fprintf(ficgp,")");                }
         }                
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");                  dateintsum=dateintsum+k2;
         i=i+ncovmodel;                  k2cpt++;
        }                }
      }                /*}*/
    }            }
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);          }
    }        }
             
   fclose(ficgp);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
 }  /* end gnuplot */        pstamp(ficresp);
         if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
 /*************** Moving average **************/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
 void movingaverage(double agedeb, double fage,double agemin, double ***mobaverage){          fprintf(ficresp, "**********\n#");
         }
   int i, cpt, cptcod;        for(i=1; i<=nlstate;i++) 
     for (agedeb=agemin; agedeb<=fage; agedeb++)          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
       for (i=1; i<=nlstate;i++)        fprintf(ficresp, "\n");
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)        
           mobaverage[(int)agedeb][i][cptcod]=0.;        for(i=iagemin; i <= iagemax+3; i++){
              if(i==iagemax+3){
     for (agedeb=agemin+4; agedeb<=fage; agedeb++){            fprintf(ficlog,"Total");
       for (i=1; i<=nlstate;i++){          }else{
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            if(first==1){
           for (cpt=0;cpt<=4;cpt++){              first=0;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];              printf("See log file for details...\n");
           }            }
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;            fprintf(ficlog,"Age %d", i);
         }          }
       }          for(jk=1; jk <=nlstate ; jk++){
     }            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                  pp[jk] += freq[jk][m][i]; 
 }          }
           for(jk=1; jk <=nlstate ; jk++){
 /***********************************************/            for(m=-1, pos=0; m <=0 ; m++)
 /**************** Main Program *****************/              pos += freq[jk][m][i];
 /***********************************************/            if(pp[jk]>=1.e-10){
               if(first==1){
 int main(int argc, char *argv[])              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 {              }
               fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;            }else{
   double agedeb, agefin,hf;              if(first==1)
   double agemin=1.e20, agemax=-1.e20;                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   double fret;            }
   double **xi,tmp,delta;          }
   
   double dum; /* Dummy variable */          for(jk=1; jk <=nlstate ; jk++){
   double ***p3mat;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   int *indx;              pp[jk] += freq[jk][m][i];
   char line[MAXLINE], linepar[MAXLINE];          }       
   char title[MAXLINE];          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];            pos += pp[jk];
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];            posprop += prop[jk][i];
            }
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];          for(jk=1; jk <=nlstate ; jk++){
             if(pos>=1.e-5){
   char filerest[FILENAMELENGTH];              if(first==1)
   char fileregp[FILENAMELENGTH];                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   char popfile[FILENAMELENGTH];              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];            }else{
   int firstobs=1, lastobs=10;              if(first==1)
   int sdeb, sfin; /* Status at beginning and end */                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   int c,  h , cpt,l;              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   int ju,jl, mi;            }
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;            if( i <= iagemax){
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;              if(pos>=1.e-5){
   int mobilav=0,popforecast=0;                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   int hstepm, nhstepm;                /*probs[i][jk][j1]= pp[jk]/pos;*/
   int *popage;/*boolprev=0 if date and zero if wave*/                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2;              }
               else
   double bage, fage, age, agelim, agebase;                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   double ftolpl=FTOL;            }
   double **prlim;          }
   double *severity;          
   double ***param; /* Matrix of parameters */          for(jk=-1; jk <=nlstate+ndeath; jk++)
   double  *p;            for(m=-1; m <=nlstate+ndeath; m++)
   double **matcov; /* Matrix of covariance */              if(freq[jk][m][i] !=0 ) {
   double ***delti3; /* Scale */              if(first==1)
   double *delti; /* Scale */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   double ***eij, ***vareij;                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   double **varpl; /* Variances of prevalence limits by age */              }
   double *epj, vepp;          if(i <= iagemax)
   double kk1, kk2;            fprintf(ficresp,"\n");
   double *popeffectif,*popcount;          if(first==1)
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,jprojmean,mprojmean,anprojmean, calagedate;            printf("Others in log...\n");
   double yp,yp1,yp2;          fprintf(ficlog,"\n");
         }
   char version[80]="Imach version 0.7, February 2002, INED-EUROREVES ";      }
   char *alph[]={"a","a","b","c","d","e"}, str[4];    }
     dateintmean=dateintsum/k2cpt; 
    
   char z[1]="c", occ;    fclose(ficresp);
 #include <sys/time.h>    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
 #include <time.h>    free_vector(pp,1,nlstate);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
      /* End of Freq */
   /* long total_usecs;  }
   struct timeval start_time, end_time;  
    /************ Prevalence ********************/
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   printf("\n%s",version);       in each health status at the date of interview (if between dateprev1 and dateprev2).
   if(argc <=1){       We still use firstpass and lastpass as another selection.
     printf("\nEnter the parameter file name: ");    */
     scanf("%s",pathtot);   
   }    int i, m, jk, k1, i1, j1, bool, z1,j;
   else{    double ***freq; /* Frequencies */
     strcpy(pathtot,argv[1]);    double *pp, **prop;
   }    double pos,posprop; 
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/    double  y2; /* in fractional years */
   /*cygwin_split_path(pathtot,path,optionfile);    int iagemin, iagemax;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/  
   /* cutv(path,optionfile,pathtot,'\\');*/    iagemin= (int) agemin;
     iagemax= (int) agemax;
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    /*pp=vector(1,nlstate);*/
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
   chdir(path);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   replace(pathc,path);    j1=0;
     
 /*-------- arguments in the command line --------*/    j=cptcoveff;
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
   strcpy(fileres,"r");    
   strcat(fileres, optionfilefiname);    for(k1=1; k1<=j;k1++){
   strcat(fileres,".txt");    /* Other files have txt extension */      for(i1=1; i1<=ncodemax[k1];i1++){
         j1++;
   /*---------arguments file --------*/        
         for (i=1; i<=nlstate; i++)  
   if((ficpar=fopen(optionfile,"r"))==NULL)    {          for(m=iagemin; m <= iagemax+3; m++)
     printf("Problem with optionfile %s\n",optionfile);            prop[i][m]=0.0;
     goto end;       
   }        for (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
   strcpy(filereso,"o");          if  (cptcovn>0) {
   strcat(filereso,fileres);            for (z1=1; z1<=cptcoveff; z1++) 
   if((ficparo=fopen(filereso,"w"))==NULL) {              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;                bool=0;
   }          } 
           if (bool==1) { 
   /* Reads comments: lines beginning with '#' */            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
   while((c=getc(ficpar))=='#' && c!= EOF){              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
     ungetc(c,ficpar);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
     fgets(line, MAXLINE, ficpar);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
     puts(line);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
     fputs(line,ficparo);                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) { 
   ungetc(c,ficpar);                  /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
                   prop[s[m][i]][(int)agev[m][i]] += weight[i];
   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);                  prop[s[m][i]][iagemax+3] += weight[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);                } 
   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);              }
 while((c=getc(ficpar))=='#' && c!= EOF){            } /* end selection of waves */
     ungetc(c,ficpar);          }
     fgets(line, MAXLINE, ficpar);        }
     puts(line);        for(i=iagemin; i <= iagemax+3; i++){  
     fputs(line,ficparo);          
   }          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
   ungetc(c,ficpar);            posprop += prop[jk][i]; 
            } 
      
   covar=matrix(0,NCOVMAX,1,n);          for(jk=1; jk <=nlstate ; jk++){     
   cptcovn=0;            if( i <=  iagemax){ 
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;              if(posprop>=1.e-5){ 
                 probs[i][jk][j1]= prop[jk][i]/posprop;
   ncovmodel=2+cptcovn;              } else
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
              } 
   /* Read guess parameters */          }/* end jk */ 
   /* Reads comments: lines beginning with '#' */        }/* end i */ 
   while((c=getc(ficpar))=='#' && c!= EOF){      } /* end i1 */
     ungetc(c,ficpar);    } /* end k1 */
     fgets(line, MAXLINE, ficpar);    
     puts(line);    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     fputs(line,ficparo);    /*free_vector(pp,1,nlstate);*/
   }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   ungetc(c,ficpar);  }  /* End of prevalence */
    
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  /************* Waves Concatenation ***************/
     for(i=1; i <=nlstate; i++)  
     for(j=1; j <=nlstate+ndeath-1; j++){  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
       fscanf(ficpar,"%1d%1d",&i1,&j1);  {
       fprintf(ficparo,"%1d%1d",i1,j1);    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       printf("%1d%1d",i,j);       Death is a valid wave (if date is known).
       for(k=1; k<=ncovmodel;k++){       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
         fscanf(ficpar," %lf",&param[i][j][k]);       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
         printf(" %lf",param[i][j][k]);       and mw[mi+1][i]. dh depends on stepm.
         fprintf(ficparo," %lf",param[i][j][k]);       */
       }  
       fscanf(ficpar,"\n");    int i, mi, m;
       printf("\n");    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       fprintf(ficparo,"\n");       double sum=0., jmean=0.;*/
     }    int first;
      int j, k=0,jk, ju, jl;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    double sum=0.;
     first=0;
   p=param[1][1];    jmin=1e+5;
      jmax=-1;
   /* Reads comments: lines beginning with '#' */    jmean=0.;
   while((c=getc(ficpar))=='#' && c!= EOF){    for(i=1; i<=imx; i++){
     ungetc(c,ficpar);      mi=0;
     fgets(line, MAXLINE, ficpar);      m=firstpass;
     puts(line);      while(s[m][i] <= nlstate){
     fputs(line,ficparo);        if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
   }          mw[++mi][i]=m;
   ungetc(c,ficpar);        if(m >=lastpass)
           break;
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);        else
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */          m++;
   for(i=1; i <=nlstate; i++){      }/* end while */
     for(j=1; j <=nlstate+ndeath-1; j++){      if (s[m][i] > nlstate){
       fscanf(ficpar,"%1d%1d",&i1,&j1);        mi++;     /* Death is another wave */
       printf("%1d%1d",i,j);        /* if(mi==0)  never been interviewed correctly before death */
       fprintf(ficparo,"%1d%1d",i1,j1);           /* Only death is a correct wave */
       for(k=1; k<=ncovmodel;k++){        mw[mi][i]=m;
         fscanf(ficpar,"%le",&delti3[i][j][k]);      }
         printf(" %le",delti3[i][j][k]);  
         fprintf(ficparo," %le",delti3[i][j][k]);      wav[i]=mi;
       }      if(mi==0){
       fscanf(ficpar,"\n");        nbwarn++;
       printf("\n");        if(first==0){
       fprintf(ficparo,"\n");          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     }          first=1;
   }        }
   delti=delti3[1][1];        if(first==1){
            fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
   /* Reads comments: lines beginning with '#' */        }
   while((c=getc(ficpar))=='#' && c!= EOF){      } /* end mi==0 */
     ungetc(c,ficpar);    } /* End individuals */
     fgets(line, MAXLINE, ficpar);  
     puts(line);    for(i=1; i<=imx; i++){
     fputs(line,ficparo);      for(mi=1; mi<wav[i];mi++){
   }        if (stepm <=0)
   ungetc(c,ficpar);          dh[mi][i]=1;
          else{
   matcov=matrix(1,npar,1,npar);          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
   for(i=1; i <=npar; i++){            if (agedc[i] < 2*AGESUP) {
     fscanf(ficpar,"%s",&str);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     printf("%s",str);              if(j==0) j=1;  /* Survives at least one month after exam */
     fprintf(ficparo,"%s",str);              else if(j<0){
     for(j=1; j <=i; j++){                nberr++;
       fscanf(ficpar," %le",&matcov[i][j]);                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
       printf(" %.5le",matcov[i][j]);                j=1; /* Temporary Dangerous patch */
       fprintf(ficparo," %.5le",matcov[i][j]);                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     }                fprintf(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]);
     fscanf(ficpar,"\n");                fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
     printf("\n");              }
     fprintf(ficparo,"\n");              k=k+1;
   }              if (j >= jmax){
   for(i=1; i <=npar; i++)                jmax=j;
     for(j=i+1;j<=npar;j++)                ijmax=i;
       matcov[i][j]=matcov[j][i];              }
                  if (j <= jmin){
   printf("\n");                jmin=j;
                 ijmin=i;
               }
     /*-------- data file ----------*/              sum=sum+j;
     if((ficres =fopen(fileres,"w"))==NULL) {              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       printf("Problem with resultfile: %s\n", fileres);goto end;              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
     }            }
     fprintf(ficres,"#%s\n",version);          }
              else{
     if((fic=fopen(datafile,"r"))==NULL)    {            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       printf("Problem with datafile: %s\n", datafile);goto end;  /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
     }  
             k=k+1;
     n= lastobs;            if (j >= jmax) {
     severity = vector(1,maxwav);              jmax=j;
     outcome=imatrix(1,maxwav+1,1,n);              ijmax=i;
     num=ivector(1,n);            }
     moisnais=vector(1,n);            else if (j <= jmin){
     annais=vector(1,n);              jmin=j;
     moisdc=vector(1,n);              ijmin=i;
     andc=vector(1,n);            }
     agedc=vector(1,n);            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
     cod=ivector(1,n);            /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
     weight=vector(1,n);            if(j<0){
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */              nberr++;
     mint=matrix(1,maxwav,1,n);              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     anint=matrix(1,maxwav,1,n);              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
     s=imatrix(1,maxwav+1,1,n);            }
     adl=imatrix(1,maxwav+1,1,n);                sum=sum+j;
     tab=ivector(1,NCOVMAX);          }
     ncodemax=ivector(1,8);          jk= j/stepm;
           jl= j -jk*stepm;
     i=1;          ju= j -(jk+1)*stepm;
     while (fgets(line, MAXLINE, fic) != NULL)    {          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
       if ((i >= firstobs) && (i <=lastobs)) {            if(jl==0){
                      dh[mi][i]=jk;
         for (j=maxwav;j>=1;j--){              bh[mi][i]=0;
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);            }else{ /* We want a negative bias in order to only have interpolation ie
           strcpy(line,stra);                    * at the price of an extra matrix product in likelihood */
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);              dh[mi][i]=jk+1;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);              bh[mi][i]=ju;
         }            }
                  }else{
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);            if(jl <= -ju){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);              dh[mi][i]=jk;
               bh[mi][i]=jl;       /* bias is positive if real duration
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);                                   * is higher than the multiple of stepm and negative otherwise.
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);                                   */
             }
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);            else{
         for (j=ncov;j>=1;j--){              dh[mi][i]=jk+1;
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);              bh[mi][i]=ju;
         }            }
         num[i]=atol(stra);            if(dh[mi][i]==0){
                      dh[mi][i]=1; /* At least one step */
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){              bh[mi][i]=ju; /* At least one step */
           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;}*/              /*  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);*/
             }
         i=i+1;          } /* end if mle */
       }        }
     }      } /* end wave */
     /* printf("ii=%d", ij);    }
        scanf("%d",i);*/    jmean=sum/k;
   imx=i-1; /* Number of individuals */    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);
   /* 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;  /*********** Tricode ****************************/
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;  void tricode(int *Tvar, int **nbcode, int imx)
     }  {
     
     for (i=1; i<=imx; i++)    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
     if (covar[1][i]==0) printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/  
     int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=19;
   /* Calculation of the number of parameter from char model*/    int cptcode=0;
   Tvar=ivector(1,15);    cptcoveff=0; 
   Tprod=ivector(1,15);   
   Tvaraff=ivector(1,15);    for (k=0; k<maxncov; k++) Ndum[k]=0;
   Tvard=imatrix(1,15,1,2);    for (k=1; k<=7; k++) ncodemax[k]=0;
   Tage=ivector(1,15);        
        for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
   if (strlen(model) >1){      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
     j=0, j1=0, k1=1, k2=1;                                 modality*/ 
     j=nbocc(model,'+');        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
     j1=nbocc(model,'*');        Ndum[ij]++; /*store the modality */
     cptcovn=j+1;        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     cptcovprod=j1;        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
                                             Tvar[j]. If V=sex and male is 0 and 
                                             female is 1, then  cptcode=1.*/
     strcpy(modelsav,model);      }
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){  
       printf("Error. Non available option model=%s ",model);      for (i=0; i<=cptcode; i++) {
       goto end;        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 */
     }      }
      
     for(i=(j+1); i>=1;i--){      ij=1; 
       cutv(stra,strb,modelsav,'+');      for (i=1; i<=ncodemax[j]; i++) {
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);        for (k=0; k<= maxncov; k++) {
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          if (Ndum[k] != 0) {
       /*scanf("%d",i);*/            nbcode[Tvar[j]][ij]=k; 
       if (strchr(strb,'*')) {            /* 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; */
         cutv(strd,strc,strb,'*');            
         if (strcmp(strc,"age")==0) {            ij++;
           cptcovprod--;          }
           cutv(strb,stre,strd,'V');          if (ij > ncodemax[j]) break; 
           Tvar[i]=atoi(stre);        }  
           cptcovage++;      } 
             Tage[cptcovage]=i;    }  
             /*printf("stre=%s ", stre);*/  
         }   for (k=0; k< maxncov; k++) Ndum[k]=0;
         else if (strcmp(strd,"age")==0) {  
           cptcovprod--;   for (i=1; i<=ncovmodel-2; i++) { 
           cutv(strb,stre,strc,'V');     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
           Tvar[i]=atoi(stre);     ij=Tvar[i];
           cptcovage++;     Ndum[ij]++;
           Tage[cptcovage]=i;   }
         }  
         else {   ij=1;
           cutv(strb,stre,strc,'V');   for (i=1; i<= maxncov; i++) {
           Tvar[i]=ncov+k1;     if((Ndum[i]!=0) && (i<=ncovcol)){
           cutv(strb,strc,strd,'V');       Tvaraff[ij]=i; /*For printing */
           Tprod[k1]=i;       ij++;
           Tvard[k1][1]=atoi(strc);     }
           Tvard[k1][2]=atoi(stre);   }
           Tvar[cptcovn+k2]=Tvard[k1][1];   
           Tvar[cptcovn+k2+1]=Tvard[k1][2];   cptcoveff=ij-1; /*Number of simple covariates*/
           for (k=1; k<=lastobs;k++)  }
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];  
           k1++;  /*********** Health Expectancies ****************/
           k2=k2+2;  
         }  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
       }  
       else {  {
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/    /* Health expectancies, no variances */
        /*  scanf("%d",i);*/    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
       cutv(strd,strc,strb,'V');    int nhstepma, nstepma; /* Decreasing with age */
       Tvar[i]=atoi(strc);    double age, agelim, hf;
       }    double ***p3mat;
       strcpy(modelsav,stra);      double eip;
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);  
         scanf("%d",i);*/    pstamp(ficreseij);
     }    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
 }    fprintf(ficreseij,"# Age");
      for(i=1; i<=nlstate;i++){
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);      for(j=1; j<=nlstate;j++){
   printf("cptcovprod=%d ", cptcovprod);        fprintf(ficreseij," e%1d%1d ",i,j);
   scanf("%d ",i);*/      }
     fclose(fic);      fprintf(ficreseij," e%1d. ",i);
     }
     /*  if(mle==1){*/    fprintf(ficreseij,"\n");
     if (weightopt != 1) { /* Maximisation without weights*/  
       for(i=1;i<=n;i++) weight[i]=1.0;    
     }    if(estepm < stepm){
     /*-calculation of age at interview from date of interview and age at death -*/      printf ("Problem %d lower than %d\n",estepm, stepm);
     agev=matrix(1,maxwav,1,imx);    }
     else  hstepm=estepm;   
    for (i=1; i<=imx; i++)    /* We compute the life expectancy from trapezoids spaced every estepm months
      for(m=2; (m<= maxwav); m++)     * This is mainly to measure the difference between two models: for example
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){     * if stepm=24 months pijx are given only every 2 years and by summing them
          anint[m][i]=9999;     * we are calculating an estimate of the Life Expectancy assuming a linear 
          s[m][i]=-1;     * progression in between and thus overestimating or underestimating according
        }     * to the curvature of the survival function. If, for the same date, we 
         * estimate the model with stepm=1 month, we can keep estepm to 24 months
     for (i=1; i<=imx; i++)  {     * to compare the new estimate of Life expectancy with the same linear 
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);     * hypothesis. A more precise result, taking into account a more precise
       for(m=1; (m<= maxwav); m++){     * curvature will be obtained if estepm is as small as stepm. */
         if(s[m][i] >0){  
           if (s[m][i] == nlstate+1) {    /* For example we decided to compute the life expectancy with the smallest unit */
             if(agedc[i]>0)    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
               if(moisdc[i]!=99 && andc[i]!=9999)       nhstepm is the number of hstepm from age to agelim 
               agev[m][i]=agedc[i];       nstepm is the number of stepm from age to agelin. 
             else {       Look at hpijx to understand the reason of that which relies in memory size
               if (andc[i]!=9999){       and note for a fixed period like estepm months */
               printf("Warning negative age at death: %d line:%d\n",num[i],i);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
               agev[m][i]=-1;       survival function given by stepm (the optimization length). Unfortunately it
               }       means that if the survival funtion is printed only each two years of age and if
             }       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           }       results. So we changed our mind and took the option of the best precision.
           else if(s[m][i] !=9){ /* Should no more exist */    */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
             if(mint[m][i]==99 || anint[m][i]==9999)  
               agev[m][i]=1;    agelim=AGESUP;
             else if(agev[m][i] <agemin){    /* If stepm=6 months */
               agemin=agev[m][i];      /* Computed by stepm unit matrices, product of hstepm matrices, stored
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
             }      
             else if(agev[m][i] >agemax){  /* nhstepm age range expressed in number of stepm */
               agemax=agev[m][i];    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
             }    /* if (stepm >= YEARM) hstepm=1;*/
             /*agev[m][i]=anint[m][i]-annais[i];*/    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
             /*   agev[m][i] = age[i]+2*m;*/    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }  
           else { /* =9 */    for (age=bage; age<=fage; age ++){ 
             agev[m][i]=1;      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
             s[m][i]=-1;      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           }      /* if (stepm >= YEARM) hstepm=1;*/
         }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
         else /*= 0 Unknown */  
           agev[m][i]=1;      /* If stepm=6 months */
       }      /* Computed by stepm unit matrices, product of hstepma matrices, stored
             in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     }      
     for (i=1; i<=imx; i++)  {      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(m=1; (m<= maxwav); m++){      
         if (s[m][i] > (nlstate+ndeath)) {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
           printf("Error: Wrong value in nlstate or ndeath\n");        
           goto end;      printf("%d|",(int)age);fflush(stdout);
         }      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       }      
     }      /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);        for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     free_vector(severity,1,maxwav);            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
     free_imatrix(outcome,1,maxwav+1,1,n);            
     free_vector(moisnais,1,n);            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
     free_vector(annais,1,n);  
     /* free_matrix(mint,1,maxwav,1,n);          }
        free_matrix(anint,1,maxwav,1,n);*/  
     free_vector(moisdc,1,n);      fprintf(ficreseij,"%3.0f",age );
     free_vector(andc,1,n);      for(i=1; i<=nlstate;i++){
         eip=0;
            for(j=1; j<=nlstate;j++){
     wav=ivector(1,imx);          eip +=eij[i][j][(int)age];
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
     mw=imatrix(1,lastpass-firstpass+1,1,imx);        }
            fprintf(ficreseij,"%9.4f", eip );
     /* Concatenates waves */      }
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);      fprintf(ficreseij,"\n");
       
     }
       Tcode=ivector(1,100);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);    printf("\n");
       ncodemax[1]=1;    fprintf(ficlog,"\n");
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);    
        }
    codtab=imatrix(1,100,1,10);  
    h=0;  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
    m=pow(2,cptcoveff);  
    {
    for(k=1;k<=cptcoveff; k++){    /* Covariances of health expectancies eij and of total life expectancies according
      for(i=1; i <=(m/pow(2,k));i++){     to initial status i, ei. .
        for(j=1; j <= ncodemax[k]; j++){    */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
            h++;    int nhstepma, nstepma; /* Decreasing with age */
            if (h>m) h=1;codtab[h][k]=j;    double age, agelim, hf;
          }    double ***p3matp, ***p3matm, ***varhe;
        }    double **dnewm,**doldm;
      }    double *xp, *xm;
    }    double **gp, **gm;
     double ***gradg, ***trgradg;
     int theta;
    /*for(i=1; i <=m ;i++){  
      for(k=1; k <=cptcovn; k++){    double eip, vip;
        printf("i=%d k=%d %d %d",i,k,codtab[i][k], cptcoveff);  
      }    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
      printf("\n");    xp=vector(1,npar);
    }    xm=vector(1,npar);
    scanf("%d",i);*/    dnewm=matrix(1,nlstate*nlstate,1,npar);
        doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
    /* Calculates basic frequencies. Computes observed prevalence at single age    
        and prints on file fileres'p'. */    pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
        fprintf(ficresstdeij,"# Age");
        for(i=1; i<=nlstate;i++){
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(j=1; j<=nlstate;j++)
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresstdeij," e%1d. ",i);
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    }
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fprintf(ficresstdeij,"\n");
        
     /* For Powell, parameters are in a vector p[] starting at p[1]    pstamp(ficrescveij);
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    fprintf(ficrescveij,"# Age");
     for(i=1; i<=nlstate;i++)
     if(mle==1){      for(j=1; j<=nlstate;j++){
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);        cptj= (j-1)*nlstate+i;
     }        for(i2=1; i2<=nlstate;i2++)
              for(j2=1; j2<=nlstate;j2++){
     /*--------- results files --------------*/            cptj2= (j2-1)*nlstate+i2;
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);            if(cptj2 <= cptj)
                fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
    jk=1;      }
    fprintf(ficres,"# Parameters\n");    fprintf(ficrescveij,"\n");
    printf("# Parameters\n");    
    for(i=1,jk=1; i <=nlstate; i++){    if(estepm < stepm){
      for(k=1; k <=(nlstate+ndeath); k++){      printf ("Problem %d lower than %d\n",estepm, stepm);
        if (k != i)    }
          {    else  hstepm=estepm;   
            printf("%d%d ",i,k);    /* We compute the life expectancy from trapezoids spaced every estepm months
            fprintf(ficres,"%1d%1d ",i,k);     * This is mainly to measure the difference between two models: for example
            for(j=1; j <=ncovmodel; j++){     * if stepm=24 months pijx are given only every 2 years and by summing them
              printf("%f ",p[jk]);     * we are calculating an estimate of the Life Expectancy assuming a linear 
              fprintf(ficres,"%f ",p[jk]);     * progression in between and thus overestimating or underestimating according
              jk++;     * 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
            printf("\n");     * to compare the new estimate of Life expectancy with the same linear 
            fprintf(ficres,"\n");     * hypothesis. A more precise result, taking into account a more precise
          }     * curvature will be obtained if estepm is as small as stepm. */
      }  
    }    /* For example we decided to compute the life expectancy with the smallest unit */
  if(mle==1){    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     /* Computing hessian and covariance matrix */       nhstepm is the number of hstepm from age to agelim 
     ftolhess=ftol; /* Usually correct */       nstepm is the number of stepm from age to agelin. 
     hesscov(matcov, p, npar, delti, ftolhess, func);       Look at hpijx to understand the reason of that which relies in memory size
  }       and note for a fixed period like estepm months */
     fprintf(ficres,"# Scales\n");    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     printf("# Scales\n");       survival function given by stepm (the optimization length). Unfortunately it
      for(i=1,jk=1; i <=nlstate; i++){       means that if the survival funtion is printed only each two years of age and if
       for(j=1; j <=nlstate+ndeath; j++){       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
         if (j!=i) {       results. So we changed our mind and took the option of the best precision.
           fprintf(ficres,"%1d%1d",i,j);    */
           printf("%1d%1d",i,j);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           for(k=1; k<=ncovmodel;k++){  
             printf(" %.5e",delti[jk]);    /* If stepm=6 months */
             fprintf(ficres," %.5e",delti[jk]);    /* nhstepm age range expressed in number of stepm */
             jk++;    agelim=AGESUP;
           }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
           printf("\n");    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           fprintf(ficres,"\n");    /* if (stepm >= YEARM) hstepm=1;*/
         }    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       }    
      }    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     k=1;    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
     fprintf(ficres,"# Covariance\n");    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
     printf("# Covariance\n");    gp=matrix(0,nhstepm,1,nlstate*nlstate);
     for(i=1;i<=npar;i++){    gm=matrix(0,nhstepm,1,nlstate*nlstate);
       /*  if (k>nlstate) k=1;  
       i1=(i-1)/(ncovmodel*nlstate)+1;    for (age=bage; age<=fage; age ++){ 
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       printf("%s%d%d",alph[k],i1,tab[i]);*/      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       fprintf(ficres,"%3d",i);      /* if (stepm >= YEARM) hstepm=1;*/
       printf("%3d",i);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
       for(j=1; j<=i;j++){  
         fprintf(ficres," %.5e",matcov[i][j]);      /* If stepm=6 months */
         printf(" %.5e",matcov[i][j]);      /* Computed by stepm unit matrices, product of hstepma matrices, stored
       }         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       fprintf(ficres,"\n");      
       printf("\n");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       k++;  
     }      /* Computing  Variances of health expectancies */
          /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
     while((c=getc(ficpar))=='#' && c!= EOF){         decrease memory allocation */
       ungetc(c,ficpar);      for(theta=1; theta <=npar; theta++){
       fgets(line, MAXLINE, ficpar);        for(i=1; i<=npar; i++){ 
       puts(line);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       fputs(line,ficparo);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
     }        }
     ungetc(c,ficpar);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
          hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    
            for(j=1; j<= nlstate; j++){
     if (fage <= 2) {          for(i=1; i<=nlstate; i++){
       bage = agemin;            for(h=0; h<=nhstepm-1; h++){
       fage = agemax;              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.;
                }
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");          }
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        }
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);       
          for(ij=1; ij<= nlstate*nlstate; ij++)
     while((c=getc(ficpar))=='#' && c!= EOF){          for(h=0; h<=nhstepm-1; h++){
     ungetc(c,ficpar);            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
     fgets(line, MAXLINE, ficpar);          }
     puts(line);      }/* End theta */
     fputs(line,ficparo);      
   }      
   ungetc(c,ficpar);      for(h=0; h<=nhstepm-1; h++)
          for(j=1; j<=nlstate*nlstate;j++)
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);          for(theta=1; theta <=npar; theta++)
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);            trgradg[h][j][theta]=gradg[h][theta][j];
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      
        
   while((c=getc(ficpar))=='#' && c!= EOF){       for(ij=1;ij<=nlstate*nlstate;ij++)
     ungetc(c,ficpar);        for(ji=1;ji<=nlstate*nlstate;ji++)
     fgets(line, MAXLINE, ficpar);          varhe[ij][ji][(int)age] =0.;
     puts(line);  
     fputs(line,ficparo);       printf("%d|",(int)age);fflush(stdout);
   }       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   ungetc(c,ficpar);       for(h=0;h<=nhstepm-1;h++){
          for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
    dateprev1=anprev1+mprev1/12.+jprev1/365.;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;          for(ij=1;ij<=nlstate*nlstate;ij++)
             for(ji=1;ji<=nlstate*nlstate;ji++)
   fscanf(ficpar,"pop_based=%d\n",&popbased);              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
    fprintf(ficparo,"pop_based=%d\n",popbased);          }
    fprintf(ficres,"pop_based=%d\n",popbased);        }
   
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Computing expectancies */
     ungetc(c,ficpar);      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
     fgets(line, MAXLINE, ficpar);      for(i=1; i<=nlstate;i++)
     puts(line);        for(j=1; j<=nlstate;j++)
     fputs(line,ficparo);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   }            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
   ungetc(c,ficpar);            
   fscanf(ficpar,"popforecast=%d popfile=%s starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mob_average=%d\n",&popforecast,popfile,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
 fprintf(ficparo,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mob_average=%d\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);  
 fprintf(ficres,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mob_average=%d\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);          }
   
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2);      fprintf(ficresstdeij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
 /*------------ gnuplot -------------*/        eip=0.;
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, agemin,agemax,fage, pathc,p);        vip=0.;
          for(j=1; j<=nlstate;j++){
 /*------------ free_vector  -------------*/          eip += eij[i][j][(int)age];
  chdir(path);          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];
  free_ivector(wav,1,imx);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);        }
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
  free_ivector(num,1,n);      }
  free_vector(agedc,1,n);      fprintf(ficresstdeij,"\n");
  /*free_matrix(covar,1,NCOVMAX,1,n);*/  
  fclose(ficparo);      fprintf(ficrescveij,"%3.0f",age );
  fclose(ficres);      for(i=1; i<=nlstate;i++)
          for(j=1; j<=nlstate;j++){
   /* Reads comments: lines beginning with '#' */          cptj= (j-1)*nlstate+i;
   while((c=getc(ficpar))=='#' && c!= EOF){          for(i2=1; i2<=nlstate;i2++)
     ungetc(c,ficpar);            for(j2=1; j2<=nlstate;j2++){
     fgets(line, MAXLINE, ficpar);              cptj2= (j2-1)*nlstate+i2;
     puts(line);              if(cptj2 <= cptj)
     fputs(line,ficparo);                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
   }            }
   ungetc(c,ficpar);        }
        fprintf(ficrescveij,"\n");
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);     
   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);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
 /*--------- index.htm --------*/    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   /*--------------- Prevalence limit --------------*/    printf("\n");
      fprintf(ficlog,"\n");
   strcpy(filerespl,"pl");  
   strcat(filerespl,fileres);    free_vector(xm,1,npar);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    free_vector(xp,1,npar);
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   }    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   fprintf(ficrespl,"#Prevalence limit\n");  }
   fprintf(ficrespl,"#Age ");  
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  /************ Variance ******************/
   fprintf(ficrespl,"\n");  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[])
    {
   prlim=matrix(1,nlstate,1,nlstate);    /* Variance of health expectancies */
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    /* double **newm;*/
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **dnewm,**doldm;
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double **dnewmp,**doldmp;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    int i, j, nhstepm, hstepm, h, nstepm ;
   k=0;    int k, cptcode;
   agebase=agemin;    double *xp;
   agelim=agemax;    double **gp, **gm;  /* for var eij */
   ftolpl=1.e-10;    double ***gradg, ***trgradg; /*for var eij */
   i1=cptcoveff;    double **gradgp, **trgradgp; /* for var p point j */
   if (cptcovn < 1){i1=1;}    double *gpp, *gmp; /* for var p point j */
     double **varppt; /* for var p point j nlstate to nlstate+ndeath */
   for(cptcov=1;cptcov<=i1;cptcov++){    double ***p3mat;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double age,agelim, hf;
         k=k+1;    double ***mobaverage;
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    int theta;
         fprintf(ficrespl,"\n#******");    char digit[4];
         for(j=1;j<=cptcoveff;j++)    char digitp[25];
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
         fprintf(ficrespl,"******\n");    char fileresprobmorprev[FILENAMELENGTH];
          
         for (age=agebase; age<=agelim; age++){    if(popbased==1){
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      if(mobilav!=0)
           fprintf(ficrespl,"%.0f",age );        strcpy(digitp,"-populbased-mobilav-");
           for(i=1; i<=nlstate;i++)      else strcpy(digitp,"-populbased-nomobil-");
           fprintf(ficrespl," %.5f", prlim[i][i]);    }
           fprintf(ficrespl,"\n");    else 
         }      strcpy(digitp,"-stablbased-");
       }  
     }    if (mobilav!=0) {
   fclose(ficrespl);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   /*------------- h Pij x at various ages ------------*/        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
          printf(" Error in movingaverage mobilav=%d\n",mobilav);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);      }
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    }
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  
   }    strcpy(fileresprobmorprev,"prmorprev"); 
   printf("Computing pij: result on file '%s' \n", filerespij);    sprintf(digit,"%-d",ij);
      /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   stepsize=(int) (stepm+YEARM-1)/YEARM;    strcat(fileresprobmorprev,digit); /* Tvar to be done */
   /*if (stepm<=24) stepsize=2;*/    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
   agelim=AGESUP;    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   hstepm=stepsize*YEARM; /* Every year of age */      printf("Problem with resultfile: %s\n", fileresprobmorprev);
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
      }
   k=0;    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   for(cptcov=1;cptcov<=i1;cptcov++){   
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
       k=k+1;    pstamp(ficresprobmorprev);
         fprintf(ficrespij,"\n#****** ");    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
         for(j=1;j<=cptcoveff;j++)    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficrespij,"******\n");      fprintf(ficresprobmorprev," p.%-d SE",j);
              for(i=1; i<=nlstate;i++)
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    }  
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    fprintf(ficresprobmorprev,"\n");
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficgp,"\n# Routine varevsij");
           oldm=oldms;savm=savms;    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
           fprintf(ficrespij,"# Age");    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
           for(i=1; i<=nlstate;i++)  /*   } */
             for(j=1; j<=nlstate+ndeath;j++)    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
               fprintf(ficrespij," %1d-%1d",i,j);    pstamp(ficresvij);
           fprintf(ficrespij,"\n");    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
           for (h=0; h<=nhstepm; h++){    if(popbased==1)
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
             for(i=1; i<=nlstate;i++)    else
               for(j=1; j<=nlstate+ndeath;j++)      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);    fprintf(ficresvij,"# Age");
             fprintf(ficrespij,"\n");    for(i=1; i<=nlstate;i++)
           }      for(j=1; j<=nlstate;j++)
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
           fprintf(ficrespij,"\n");    fprintf(ficresvij,"\n");
         }  
     }    xp=vector(1,npar);
   }    dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   fclose(ficrespij);  
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   if(stepm == 1) {    gpp=vector(nlstate+1,nlstate+ndeath);
   /*---------- Forecasting ------------------*/    gmp=vector(nlstate+1,nlstate+ndeath);
   calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
   /*printf("calage= %f", calagedate);*/    if(estepm < stepm){
        printf ("Problem %d lower than %d\n",estepm, stepm);
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    }
     else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
   strcpy(fileresf,"f");    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   strcat(fileresf,fileres);       nhstepm is the number of hstepm from age to agelim 
   if((ficresf=fopen(fileresf,"w"))==NULL) {       nstepm is the number of stepm from age to agelin. 
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;       Look at function hpijx to understand why (it is linked to memory size questions) */
   }    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   printf("Computing forecasting: result on file '%s' \n", fileresf);       survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
   free_matrix(mint,1,maxwav,1,n);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   free_matrix(anint,1,maxwav,1,n);       results. So we changed our mind and took the option of the best precision.
   free_matrix(agev,1,maxwav,1,imx);    */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   /* Mobile average */    agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
   if (mobilav==1) {      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
     movingaverage(agedeb, fage, agemin, mobaverage);      gp=matrix(0,nhstepm,1,nlstate);
   }      gm=matrix(0,nhstepm,1,nlstate);
   
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=12) stepsize=1;      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
   agelim=AGESUP;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   /*hstepm=stepsize*YEARM; *//* Every year of age */        }
   hstepm=1;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   yp1=modf(dateintmean,&yp);  
   anprojmean=yp;        if (popbased==1) {
   yp2=modf((yp1*12),&yp);          if(mobilav ==0){
   mprojmean=yp;            for(i=1; i<=nlstate;i++)
   yp1=modf((yp2*30.5),&yp);              prlim[i][i]=probs[(int)age][i][ij];
   jprojmean=yp;          }else{ /* mobilav */ 
   if(jprojmean==0) jprojmean=1;            for(i=1; i<=nlstate;i++)
   if(mprojmean==0) jprojmean=1;              prlim[i][i]=mobaverage[(int)age][i][ij];
           }
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);        }
     
   if (popforecast==1) {        for(j=1; j<= nlstate; j++){
     if((ficpop=fopen(popfile,"r"))==NULL)    {          for(h=0; h<=nhstepm; h++){
       printf("Problem with population file : %s\n",popfile);goto end;            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
     }              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
     popage=ivector(0,AGESUP);          }
     popeffectif=vector(0,AGESUP);        }
     popcount=vector(0,AGESUP);        /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
     i=1;             as a weighted average of prlim.
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)        */
       {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
         i=i+1;          for(i=1,gpp[j]=0.; i<= nlstate; i++)
       }            gpp[j] += prlim[i][i]*p3mat[i][j][1];
     imx=i;        }    
            /* end probability of death */
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];  
   }        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
   for(cptcov=1;cptcov<=i1;cptcov++){        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
       k=k+1;   
       fprintf(ficresf,"\n#******");        if (popbased==1) {
       for(j=1;j<=cptcoveff;j++) {          if(mobilav ==0){
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            for(i=1; i<=nlstate;i++)
       }              prlim[i][i]=probs[(int)age][i][ij];
       fprintf(ficresf,"******\n");          }else{ /* mobilav */ 
       fprintf(ficresf,"# StartingAge FinalAge");            for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);              prlim[i][i]=mobaverage[(int)age][i][ij];
       if (popforecast==1)  fprintf(ficresf," [Population]");          }
              }
      for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {  
         fprintf(ficresf,"\n");        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);            for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(agemin-((int)calagedate %12)/12.); agedeb--){              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          }
         nhstepm = nhstepm/hstepm;        }
                /* This for computing probability of death (h=1 means
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           computed over hstepm matrices product = hstepm*stepm months) 
         oldm=oldms;savm=savms;           as a weighted average of prlim.
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          */
                for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for (h=0; h<=nhstepm; h++){          for(i=1,gmp[j]=0.; i<= nlstate; i++)
           if (h==(int) (calagedate+YEARM*cpt)) {           gmp[j] += prlim[i][i]*p3mat[i][j][1];
             fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);        }    
           }        /* end probability of death */
           for(j=1; j<=nlstate+ndeath;j++) {  
             kk1=0.;kk2=0;        for(j=1; j<= nlstate; j++) /* vareij */
             for(i=1; i<=nlstate;i++) {                  for(h=0; h<=nhstepm; h++){
               if (mobilav==1)            gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
                 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];        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
                          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
               }        }
   
               if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];      } /* End theta */
             }  
                trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
             if (h==(int)(calagedate+12*cpt)){  
               fprintf(ficresf," %.3f", kk1);      for(h=0; h<=nhstepm; h++) /* veij */
                      for(j=1; j<=nlstate;j++)
               if (popforecast==1) fprintf(ficresf," [%.f]", kk2);          for(theta=1; theta <=npar; theta++)
             }            trgradg[h][j][theta]=gradg[h][theta][j];
           }  
         }      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(theta=1; theta <=npar; theta++)
         }          trgradgp[j][theta]=gradgp[theta][j];
      }    
     }  
   }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
   if (popforecast==1) {          vareij[i][j][(int)age] =0.;
     free_ivector(popage,0,AGESUP);  
     free_vector(popeffectif,0,AGESUP);      for(h=0;h<=nhstepm;h++){
     free_vector(popcount,0,AGESUP);        for(k=0;k<=nhstepm;k++){
   }          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
   free_imatrix(s,1,maxwav+1,1,n);          matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   free_vector(weight,1,n);          for(i=1;i<=nlstate;i++)
   fclose(ficresf);            for(j=1;j<=nlstate;j++)
   }/* End forecasting */              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
   else{        }
     erreur=108;      }
     printf("Error %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d\n", erreur, stepm);    
       /* 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++)
   /*---------- Health expectancies and variances ------------*/        for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
   strcpy(filerest,"t");      /* end ppptj */
   strcat(filerest,fileres);      /*  x centered again */
   if((ficrest=fopen(filerest,"w"))==NULL) {      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
   }   
   printf("Computing Total LEs with variances: file '%s' \n", filerest);      if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
   strcpy(filerese,"e");            prlim[i][i]=probs[(int)age][i][ij];
   strcat(filerese,fileres);        }else{ /* mobilav */ 
   if((ficreseij=fopen(filerese,"w"))==NULL) {          for(i=1; i<=nlstate;i++)
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);            prlim[i][i]=mobaverage[(int)age][i][ij];
   }        }
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      }
                
  strcpy(fileresv,"v");      /* This for computing probability of death (h=1 means
   strcat(fileresv,fileres);         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
   if((ficresvij=fopen(fileresv,"w"))==NULL) {         as a weighted average of prlim.
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      */
   }      for(j=nlstate+1;j<=nlstate+ndeath;j++){
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   k=0;      }    
   for(cptcov=1;cptcov<=i1;cptcov++){      /* end probability of death */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
       k=k+1;      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       fprintf(ficrest,"\n#****** ");      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       for(j=1;j<=cptcoveff;j++)        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        for(i=1; i<=nlstate;i++){
       fprintf(ficrest,"******\n");          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       fprintf(ficreseij,"\n#****** ");      } 
       for(j=1;j<=cptcoveff;j++)      fprintf(ficresprobmorprev,"\n");
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficreseij,"******\n");      fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
       fprintf(ficresvij,"\n#****** ");        for(j=1; j<=nlstate;j++){
       for(j=1;j<=cptcoveff;j++)          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);        }
       fprintf(ficresvij,"******\n");      fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      free_matrix(gm,0,nhstepm,1,nlstate);
       oldm=oldms;savm=savms;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);        free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       oldm=oldms;savm=savms;    } /* End age */
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    free_vector(gpp,nlstate+1,nlstate+ndeath);
          free_vector(gmp,nlstate+1,nlstate+ndeath);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
       fprintf(ficrest,"\n");    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 */
       hf=1;    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
       if (stepm >= YEARM) hf=stepm/YEARM;  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
       epj=vector(1,nlstate+1);  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
       for(age=bage; age <=fage ;age++){  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
         if (popbased==1) {    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
           for(i=1; i<=nlstate;i++)    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
             prlim[i][i]=probs[(int)age][i][k];    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(ficrest," %.0f",age);  */
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];  
           }    free_vector(xp,1,npar);
           epj[nlstate+1] +=epj[j];    free_matrix(doldm,1,nlstate,1,nlstate);
         }    free_matrix(dnewm,1,nlstate,1,npar);
         for(i=1, vepp=0.;i <=nlstate;i++)    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           for(j=1;j <=nlstate;j++)    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
             vepp += vareij[i][j][(int)age];    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         for(j=1;j <=nlstate;j++){    fclose(ficresprobmorprev);
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    fflush(ficgp);
         }    fflush(fichtm); 
         fprintf(ficrest,"\n");  }  /* 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;
  fclose(ficreseij);    double **dnewm,**doldm;
  fclose(ficresvij);    int i, j, nhstepm, hstepm;
   fclose(ficrest);    int k, cptcode;
   fclose(ficpar);    double *xp;
   free_vector(epj,1,nlstate+1);    double *gp, *gm;
   /*  scanf("%d ",i); */    double **gradg, **trgradg;
     double age,agelim;
   /*------- Variance limit prevalence------*/      int theta;
     
 strcpy(fileresvpl,"vpl");    pstamp(ficresvpl);
   strcat(fileresvpl,fileres);    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    fprintf(ficresvpl,"# Age");
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    for(i=1; i<=nlstate;i++)
     exit(0);        fprintf(ficresvpl," %1d-%1d",i,i);
   }    fprintf(ficresvpl,"\n");
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);  
     xp=vector(1,npar);
  k=0;    dnewm=matrix(1,nlstate,1,npar);
  for(cptcov=1;cptcov<=i1;cptcov++){    doldm=matrix(1,nlstate,1,nlstate);
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    
      k=k+1;    hstepm=1*YEARM; /* Every year of age */
      fprintf(ficresvpl,"\n#****** ");    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
      for(j=1;j<=cptcoveff;j++)    agelim = AGESUP;
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
      fprintf(ficresvpl,"******\n");      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
            if (stepm >= YEARM) hstepm=1;
      varpl=matrix(1,nlstate,(int) bage, (int) fage);      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
      oldm=oldms;savm=savms;      gradg=matrix(1,npar,1,nlstate);
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      gp=vector(1,nlstate);
    }      gm=vector(1,nlstate);
  }  
       for(theta=1; theta <=npar; theta++){
   fclose(ficresvpl);        for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
   /*---------- End : free ----------------*/        }
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
          for(i=1;i<=nlstate;i++)
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);          gp[i] = prlim[i][i];
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);      
          for(i=1; i<=npar; i++) /* Computes gradient */
            xp[i] = x[i] - (i==theta ?delti[theta]:0);
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);        for(i=1;i<=nlstate;i++)
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);          gm[i] = prlim[i][i];
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);  
          for(i=1;i<=nlstate;i++)
   free_matrix(matcov,1,npar,1,npar);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
   free_vector(delti,1,npar);      } /* End theta */
    
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);      trgradg =matrix(1,nlstate,1,npar);
   
   if(erreur >0)      for(j=1; j<=nlstate;j++)
     printf("End of Imach with error %d\n",erreur);        for(theta=1; theta <=npar; theta++)
   else   printf("End of Imach\n");          trgradg[j][theta]=gradg[theta][j];
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */  
        for(i=1;i<=nlstate;i++)
   /* 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);*/        varpl[i][(int)age] =0.;
   /*printf("Total time was %d uSec.\n", total_usecs);*/      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
   /*------ End -----------*/      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 */
  end:  
 #ifdef windows      fprintf(ficresvpl,"%.0f ",age );
   /* chdir(pathcd);*/      for(i=1; i<=nlstate;i++)
 #endif        fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
  /*system("wgnuplot graph.plt");*/      fprintf(ficresvpl,"\n");
  /*system("../gp37mgw/wgnuplot graph.plt");*/      free_vector(gp,1,nlstate);
  /*system("cd ../gp37mgw");*/      free_vector(gm,1,nlstate);
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/      free_matrix(gradg,1,npar,1,nlstate);
  strcpy(plotcmd,GNUPLOTPROGRAM);      free_matrix(trgradg,1,nlstate,1,npar);
  strcat(plotcmd," ");    } /* End age */
  strcat(plotcmd,optionfilegnuplot);  
  system(plotcmd);    free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
 #ifdef windows    free_matrix(dnewm,1,nlstate,1,nlstate);
   while (z[0] != 'q') {  
     chdir(path);  }
     printf("\nType e to edit output files, c to start again, and q for exiting: ");  
     scanf("%s",z);  /************ Variance of one-step probabilities  ******************/
     if (z[0] == 'c') system("./imach");  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[])
     else if (z[0] == 'e') {  {
       chdir(path);    int i, j=0,  i1, k1, l1, t, tj;
       system(optionfilehtm);    int k2, l2, j1,  z1;
     }    int k=0,l, cptcode;
     else if (z[0] == 'q') exit(0);    int first=1, first1;
   }    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
 #endif    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, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=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), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     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;
     int vpopbased=0;
   
     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);
           goto end;
         }
         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; /* Number of covariates V1+V2+V3 =>2+1=3 */
       cptcovprod=j1; /*Number of products  V1*V2 =1 */
       
       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'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav=V2+V3*age+V1+V4 strb=V3*age+V1+V4 
                                        stra=V2
                                       */ 
         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 V1+V3*age+V2 strb=V3*age*/
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre);  /* V1+V3*age+V2 Tvar[2]=3 */
             cptcovage++; /* Sum the number of covariates including ages as a product */
             Tage[cptcovage]=i;  /* Tage[1] =2 */
             /*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 V1+V3*V2+V2  strb=V3*V2*/
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[i]=ncovcol+k1;  /* find 'n' in Vn and stores in Tvar. 
                                     If already ncovcol=2 and model=V2*V1 Tvar[1]=2+1 and Tvar[2]=2+2 etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;  /* Tprod[1]  */
             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);  /* modelsav=V2+V3*age+V1+V4 strb=V3*age+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
       /*  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 codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ 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("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         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); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           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(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       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(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);
     }
   }
   
   
   

Removed from v.1.25  
changed lines
  Added in v.1.130


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