Diff for /imach/src/imach.c between versions 1.20 and 1.139

version 1.20, 2002/02/20 17:22:01 version 1.139, 2010/06/14 07:50:17
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      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.139  2010/06/14 07:50:17  brouard
   individuals from different ages are interviewed on their health status    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
   or degree of  disability. At least a second wave of interviews    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
   ("longitudinal") should  measure each new individual health status.  
   Health expectancies are computed from the transistions observed between    Revision 1.138  2010/04/30 18:19:40  brouard
   waves and are computed for each degree of severity of disability (number    *** empty log message ***
   of life states). More degrees you consider, more time is necessary to  
   reach the Maximum Likelihood of the parameters involved in the model.    Revision 1.137  2010/04/29 18:11:38  brouard
   The simplest model is the multinomial logistic model where pij is    (Module): Checking covariates for more complex models
   the probabibility to be observed in state j at the second wave conditional    than V1+V2. A lot of change to be done. Unstable.
   to be observed in state i at the first wave. Therefore the model is:  
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Revision 1.136  2010/04/26 20:30:53  brouard
   is a covariate. If you want to have a more complex model than "constant and    (Module): merging some libgsl code. Fixing computation
   age", you should modify the program where the markup    of likelione (using inter/intrapolation if mle = 0) in order to
     *Covariates have to be included here again* invites you to do it.    get same likelihood as if mle=1.
   More covariates you add, less is the speed of the convergence.    Some cleaning of code and comments added.
   
   The advantage that this computer programme claims, comes from that if the    Revision 1.135  2009/10/29 15:33:14  brouard
   delay between waves is not identical for each individual, or if some    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   individual missed an interview, the information is not rounded or lost, but  
   taken into account using an interpolation or extrapolation.    Revision 1.134  2009/10/29 13:18:53  brouard
   hPijx is the probability to be    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   observed in state i at age x+h conditional to the observed state i at age  
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Revision 1.133  2009/07/06 10:21:25  brouard
   unobserved intermediate  states. This elementary transition (by month or    just nforces
   quarter trimester, semester or year) is model as a multinomial logistic.  
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.132  2009/07/06 08:22:05  brouard
   and the contribution of each individual to the likelihood is simply hPijx.    Many tings
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.131  2009/06/20 16:22:47  brouard
   of the life expectancies. It also computes the prevalence limits.    Some dimensions resccaled
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.130  2009/05/26 06:44:34  brouard
            Institut national d'études démographiques, Paris.    (Module): Max Covariate is now set to 20 instead of 8. A
   This software have been partly granted by Euro-REVES, a concerted action    lot of cleaning with variables initialized to 0. Trying to make
   from the European Union.    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   It is copyrighted identically to a GNU software product, ie programme and  
   software can be distributed freely for non commercial use. Latest version    Revision 1.129  2007/08/31 13:49:27  lievre
   can be accessed at http://euroreves.ined.fr/imach .    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   **********************************************************************/  
      Revision 1.128  2006/06/30 13:02:05  brouard
 #include <math.h>    (Module): Clarifications on computing e.j
 #include <stdio.h>  
 #include <stdlib.h>    Revision 1.127  2006/04/28 18:11:50  brouard
 #include <unistd.h>    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 #define MAXLINE 256    loop. Now we define nhstepma in the age loop.
 #define FILENAMELENGTH 80    (Module): In order to speed up (in case of numerous covariates) we
 /*#define DEBUG*/    compute health expectancies (without variances) in a first step
 #define windows    and then all the health expectancies with variances or standard
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    deviation (needs data from the Hessian matrices) which slows the
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    computation.
     In the future we should be able to stop the program is only health
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    expectancies and graph are needed without standard deviations.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.126  2006/04/28 17:23:28  brouard
 #define NINTERVMAX 8    (Module): Yes the sum of survivors was wrong since
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    imach-114 because nhstepm was no more computed in the age
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    loop. Now we define nhstepma in the age loop.
 #define NCOVMAX 8 /* Maximum number of covariates */    Version 0.98h
 #define MAXN 20000  
 #define YEARM 12. /* Number of months per year */    Revision 1.125  2006/04/04 15:20:31  lievre
 #define AGESUP 130    Errors in calculation of health expectancies. Age was not initialized.
 #define AGEBASE 40    Forecasting file added.
   
     Revision 1.124  2006/03/22 17:13:53  lievre
 int nvar;    Parameters are printed with %lf instead of %f (more numbers after the comma).
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    The log-likelihood is printed in the log file
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    Revision 1.123  2006/03/20 10:52:43  brouard
 int ndeath=1; /* Number of dead states */    * imach.c (Module): <title> changed, corresponds to .htm file
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    name. <head> headers where missing.
 int popbased=0;  
     * imach.c (Module): Weights can have a decimal point as for
 int *wav; /* Number of waves for this individuual 0 is possible */    English (a comma might work with a correct LC_NUMERIC environment,
 int maxwav; /* Maxim number of waves */    otherwise the weight is truncated).
 int jmin, jmax; /* min, max spacing between 2 waves */    Modification of warning when the covariates values are not 0 or
 int mle, weightopt;    1.
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Version 0.98g
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double jmean; /* Mean space between 2 waves */    Revision 1.122  2006/03/20 09:45:41  brouard
 double **oldm, **newm, **savm; /* Working pointers to matrices */    (Module): Weights can have a decimal point as for
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    English (a comma might work with a correct LC_NUMERIC environment,
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf;    otherwise the weight is truncated).
 FILE *ficgp, *fichtm,*ficresprob,*ficpop;    Modification of warning when the covariates values are not 0 or
 FILE *ficreseij;    1.
   char filerese[FILENAMELENGTH];    Version 0.98g
  FILE  *ficresvij;  
   char fileresv[FILENAMELENGTH];    Revision 1.121  2006/03/16 17:45:01  lievre
  FILE  *ficresvpl;    * imach.c (Module): Comments concerning covariates added
   char fileresvpl[FILENAMELENGTH];  
     * imach.c (Module): refinements in the computation of lli if
 #define NR_END 1    status=-2 in order to have more reliable computation if stepm is
 #define FREE_ARG char*    not 1 month. Version 0.98f
 #define FTOL 1.0e-10  
     Revision 1.120  2006/03/16 15:10:38  lievre
 #define NRANSI    (Module): refinements in the computation of lli if
 #define ITMAX 200    status=-2 in order to have more reliable computation if stepm is
     not 1 month. Version 0.98f
 #define TOL 2.0e-4  
     Revision 1.119  2006/03/15 17:42:26  brouard
 #define CGOLD 0.3819660    (Module): Bug if status = -2, the loglikelihood was
 #define ZEPS 1.0e-10    computed as likelihood omitting the logarithm. Version O.98e
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);  
     Revision 1.118  2006/03/14 18:20:07  brouard
 #define GOLD 1.618034    (Module): varevsij Comments added explaining the second
 #define GLIMIT 100.0    table of variances if popbased=1 .
 #define TINY 1.0e-20    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 static double maxarg1,maxarg2;    (Module): Version 0.98d
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.117  2006/03/14 17:16:22  brouard
      (Module): varevsij Comments added explaining the second
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    table of variances if popbased=1 .
 #define rint(a) floor(a+0.5)    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 static double sqrarg;    (Module): Version 0.98d
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.116  2006/03/06 10:29:27  brouard
     (Module): Variance-covariance wrong links and
 int imx;    varian-covariance of ej. is needed (Saito).
 int stepm;  
 /* Stepm, step in month: minimum step interpolation*/    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
 int m,nb;  
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    Revision 1.114  2006/02/26 12:57:58  brouard
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    (Module): Some improvements in processing parameter
 double **pmmij, ***probs, ***mobaverage;    filename with strsep.
 double dateintmean=0;  
     Revision 1.113  2006/02/24 14:20:24  brouard
 double *weight;    (Module): Memory leaks checks with valgrind and:
 int **s; /* Status */    datafile was not closed, some imatrix were not freed and on matrix
 double *agedc, **covar, idx;    allocation too.
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;  
     Revision 1.112  2006/01/30 09:55:26  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.111  2006/01/25 20:38:18  brouard
 /**************** split *************************/    (Module): Lots of cleaning and bugs added (Gompertz)
 static  int split( char *path, char *dirc, char *name )    (Module): Comments can be added in data file. Missing date values
 {    can be a simple dot '.'.
    char *s;                             /* pointer */  
    int  l1, l2;                         /* length counters */    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.109  2006/01/24 19:37:15  brouard
    s = strrchr( path, '\\' );           /* find last / */    (Module): Comments (lines starting with a #) are allowed in data.
    if ( s == NULL ) {                   /* no directory, so use current */  
 #if     defined(__bsd__)                /* get current working directory */    Revision 1.108  2006/01/19 18:05:42  lievre
       extern char       *getwd( );    Gnuplot problem appeared...
     To be fixed
       if ( getwd( dirc ) == NULL ) {  
 #else    Revision 1.107  2006/01/19 16:20:37  brouard
       extern char       *getcwd( );    Test existence of gnuplot in imach path
   
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    Revision 1.106  2006/01/19 13:24:36  brouard
 #endif    Some cleaning and links added in html output
          return( GLOCK_ERROR_GETCWD );  
       }    Revision 1.105  2006/01/05 20:23:19  lievre
       strcpy( name, path );             /* we've got it */    *** empty log message ***
    } else {                             /* strip direcotry from path */  
       s++;                              /* after this, the filename */    Revision 1.104  2005/09/30 16:11:43  lievre
       l2 = strlen( s );                 /* length of filename */    (Module): sump fixed, loop imx fixed, and simplifications.
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    (Module): If the status is missing at the last wave but we know
       strcpy( name, s );                /* save file name */    that the person is alive, then we can code his/her status as -2
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    (instead of missing=-1 in earlier versions) and his/her
       dirc[l1-l2] = 0;                  /* add zero */    contributions to the likelihood is 1 - Prob of dying from last
    }    health status (= 1-p13= p11+p12 in the easiest case of somebody in
    l1 = strlen( dirc );                 /* length of directory */    the healthy state at last known wave). Version is 0.98
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }  
    return( 0 );                         /* we're done */    Revision 1.103  2005/09/30 15:54:49  lievre
 }    (Module): sump fixed, loop imx fixed, and simplifications.
   
     Revision 1.102  2004/09/15 17:31:30  brouard
 /******************************************/    Add the possibility to read data file including tab characters.
   
 void replace(char *s, char*t)    Revision 1.101  2004/09/15 10:38:38  brouard
 {    Fix on curr_time
   int i;  
   int lg=20;    Revision 1.100  2004/07/12 18:29:06  brouard
   i=0;    Add version for Mac OS X. Just define UNIX in Makefile
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.99  2004/06/05 08:57:40  brouard
     (s[i] = t[i]);    *** empty log message ***
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.98  2004/05/16 15:05:56  brouard
 }    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 int nbocc(char *s, char occ)    state at each age, but using a Gompertz model: log u =a + b*age .
 {    This is the basic analysis of mortality and should be done before any
   int i,j=0;    other analysis, in order to test if the mortality estimated from the
   int lg=20;    cross-longitudinal survey is different from the mortality estimated
   i=0;    from other sources like vital statistic data.
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {    The same imach parameter file can be used but the option for mle should be -3.
   if  (s[i] == occ ) j++;  
   }    Agnès, who wrote this part of the code, tried to keep most of the
   return j;    former routines in order to include the new code within the former code.
 }  
     The output is very simple: only an estimate of the intercept and of
 void cutv(char *u,char *v, char*t, char occ)    the slope with 95% confident intervals.
 {  
   int i,lg,j,p=0;    Current limitations:
   i=0;    A) Even if you enter covariates, i.e. with the
   for(j=0; j<=strlen(t)-1; j++) {    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    B) There is no computation of Life Expectancy nor Life Table.
   }  
     Revision 1.97  2004/02/20 13:25:42  lievre
   lg=strlen(t);    Version 0.96d. Population forecasting command line is (temporarily)
   for(j=0; j<p; j++) {    suppressed.
     (u[j] = t[j]);  
   }    Revision 1.96  2003/07/15 15:38:55  brouard
      u[p]='\0';    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
     rewritten within the same printf. Workaround: many printfs.
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);    Revision 1.95  2003/07/08 07:54:34  brouard
   }    * imach.c (Repository):
 }    (Repository): Using imachwizard code to output a more meaningful covariance
     matrix (cov(a12,c31) instead of numbers.
 /********************** nrerror ********************/  
     Revision 1.94  2003/06/27 13:00:02  brouard
 void nrerror(char error_text[])    Just cleaning
 {  
   fprintf(stderr,"ERREUR ...\n");    Revision 1.93  2003/06/25 16:33:55  brouard
   fprintf(stderr,"%s\n",error_text);    (Module): On windows (cygwin) function asctime_r doesn't
   exit(1);    exist so I changed back to asctime which exists.
 }    (Module): Version 0.96b
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    Revision 1.92  2003/06/25 16:30:45  brouard
 {    (Module): On windows (cygwin) function asctime_r doesn't
   double *v;    exist so I changed back to asctime which exists.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Revision 1.91  2003/06/25 15:30:29  brouard
   return v-nl+NR_END;    * imach.c (Repository): Duplicated warning errors corrected.
 }    (Repository): Elapsed time after each iteration is now output. It
     helps to forecast when convergence will be reached. Elapsed time
 /************************ free vector ******************/    is stamped in powell.  We created a new html file for the graphs
 void free_vector(double*v, int nl, int nh)    concerning matrix of covariance. It has extension -cov.htm.
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.90  2003/06/24 12:34:15  brouard
 }    (Module): Some bugs corrected for windows. Also, when
     mle=-1 a template is output in file "or"mypar.txt with the design
 /************************ivector *******************************/    of the covariance matrix to be input.
 int *ivector(long nl,long nh)  
 {    Revision 1.89  2003/06/24 12:30:52  brouard
   int *v;    (Module): Some bugs corrected for windows. Also, when
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    mle=-1 a template is output in file "or"mypar.txt with the design
   if (!v) nrerror("allocation failure in ivector");    of the covariance matrix to be input.
   return v-nl+NR_END;  
 }    Revision 1.88  2003/06/23 17:54:56  brouard
     * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 /******************free ivector **************************/  
 void free_ivector(int *v, long nl, long nh)    Revision 1.87  2003/06/18 12:26:01  brouard
 {    Version 0.96
   free((FREE_ARG)(v+nl-NR_END));  
 }    Revision 1.86  2003/06/17 20:04:08  brouard
     (Module): Change position of html and gnuplot routines and added
 /******************* imatrix *******************************/    routine fileappend.
 int **imatrix(long nrl, long nrh, long ncl, long nch)  
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    Revision 1.85  2003/06/17 13:12:43  brouard
 {    * imach.c (Repository): Check when date of death was earlier that
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    current date of interview. It may happen when the death was just
   int **m;    prior to the death. In this case, dh was negative and likelihood
      was wrong (infinity). We still send an "Error" but patch by
   /* allocate pointers to rows */    assuming that the date of death was just one stepm after the
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    interview.
   if (!m) nrerror("allocation failure 1 in matrix()");    (Repository): Because some people have very long ID (first column)
   m += NR_END;    we changed int to long in num[] and we added a new lvector for
   m -= nrl;    memory allocation. But we also truncated to 8 characters (left
      truncation)
      (Repository): No more line truncation errors.
   /* allocate rows and set pointers to them */  
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    Revision 1.84  2003/06/13 21:44:43  brouard
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    * imach.c (Repository): Replace "freqsummary" at a correct
   m[nrl] += NR_END;    place. It differs from routine "prevalence" which may be called
   m[nrl] -= ncl;    many times. Probs is memory consuming and must be used with
      parcimony.
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
    
   /* return pointer to array of pointers to rows */    Revision 1.83  2003/06/10 13:39:11  lievre
   return m;    *** empty log message ***
 }  
     Revision 1.82  2003/06/05 15:57:20  brouard
 /****************** free_imatrix *************************/    Add log in  imach.c and  fullversion number is now printed.
 void free_imatrix(m,nrl,nrh,ncl,nch)  
       int **m;  */
       long nch,ncl,nrh,nrl;  /*
      /* free an int matrix allocated by imatrix() */     Interpolated Markov Chain
 {  
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    Short summary of the programme:
   free((FREE_ARG) (m+nrl-NR_END));    
 }    This program computes Healthy Life Expectancies from
     cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 /******************* matrix *******************************/    first survey ("cross") where individuals from different ages are
 double **matrix(long nrl, long nrh, long ncl, long nch)    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
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    second wave of interviews ("longitudinal") which measure each change
   double **m;    (if any) in individual health status.  Health expectancies are
     computed from the time spent in each health state according to a
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    model. More health states you consider, more time is necessary to reach the
   if (!m) nrerror("allocation failure 1 in matrix()");    Maximum Likelihood of the parameters involved in the model.  The
   m += NR_END;    simplest model is the multinomial logistic model where pij is the
   m -= nrl;    probability to be observed in state j at the second wave
     conditional to be observed in state i at the first wave. Therefore
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    'age' is age and 'sex' is a covariate. If you want to have a more
   m[nrl] += NR_END;    complex model than "constant and age", you should modify the program
   m[nrl] -= ncl;    where the markup *Covariates have to be included here again* invites
     you to do it.  More covariates you add, slower the
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    convergence.
   return m;  
 }    The advantage of this computer programme, compared to a simple
     multinomial logistic model, is clear when the delay between waves is not
 /*************************free matrix ************************/    identical for each individual. Also, if a individual missed an
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    intermediate interview, the information is lost, but taken into
 {    account using an interpolation or extrapolation.  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));    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
     split into an exact number (nh*stepm) of unobserved intermediate
 /******************* ma3x *******************************/    states. This elementary transition (by month, quarter,
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    semester or year) is modelled as a multinomial logistic.  The hPx
 {    matrix is simply the matrix product of nh*stepm elementary matrices
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    and the contribution of each individual to the likelihood is simply
   double ***m;    hPijx.
   
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Also this programme outputs the covariance matrix of the parameters but also
   if (!m) nrerror("allocation failure 1 in matrix()");    of the life expectancies. It also computes the period (stable) prevalence. 
   m += NR_END;    
   m -= nrl;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
              Institut national d'études démographiques, Paris.
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    This software have been partly granted by Euro-REVES, a concerted action
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    from the European Union.
   m[nrl] += NR_END;    It is copyrighted identically to a GNU software product, ie programme and
   m[nrl] -= ncl;    software can be distributed freely for non commercial use. Latest version
     can be accessed at http://euroreves.ined.fr/imach .
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
     Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   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++)    main
     m[nrl][j]=m[nrl][j-1]+nlay;    read parameterfile
      read datafile
   for (i=nrl+1; i<=nrh; i++) {    concatwav
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    freqsummary
     for (j=ncl+1; j<=nch; j++)    if (mle >= 1)
       m[i][j]=m[i][j-1]+nlay;      mlikeli
   }    print results files
   return m;    if mle==1 
 }       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 /*************************free ma3x ************************/        begin-prev-date,...
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    open gnuplot file
 {    open html file
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    period (stable) prevalence
   free((FREE_ARG)(m[nrl]+ncl-NR_END));     for age prevalim()
   free((FREE_ARG)(m+nrl-NR_END));    h Pij x
 }    variance of p varprob
     forecasting if prevfcast==1 prevforecast call prevalence()
 /***************** f1dim *************************/    health expectancies
 extern int ncom;    Variance-covariance of DFLE
 extern double *pcom,*xicom;    prevalence()
 extern double (*nrfunc)(double []);     movingaverage()
      varevsij() 
 double f1dim(double x)    if popbased==1 varevsij(,popbased)
 {    total life expectancies
   int j;    Variance of period (stable) prevalence
   double f;   end
   double *xt;  */
    
   xt=vector(1,ncom);  
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  
   f=(*nrfunc)(xt);   
   free_vector(xt,1,ncom);  #include <math.h>
   return f;  #include <stdio.h>
 }  #include <stdlib.h>
   #include <string.h>
 /*****************brent *************************/  #include <unistd.h>
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  
 {  #include <limits.h>
   int iter;  #include <sys/types.h>
   double a,b,d,etemp;  #include <sys/stat.h>
   double fu,fv,fw,fx;  #include <errno.h>
   double ftemp;  extern int errno;
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;  /* #include <sys/time.h> */
    #include <time.h>
   a=(ax < cx ? ax : cx);  #include "timeval.h"
   b=(ax > cx ? ax : cx);  
   x=w=v=bx;  #ifdef GSL
   fw=fv=fx=(*f)(x);  #include <gsl/gsl_errno.h>
   for (iter=1;iter<=ITMAX;iter++) {  #include <gsl/gsl_multimin.h>
     xm=0.5*(a+b);  #endif
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  /* #include <libintl.h> */
     printf(".");fflush(stdout);  /* #define _(String) gettext (String) */
 #ifdef DEBUG  
     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);  #define MAXLINE 256
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif  #define GNUPLOTPROGRAM "gnuplot"
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
       *xmin=x;  #define FILENAMELENGTH 132
       return fx;  
     }  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
     ftemp=fu;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
       q=(x-v)*(fx-fw);  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
       p=(x-v)*q-(x-w)*r;  
       q=2.0*(q-r);  #define NINTERVMAX 8
       if (q > 0.0) p = -p;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
       q=fabs(q);  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
       etemp=e;  #define NCOVMAX 20 /* Maximum number of covariates */
       e=d;  #define MAXN 20000
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  #define YEARM 12. /* Number of months per year */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define AGESUP 130
       else {  #define AGEBASE 40
         d=p/q;  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
         u=x+d;  #ifdef UNIX
         if (u-a < tol2 || b-u < tol2)  #define DIRSEPARATOR '/'
           d=SIGN(tol1,xm-x);  #define CHARSEPARATOR "/"
       }  #define ODIRSEPARATOR '\\'
     } else {  #else
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define DIRSEPARATOR '\\'
     }  #define CHARSEPARATOR "\\"
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  #define ODIRSEPARATOR '/'
     fu=(*f)(u);  #endif
     if (fu <= fx) {  
       if (u >= x) a=x; else b=x;  /* $Id$ */
       SHFT(v,w,x,u)  /* $State$ */
         SHFT(fv,fw,fx,fu)  
         } else {  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
           if (u < x) a=u; else b=u;  char fullversion[]="$Revision$ $Date$"; 
           if (fu <= fw || w == x) {  char strstart[80];
             v=w;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
             w=u;  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
             fv=fw;  int nvar=0, nforce=0; /* Number of variables, number of forces */
             fw=fu;  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
           } else if (fu <= fv || v == x || v == w) {  int npar=NPARMAX;
             v=u;  int nlstate=2; /* Number of live states */
             fv=fu;  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 popbased=0;
   }  
   nrerror("Too many iterations in brent");  int *wav; /* Number of waves for this individuual 0 is possible */
   *xmin=x;  int maxwav=0; /* Maxim number of waves */
   return fx;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
 }  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
   int gipmx=0, gsw=0; /* Global variables on the number of contributions 
 /****************** mnbrak ***********************/                     to the likelihood and the sum of weights (done by funcone)*/
   int mle=1, weightopt=0;
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
             double (*func)(double))  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
 {  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
   double ulim,u,r,q, dum;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   double fu;  double jmean=1; /* Mean space between 2 waves */
    double **oldm, **newm, **savm; /* Working pointers to matrices */
   *fa=(*func)(*ax);  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   *fb=(*func)(*bx);  /*FILE *fic ; */ /* Used in readdata only */
   if (*fb > *fa) {  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
     SHFT(dum,*ax,*bx,dum)  FILE *ficlog, *ficrespow;
       SHFT(dum,*fb,*fa,dum)  int globpr=0; /* Global variable for printing or not */
       }  double fretone; /* Only one call to likelihood */
   *cx=(*bx)+GOLD*(*bx-*ax);  long ipmx=0; /* Number of contributions */
   *fc=(*func)(*cx);  double sw; /* Sum of weights */
   while (*fb > *fc) {  char filerespow[FILENAMELENGTH];
     r=(*bx-*ax)*(*fb-*fc);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     q=(*bx-*cx)*(*fb-*fa);  FILE *ficresilk;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  FILE *ficresprobmorprev;
     ulim=(*bx)+GLIMIT*(*cx-*bx);  FILE *fichtm, *fichtmcov; /* Html File */
     if ((*bx-u)*(u-*cx) > 0.0) {  FILE *ficreseij;
       fu=(*func)(u);  char filerese[FILENAMELENGTH];
     } else if ((*cx-u)*(u-ulim) > 0.0) {  FILE *ficresstdeij;
       fu=(*func)(u);  char fileresstde[FILENAMELENGTH];
       if (fu < *fc) {  FILE *ficrescveij;
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  char filerescve[FILENAMELENGTH];
           SHFT(*fb,*fc,fu,(*func)(u))  FILE  *ficresvij;
           }  char fileresv[FILENAMELENGTH];
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  FILE  *ficresvpl;
       u=ulim;  char fileresvpl[FILENAMELENGTH];
       fu=(*func)(u);  char title[MAXLINE];
     } else {  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       u=(*cx)+GOLD*(*cx-*bx);  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
       fu=(*func)(u);  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
     }  char command[FILENAMELENGTH];
     SHFT(*ax,*bx,*cx,u)  int  outcmd=0;
       SHFT(*fa,*fb,*fc,fu)  
       }  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 }  
   char filelog[FILENAMELENGTH]; /* Log file */
 /*************** linmin ************************/  char filerest[FILENAMELENGTH];
   char fileregp[FILENAMELENGTH];
 int ncom;  char popfile[FILENAMELENGTH];
 double *pcom,*xicom;  
 double (*nrfunc)(double []);  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
    
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
 {  struct timezone tzp;
   double brent(double ax, double bx, double cx,  extern int gettimeofday();
                double (*f)(double), double tol, double *xmin);  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   double f1dim(double x);  long time_value;
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  extern long time();
               double *fc, double (*func)(double));  char strcurr[80], strfor[80];
   int j;  
   double xx,xmin,bx,ax;  char *endptr;
   double fx,fb,fa;  long lval;
    double dval;
   ncom=n;  
   pcom=vector(1,n);  #define NR_END 1
   xicom=vector(1,n);  #define FREE_ARG char*
   nrfunc=func;  #define FTOL 1.0e-10
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  #define NRANSI 
     xicom[j]=xi[j];  #define ITMAX 200 
   }  
   ax=0.0;  #define TOL 2.0e-4 
   xx=1.0;  
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  #define CGOLD 0.3819660 
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  #define ZEPS 1.0e-10 
 #ifdef DEBUG  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
 #endif  #define GOLD 1.618034 
   for (j=1;j<=n;j++) {  #define GLIMIT 100.0 
     xi[j] *= xmin;  #define TINY 1.0e-20 
     p[j] += xi[j];  
   }  static double maxarg1,maxarg2;
   free_vector(xicom,1,n);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   free_vector(pcom,1,n);  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 }    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 /*************** powell ************************/  #define rint(a) floor(a+0.5)
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  
             double (*func)(double []))  static double sqrarg;
 {  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   void linmin(double p[], double xi[], int n, double *fret,  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
               double (*func)(double []));  int agegomp= AGEGOMP;
   int i,ibig,j;  
   double del,t,*pt,*ptt,*xit;  int imx; 
   double fp,fptt;  int stepm=1;
   double *xits;  /* Stepm, step in month: minimum step interpolation*/
   pt=vector(1,n);  
   ptt=vector(1,n);  int estepm;
   xit=vector(1,n);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   xits=vector(1,n);  
   *fret=(*func)(p);  int m,nb;
   for (j=1;j<=n;j++) pt[j]=p[j];  long *num;
   for (*iter=1;;++(*iter)) {  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
     fp=(*fret);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
     ibig=0;  double **pmmij, ***probs;
     del=0.0;  double *ageexmed,*agecens;
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  double dateintmean=0;
     for (i=1;i<=n;i++)  
       printf(" %d %.12f",i, p[i]);  double *weight;
     printf("\n");  int **s; /* Status */
     for (i=1;i<=n;i++) {  double *agedc, **covar, idx;
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
       fptt=(*fret);  double *lsurv, *lpop, *tpop;
 #ifdef DEBUG  
       printf("fret=%lf \n",*fret);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 #endif  double ftolhess; /* Tolerance for computing hessian */
       printf("%d",i);fflush(stdout);  
       linmin(p,xit,n,fret,func);  /**************** split *************************/
       if (fabs(fptt-(*fret)) > del) {  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
         del=fabs(fptt-(*fret));  {
         ibig=i;    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       }       the name of the file (name), its extension only (ext) and its first part of the name (finame)
 #ifdef DEBUG    */ 
       printf("%d %.12e",i,(*fret));    char  *ss;                            /* pointer */
       for (j=1;j<=n;j++) {    int   l1, l2;                         /* length counters */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  
         printf(" x(%d)=%.12e",j,xit[j]);    l1 = strlen(path );                   /* length of path */
       }    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       for(j=1;j<=n;j++)    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
         printf(" p=%.12e",p[j]);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       printf("\n");      strcpy( name, path );               /* we got the fullname name because no directory */
 #endif      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {      /* get current working directory */
 #ifdef DEBUG      /*    extern  char* getcwd ( char *buf , int len);*/
       int k[2],l;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
       k[0]=1;        return( GLOCK_ERROR_GETCWD );
       k[1]=-1;      }
       printf("Max: %.12e",(*func)(p));      /* got dirc from getcwd*/
       for (j=1;j<=n;j++)      printf(" DIRC = %s \n",dirc);
         printf(" %.12e",p[j]);    } else {                              /* strip direcotry from path */
       printf("\n");      ss++;                               /* after this, the filename */
       for(l=0;l<=1;l++) {      l2 = strlen( ss );                  /* length of filename */
         for (j=1;j<=n;j++) {      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];      strcpy( name, ss );         /* save file name */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);      strncpy( dirc, path, l1 - l2 );     /* now the directory */
         }      dirc[l1-l2] = 0;                    /* add zero */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));      printf(" DIRC2 = %s \n",dirc);
       }    }
 #endif    /* We add a separator at the end of dirc if not exists */
     l1 = strlen( dirc );                  /* length of directory */
     if( dirc[l1-1] != DIRSEPARATOR ){
       free_vector(xit,1,n);      dirc[l1] =  DIRSEPARATOR;
       free_vector(xits,1,n);      dirc[l1+1] = 0; 
       free_vector(ptt,1,n);      printf(" DIRC3 = %s \n",dirc);
       free_vector(pt,1,n);    }
       return;    ss = strrchr( name, '.' );            /* find last / */
     }    if (ss >0){
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");      ss++;
     for (j=1;j<=n;j++) {      strcpy(ext,ss);                     /* save extension */
       ptt[j]=2.0*p[j]-pt[j];      l1= strlen( name);
       xit[j]=p[j]-pt[j];      l2= strlen(ss)+1;
       pt[j]=p[j];      strncpy( finame, name, l1-l2);
     }      finame[l1-l2]= 0;
     fptt=(*func)(ptt);    }
     if (fptt < fp) {  
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    return( 0 );                          /* we're done */
       if (t < 0.0) {  }
         linmin(p,xit,n,fret,func);  
         for (j=1;j<=n;j++) {  
           xi[j][ibig]=xi[j][n];  /******************************************/
           xi[j][n]=xit[j];  
         }  void replace_back_to_slash(char *s, char*t)
 #ifdef DEBUG  {
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    int i;
         for(j=1;j<=n;j++)    int lg=0;
           printf(" %.12e",xit[j]);    i=0;
         printf("\n");    lg=strlen(t);
 #endif    for(i=0; i<= lg; i++) {
       }      (s[i] = t[i]);
     }      if (t[i]== '\\') s[i]='/';
   }    }
 }  }
   
 /**** Prevalence limit ****************/  char *trimbb(char *out, char *in)
   { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)    char *s;
 {    s=out;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    while (*in != '\0'){
      matrix by transitions matrix until convergence is reached */      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
         in++;
   int i, ii,j,k;      }
   double min, max, maxmin, maxmax,sumnew=0.;      *out++ = *in++;
   double **matprod2();    }
   double **out, cov[NCOVMAX], **pmij();    *out='\0';
   double **newm;    return s;
   double agefin, delaymax=50 ; /* Max number of years to converge */  }
   
   for (ii=1;ii<=nlstate+ndeath;ii++)  char *cutv(char *blocc, char *alocc, char *in, char occ)
     for (j=1;j<=nlstate+ndeath;j++){  {
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
     }       and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
        gives blocc="abcdef2ghi" and alocc="j".
    cov[1]=1.;       If occ is not found blocc is null and alocc is equal to in. Returns alocc
      */
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    char *s, *t;
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    t=in;s=in;
     newm=savm;    while (*in != '\0'){
     /* Covariates have to be included here again */      while( *in == occ){
      cov[2]=agefin;        *blocc++ = *in++;
          s=in;
       for (k=1; k<=cptcovn;k++) {      }
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];      *blocc++ = *in++;
         /*printf("ij=%d Tvar[k]=%d nbcode=%d cov=%lf\n",ij, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k]);*/    }
       }    if (s == t) /* occ not found */
       for (k=1; k<=cptcovage;k++)      *(blocc-(in-s))='\0';
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    else
       for (k=1; k<=cptcovprod;k++)      *(blocc-(in-s)-1)='\0';
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    in=s;
     while ( *in != '\0'){
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/      *alocc++ = *in++;
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    }
   
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);    *alocc='\0';
     return s;
     savm=oldm;  }
     oldm=newm;  
     maxmax=0.;  int nbocc(char *s, char occ)
     for(j=1;j<=nlstate;j++){  {
       min=1.;    int i,j=0;
       max=0.;    int lg=20;
       for(i=1; i<=nlstate; i++) {    i=0;
         sumnew=0;    lg=strlen(s);
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    for(i=0; i<= lg; i++) {
         prlim[i][j]= newm[i][j]/(1-sumnew);    if  (s[i] == occ ) j++;
         max=FMAX(max,prlim[i][j]);    }
         min=FMIN(min,prlim[i][j]);    return j;
       }  }
       maxmin=max-min;  
       maxmax=FMAX(maxmax,maxmin);  /* void cutv(char *u,char *v, char*t, char occ) */
     }  /* { */
     if(maxmax < ftolpl){  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       return prlim;  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
     }  /*      gives u="abcdef2ghi" and v="j" *\/ */
   }  /*   int i,lg,j,p=0; */
 }  /*   i=0; */
   /*   lg=strlen(t); */
 /*************** transition probabilities ***************/  /*   for(j=0; j<=lg-1; j++) { */
   /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  /*   } */
 {  
   double s1, s2;  /*   for(j=0; j<p; j++) { */
   /*double t34;*/  /*     (u[j] = t[j]); */
   int i,j,j1, nc, ii, jj;  /*   } */
   /*      u[p]='\0'; */
     for(i=1; i<= nlstate; i++){  
     for(j=1; j<i;j++){  /*    for(j=0; j<= lg; j++) { */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
         /*s2 += param[i][j][nc]*cov[nc];*/  /*   } */
         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);*/  
       }  /********************** nrerror ********************/
       ps[i][j]=s2;  
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  void nrerror(char error_text[])
     }  {
     for(j=i+1; j<=nlstate+ndeath;j++){    fprintf(stderr,"ERREUR ...\n");
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    fprintf(stderr,"%s\n",error_text);
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];    exit(EXIT_FAILURE);
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  }
       }  /*********************** vector *******************/
       ps[i][j]=(s2);  double *vector(int nl, int nh)
     }  {
   }    double *v;
     /*ps[3][2]=1;*/    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     if (!v) nrerror("allocation failure in vector");
   for(i=1; i<= nlstate; i++){    return v-nl+NR_END;
      s1=0;  }
     for(j=1; j<i; j++)  
       s1+=exp(ps[i][j]);  /************************ free vector ******************/
     for(j=i+1; j<=nlstate+ndeath; j++)  void free_vector(double*v, int nl, int nh)
       s1+=exp(ps[i][j]);  {
     ps[i][i]=1./(s1+1.);    free((FREE_ARG)(v+nl-NR_END));
     for(j=1; j<i; j++)  }
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     for(j=i+1; j<=nlstate+ndeath; j++)  /************************ivector *******************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  int *ivector(long nl,long nh)
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  {
   } /* end i */    int *v;
     v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    if (!v) nrerror("allocation failure in ivector");
     for(jj=1; jj<= nlstate+ndeath; jj++){    return v-nl+NR_END;
       ps[ii][jj]=0;  }
       ps[ii][ii]=1;  
     }  /******************free ivector **************************/
   }  void free_ivector(int *v, long nl, long nh)
   {
     free((FREE_ARG)(v+nl-NR_END));
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
      printf("%lf ",ps[ii][jj]);  /************************lvector *******************************/
    }  long *lvector(long nl,long nh)
     printf("\n ");  {
     }    long *v;
     printf("\n ");printf("%lf ",cov[2]);*/    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
 /*    if (!v) nrerror("allocation failure in ivector");
   for(i=1; i<= npar; i++) printf("%f ",x[i]);    return v-nl+NR_END;
   goto end;*/  }
     return ps;  
 }  /******************free lvector **************************/
   void free_lvector(long *v, long nl, long nh)
 /**************** Product of 2 matrices ******************/  {
     free((FREE_ARG)(v+nl-NR_END));
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  }
 {  
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  /******************* imatrix *******************************/
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   /* in, b, out are matrice of pointers which should have been initialized       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
      before: only the contents of out is modified. The function returns  { 
      a pointer to pointers identical to out */    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   long i, j, k;    int **m; 
   for(i=nrl; i<= nrh; i++)    
     for(k=ncolol; k<=ncoloh; k++)    /* allocate pointers to rows */ 
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
         out[i][k] +=in[i][j]*b[j][k];    if (!m) nrerror("allocation failure 1 in matrix()"); 
     m += NR_END; 
   return out;    m -= nrl; 
 }    
     
     /* allocate rows and set pointers to them */ 
 /************* Higher Matrix Product ***************/    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    m[nrl] += NR_END; 
 {    m[nrl] -= ncl; 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    
      duration (i.e. until    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    /* return pointer to array of pointers to rows */ 
      (typically every 2 years instead of every month which is too big).    return m; 
      Model is determined by parameters x and covariates have to be  } 
      included manually here.  
   /****************** free_imatrix *************************/
      */  void free_imatrix(m,nrl,nrh,ncl,nch)
         int **m;
   int i, j, d, h, k;        long nch,ncl,nrh,nrl; 
   double **out, cov[NCOVMAX];       /* free an int matrix allocated by imatrix() */ 
   double **newm;  { 
     free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   /* Hstepm could be zero and should return the unit matrix */    free((FREE_ARG) (m+nrl-NR_END)); 
   for (i=1;i<=nlstate+ndeath;i++)  } 
     for (j=1;j<=nlstate+ndeath;j++){  
       oldm[i][j]=(i==j ? 1.0 : 0.0);  /******************* matrix *******************************/
       po[i][j][0]=(i==j ? 1.0 : 0.0);  double **matrix(long nrl, long nrh, long ncl, long nch)
     }  {
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   for(h=1; h <=nhstepm; h++){    double **m;
     for(d=1; d <=hstepm; d++){  
       newm=savm;    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       /* Covariates have to be included here again */    if (!m) nrerror("allocation failure 1 in matrix()");
       cov[1]=1.;    m += NR_END;
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    m -= nrl;
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];  
       for (k=1; k<=cptcovage;k++)    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for (k=1; k<=cptcovprod;k++)    m[nrl] += NR_END;
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    m[nrl] -= ncl;
   
     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    return m;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,     */
                    pmij(pmmij,cov,ncovmodel,x,nlstate));  }
       savm=oldm;  
       oldm=newm;  /*************************free matrix ************************/
     }  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
     for(i=1; i<=nlstate+ndeath; i++)  {
       for(j=1;j<=nlstate+ndeath;j++) {    free((FREE_ARG)(m[nrl]+ncl-NR_END));
         po[i][j][h]=newm[i][j];    free((FREE_ARG)(m+nrl-NR_END));
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  }
          */  
       }  /******************* ma3x *******************************/
   } /* end h */  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
   return po;  {
 }    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     double ***m;
   
 /*************** log-likelihood *************/    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
 double func( double *x)    if (!m) nrerror("allocation failure 1 in matrix()");
 {    m += NR_END;
   int i, ii, j, k, mi, d, kk;    m -= nrl;
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   double sw; /* Sum of weights */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double lli; /* Individual log likelihood */    m[nrl] += NR_END;
   long ipmx;    m[nrl] -= ncl;
   /*extern weight */  
   /* We are differentiating ll according to initial status */    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  
   /*for(i=1;i<imx;i++)    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     printf(" %d\n",s[4][i]);    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
   */    m[nrl][ncl] += NR_END;
   cov[1]=1.;    m[nrl][ncl] -= nll;
     for (j=ncl+1; j<=nch; j++) 
   for(k=1; k<=nlstate; k++) ll[k]=0.;      m[nrl][j]=m[nrl][j-1]+nlay;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    for (i=nrl+1; i<=nrh; i++) {
     for(mi=1; mi<= wav[i]-1; mi++){      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       for (ii=1;ii<=nlstate+ndeath;ii++)      for (j=ncl+1; j<=nch; j++) 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);        m[i][j]=m[i][j-1]+nlay;
       for(d=0; d<dh[mi][i]; d++){    }
         newm=savm;    return m; 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
         for (kk=1; kk<=cptcovage;kk++) {             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    */
         }  }
          
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  /*************************free ma3x ************************/
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
         savm=oldm;  {
         oldm=newm;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
            free((FREE_ARG)(m[nrl]+ncl-NR_END));
            free((FREE_ARG)(m+nrl-NR_END));
       } /* end mult */  }
        
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  /*************** function subdirf ***********/
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  char *subdirf(char fileres[])
       ipmx +=1;  {
       sw += weight[i];    /* Caution optionfilefiname is hidden */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;    strcpy(tmpout,optionfilefiname);
     } /* end of wave */    strcat(tmpout,"/"); /* Add to the right */
   } /* end of individual */    strcat(tmpout,fileres);
     return tmpout;
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  }
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  /*************** function subdirf2 ***********/
   return -l;  char *subdirf2(char fileres[], char *preop)
 }  {
     
     /* Caution optionfilefiname is hidden */
 /*********** Maximum Likelihood Estimation ***************/    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))    strcat(tmpout,preop);
 {    strcat(tmpout,fileres);
   int i,j, iter;    return tmpout;
   double **xi,*delti;  }
   double fret;  
   xi=matrix(1,npar,1,npar);  /*************** function subdirf3 ***********/
   for (i=1;i<=npar;i++)  char *subdirf3(char fileres[], char *preop, char *preop2)
     for (j=1;j<=npar;j++)  {
       xi[i][j]=(i==j ? 1.0 : 0.0);    
   printf("Powell\n");    /* Caution optionfilefiname is hidden */
   powell(p,xi,npar,ftol,&iter,&fret,func);    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    strcat(tmpout,preop);
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    strcat(tmpout,preop2);
     strcat(tmpout,fileres);
 }    return tmpout;
   }
 /**** Computes Hessian and covariance matrix ***/  
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  /***************** f1dim *************************/
 {  extern int ncom; 
   double  **a,**y,*x,pd;  extern double *pcom,*xicom;
   double **hess;  extern double (*nrfunc)(double []); 
   int i, j,jk;   
   int *indx;  double f1dim(double x) 
   { 
   double hessii(double p[], double delta, int theta, double delti[]);    int j; 
   double hessij(double p[], double delti[], int i, int j);    double f;
   void lubksb(double **a, int npar, int *indx, double b[]) ;    double *xt; 
   void ludcmp(double **a, int npar, int *indx, double *d) ;   
     xt=vector(1,ncom); 
   hess=matrix(1,npar,1,npar);    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     f=(*nrfunc)(xt); 
   printf("\nCalculation of the hessian matrix. Wait...\n");    free_vector(xt,1,ncom); 
   for (i=1;i<=npar;i++){    return f; 
     printf("%d",i);fflush(stdout);  } 
     hess[i][i]=hessii(p,ftolhess,i,delti);  
     /*printf(" %f ",p[i]);*/  /*****************brent *************************/
     /*printf(" %lf ",hess[i][i]);*/  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   }  { 
      int iter; 
   for (i=1;i<=npar;i++) {    double a,b,d,etemp;
     for (j=1;j<=npar;j++)  {    double fu,fv,fw,fx;
       if (j>i) {    double ftemp;
         printf(".%d%d",i,j);fflush(stdout);    double p,q,r,tol1,tol2,u,v,w,x,xm; 
         hess[i][j]=hessij(p,delti,i,j);    double e=0.0; 
         hess[j][i]=hess[i][j];       
         /*printf(" %lf ",hess[i][j]);*/    a=(ax < cx ? ax : cx); 
       }    b=(ax > cx ? ax : cx); 
     }    x=w=v=bx; 
   }    fw=fv=fx=(*f)(x); 
   printf("\n");    for (iter=1;iter<=ITMAX;iter++) { 
       xm=0.5*(a+b); 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
        /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
   a=matrix(1,npar,1,npar);      printf(".");fflush(stdout);
   y=matrix(1,npar,1,npar);      fprintf(ficlog,".");fflush(ficlog);
   x=vector(1,npar);  #ifdef DEBUG
   indx=ivector(1,npar);      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);
   for (i=1;i<=npar;i++)      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);
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   ludcmp(a,npar,indx,&pd);  #endif
       if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for (j=1;j<=npar;j++) {        *xmin=x; 
     for (i=1;i<=npar;i++) x[i]=0;        return fx; 
     x[j]=1;      } 
     lubksb(a,npar,indx,x);      ftemp=fu;
     for (i=1;i<=npar;i++){      if (fabs(e) > tol1) { 
       matcov[i][j]=x[i];        r=(x-w)*(fx-fv); 
     }        q=(x-v)*(fx-fw); 
   }        p=(x-v)*q-(x-w)*r; 
         q=2.0*(q-r); 
   printf("\n#Hessian matrix#\n");        if (q > 0.0) p = -p; 
   for (i=1;i<=npar;i++) {        q=fabs(q); 
     for (j=1;j<=npar;j++) {        etemp=e; 
       printf("%.3e ",hess[i][j]);        e=d; 
     }        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
     printf("\n");          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   }        else { 
           d=p/q; 
   /* Recompute Inverse */          u=x+d; 
   for (i=1;i<=npar;i++)          if (u-a < tol2 || b-u < tol2) 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];            d=SIGN(tol1,xm-x); 
   ludcmp(a,npar,indx,&pd);        } 
       } else { 
   /*  printf("\n#Hessian matrix recomputed#\n");        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
   for (j=1;j<=npar;j++) {      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     for (i=1;i<=npar;i++) x[i]=0;      fu=(*f)(u); 
     x[j]=1;      if (fu <= fx) { 
     lubksb(a,npar,indx,x);        if (u >= x) a=x; else b=x; 
     for (i=1;i<=npar;i++){        SHFT(v,w,x,u) 
       y[i][j]=x[i];          SHFT(fv,fw,fx,fu) 
       printf("%.3e ",y[i][j]);          } else { 
     }            if (u < x) a=u; else b=u; 
     printf("\n");            if (fu <= fw || w == x) { 
   }              v=w; 
   */              w=u; 
               fv=fw; 
   free_matrix(a,1,npar,1,npar);              fw=fu; 
   free_matrix(y,1,npar,1,npar);            } else if (fu <= fv || v == x || v == w) { 
   free_vector(x,1,npar);              v=u; 
   free_ivector(indx,1,npar);              fv=fu; 
   free_matrix(hess,1,npar,1,npar);            } 
           } 
     } 
 }    nrerror("Too many iterations in brent"); 
     *xmin=x; 
 /*************** hessian matrix ****************/    return fx; 
 double hessii( double x[], double delta, int theta, double delti[])  } 
 {  
   int i;  /****************** mnbrak ***********************/
   int l=1, lmax=20;  
   double k1,k2;  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   double p2[NPARMAX+1];              double (*func)(double)) 
   double res;  { 
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    double ulim,u,r,q, dum;
   double fx;    double fu; 
   int k=0,kmax=10;   
   double l1;    *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
   fx=func(x);    if (*fb > *fa) { 
   for (i=1;i<=npar;i++) p2[i]=x[i];      SHFT(dum,*ax,*bx,dum) 
   for(l=0 ; l <=lmax; l++){        SHFT(dum,*fb,*fa,dum) 
     l1=pow(10,l);        } 
     delts=delt;    *cx=(*bx)+GOLD*(*bx-*ax); 
     for(k=1 ; k <kmax; k=k+1){    *fc=(*func)(*cx); 
       delt = delta*(l1*k);    while (*fb > *fc) { 
       p2[theta]=x[theta] +delt;      r=(*bx-*ax)*(*fb-*fc); 
       k1=func(p2)-fx;      q=(*bx-*cx)*(*fb-*fa); 
       p2[theta]=x[theta]-delt;      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
       k2=func(p2)-fx;        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
       /*res= (k1-2.0*fx+k2)/delt/delt; */      ulim=(*bx)+GLIMIT*(*cx-*bx); 
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */      if ((*bx-u)*(u-*cx) > 0.0) { 
              fu=(*func)(u); 
 #ifdef DEBUG      } else if ((*cx-u)*(u-ulim) > 0.0) { 
       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);        fu=(*func)(u); 
 #endif        if (fu < *fc) { 
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){            SHFT(*fb,*fc,fu,(*func)(u)) 
         k=kmax;            } 
       }      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */        u=ulim; 
         k=kmax; l=lmax*10.;        fu=(*func)(u); 
       }      } else { 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){        u=(*cx)+GOLD*(*cx-*bx); 
         delts=delt;        fu=(*func)(u); 
       }      } 
     }      SHFT(*ax,*bx,*cx,u) 
   }        SHFT(*fa,*fb,*fc,fu) 
   delti[theta]=delts;        } 
   return res;  } 
    
 }  /*************** linmin ************************/
   
 double hessij( double x[], double delti[], int thetai,int thetaj)  int ncom; 
 {  double *pcom,*xicom;
   int i;  double (*nrfunc)(double []); 
   int l=1, l1, lmax=20;   
   double k1,k2,k3,k4,res,fx;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   double p2[NPARMAX+1];  { 
   int k;    double brent(double ax, double bx, double cx, 
                  double (*f)(double), double tol, double *xmin); 
   fx=func(x);    double f1dim(double x); 
   for (k=1; k<=2; k++) {    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
     for (i=1;i<=npar;i++) p2[i]=x[i];                double *fc, double (*func)(double)); 
     p2[thetai]=x[thetai]+delti[thetai]/k;    int j; 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    double xx,xmin,bx,ax; 
     k1=func(p2)-fx;    double fx,fb,fa;
     
     p2[thetai]=x[thetai]+delti[thetai]/k;    ncom=n; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    pcom=vector(1,n); 
     k2=func(p2)-fx;    xicom=vector(1,n); 
      nrfunc=func; 
     p2[thetai]=x[thetai]-delti[thetai]/k;    for (j=1;j<=n;j++) { 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      pcom[j]=p[j]; 
     k3=func(p2)-fx;      xicom[j]=xi[j]; 
      } 
     p2[thetai]=x[thetai]-delti[thetai]/k;    ax=0.0; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    xx=1.0; 
     k4=func(p2)-fx;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
 #ifdef DEBUG  #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);    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 #endif    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   }  #endif
   return res;    for (j=1;j<=n;j++) { 
 }      xi[j] *= xmin; 
       p[j] += xi[j]; 
 /************** Inverse of matrix **************/    } 
 void ludcmp(double **a, int n, int *indx, double *d)    free_vector(xicom,1,n); 
 {    free_vector(pcom,1,n); 
   int i,imax,j,k;  } 
   double big,dum,sum,temp;  
   double *vv;  char *asc_diff_time(long time_sec, char ascdiff[])
    {
   vv=vector(1,n);    long sec_left, days, hours, minutes;
   *d=1.0;    days = (time_sec) / (60*60*24);
   for (i=1;i<=n;i++) {    sec_left = (time_sec) % (60*60*24);
     big=0.0;    hours = (sec_left) / (60*60) ;
     for (j=1;j<=n;j++)    sec_left = (sec_left) %(60*60);
       if ((temp=fabs(a[i][j])) > big) big=temp;    minutes = (sec_left) /60;
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    sec_left = (sec_left) % (60);
     vv[i]=1.0/big;    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
   }    return ascdiff;
   for (j=1;j<=n;j++) {  }
     for (i=1;i<j;i++) {  
       sum=a[i][j];  /*************** powell ************************/
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       a[i][j]=sum;              double (*func)(double [])) 
     }  { 
     big=0.0;    void linmin(double p[], double xi[], int n, double *fret, 
     for (i=j;i<=n;i++) {                double (*func)(double [])); 
       sum=a[i][j];    int i,ibig,j; 
       for (k=1;k<j;k++)    double del,t,*pt,*ptt,*xit;
         sum -= a[i][k]*a[k][j];    double fp,fptt;
       a[i][j]=sum;    double *xits;
       if ( (dum=vv[i]*fabs(sum)) >= big) {    int niterf, itmp;
         big=dum;  
         imax=i;    pt=vector(1,n); 
       }    ptt=vector(1,n); 
     }    xit=vector(1,n); 
     if (j != imax) {    xits=vector(1,n); 
       for (k=1;k<=n;k++) {    *fret=(*func)(p); 
         dum=a[imax][k];    for (j=1;j<=n;j++) pt[j]=p[j]; 
         a[imax][k]=a[j][k];    for (*iter=1;;++(*iter)) { 
         a[j][k]=dum;      fp=(*fret); 
       }      ibig=0; 
       *d = -(*d);      del=0.0; 
       vv[imax]=vv[j];      last_time=curr_time;
     }      (void) gettimeofday(&curr_time,&tzp);
     indx[j]=imax;      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);
     if (a[j][j] == 0.0) a[j][j]=TINY;      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);
     if (j != n) {  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
       dum=1.0/(a[j][j]);     for (i=1;i<=n;i++) {
       for (i=j+1;i<=n;i++) a[i][j] *= dum;        printf(" %d %.12f",i, p[i]);
     }        fprintf(ficlog," %d %.12lf",i, p[i]);
   }        fprintf(ficrespow," %.12lf", p[i]);
   free_vector(vv,1,n);  /* Doesn't work */      }
 ;      printf("\n");
 }      fprintf(ficlog,"\n");
       fprintf(ficrespow,"\n");fflush(ficrespow);
 void lubksb(double **a, int n, int *indx, double b[])      if(*iter <=3){
 {        tm = *localtime(&curr_time.tv_sec);
   int i,ii=0,ip,j;        strcpy(strcurr,asctime(&tm));
   double sum;  /*       asctime_r(&tm,strcurr); */
          forecast_time=curr_time; 
   for (i=1;i<=n;i++) {        itmp = strlen(strcurr);
     ip=indx[i];        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
     sum=b[ip];          strcurr[itmp-1]='\0';
     b[ip]=b[i];        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     if (ii)        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        for(niterf=10;niterf<=30;niterf+=10){
     else if (sum) ii=i;          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     b[i]=sum;          tmf = *localtime(&forecast_time.tv_sec);
   }  /*      asctime_r(&tmf,strfor); */
   for (i=n;i>=1;i--) {          strcpy(strfor,asctime(&tmf));
     sum=b[i];          itmp = strlen(strfor);
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];          if(strfor[itmp-1]=='\n')
     b[i]=sum/a[i][i];          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);
 }          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);
         }
 /************ Frequencies ********************/      }
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2)      for (i=1;i<=n;i++) { 
 {  /* Some frequencies */        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
          fptt=(*fret); 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;  #ifdef DEBUG
   double ***freq; /* Frequencies */        printf("fret=%lf \n",*fret);
   double *pp;        fprintf(ficlog,"fret=%lf \n",*fret);
   double pos, k2, dateintsum=0,k2cpt=0;  #endif
   FILE *ficresp;        printf("%d",i);fflush(stdout);
   char fileresp[FILENAMELENGTH];        fprintf(ficlog,"%d",i);fflush(ficlog);
         linmin(p,xit,n,fret,func); 
   pp=vector(1,nlstate);        if (fabs(fptt-(*fret)) > del) { 
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          del=fabs(fptt-(*fret)); 
   strcpy(fileresp,"p");          ibig=i; 
   strcat(fileresp,fileres);        } 
   if((ficresp=fopen(fileresp,"w"))==NULL) {  #ifdef DEBUG
     printf("Problem with prevalence resultfile: %s\n", fileresp);        printf("%d %.12e",i,(*fret));
     exit(0);        fprintf(ficlog,"%d %.12e",i,(*fret));
   }        for (j=1;j<=n;j++) {
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   j1=0;          printf(" x(%d)=%.12e",j,xit[j]);
           fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
   j=cptcoveff;        }
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        for(j=1;j<=n;j++) {
           printf(" p=%.12e",p[j]);
   for(k1=1; k1<=j;k1++){          fprintf(ficlog," p=%.12e",p[j]);
    for(i1=1; i1<=ncodemax[k1];i1++){        }
        j1++;        printf("\n");
        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);        fprintf(ficlog,"\n");
          scanf("%d", i);*/  #endif
         for (i=-1; i<=nlstate+ndeath; i++)        } 
          for (jk=-1; jk<=nlstate+ndeath; jk++)        if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
            for(m=agemin; m <= agemax+3; m++)  #ifdef DEBUG
              freq[i][jk][m]=0;        int k[2],l;
         k[0]=1;
         dateintsum=0;        k[1]=-1;
         k2cpt=0;        printf("Max: %.12e",(*func)(p));
        for (i=1; i<=imx; i++) {        fprintf(ficlog,"Max: %.12e",(*func)(p));
          bool=1;        for (j=1;j<=n;j++) {
          if  (cptcovn>0) {          printf(" %.12e",p[j]);
            for (z1=1; z1<=cptcoveff; z1++)          fprintf(ficlog," %.12e",p[j]);
              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        }
                bool=0;        printf("\n");
          }        fprintf(ficlog,"\n");
          if (bool==1) {        for(l=0;l<=1;l++) {
            for(m=firstpass; m<=lastpass; m++){          for (j=1;j<=n;j++) {
              k2=anint[m][i]+(mint[m][i]/12.);            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
              if ((k2>=dateprev1) && (k2<=dateprev2)) {            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                if(agev[m][i]==0) agev[m][i]=agemax+1;            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                if(agev[m][i]==1) agev[m][i]=agemax+2;          }
                freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        }
                  dateintsum=dateintsum+k2;  #endif
                  k2cpt++;  
                }  
         free_vector(xit,1,n); 
              }        free_vector(xits,1,n); 
            }        free_vector(ptt,1,n); 
          }        free_vector(pt,1,n); 
        }        return; 
         if  (cptcovn>0) {      } 
          fprintf(ficresp, "\n#********** Variable ");      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);      for (j=1;j<=n;j++) { 
        fprintf(ficresp, "**********\n#");        ptt[j]=2.0*p[j]-pt[j]; 
         }        xit[j]=p[j]-pt[j]; 
        for(i=1; i<=nlstate;i++)        pt[j]=p[j]; 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);      } 
        fprintf(ficresp, "\n");      fptt=(*func)(ptt); 
              if (fptt < fp) { 
   for(i=(int)agemin; i <= (int)agemax+3; i++){        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     if(i==(int)agemax+3)        if (t < 0.0) { 
       printf("Total");          linmin(p,xit,n,fret,func); 
     else          for (j=1;j<=n;j++) { 
       printf("Age %d", i);            xi[j][ibig]=xi[j][n]; 
     for(jk=1; jk <=nlstate ; jk++){            xi[j][n]=xit[j]; 
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          }
         pp[jk] += freq[jk][m][i];  #ifdef DEBUG
     }          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     for(jk=1; jk <=nlstate ; jk++){          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       for(m=-1, pos=0; m <=0 ; m++)          for(j=1;j<=n;j++){
         pos += freq[jk][m][i];            printf(" %.12e",xit[j]);
       if(pp[jk]>=1.e-10)            fprintf(ficlog," %.12e",xit[j]);
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);          }
       else          printf("\n");
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          fprintf(ficlog,"\n");
     }  #endif
         }
      for(jk=1; jk <=nlstate ; jk++){      } 
       for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)    } 
         pp[jk] += freq[jk][m][i];  } 
      }  
   /**** Prevalence limit (stable or period prevalence)  ****************/
     for(jk=1,pos=0; jk <=nlstate ; jk++)  
       pos += pp[jk];  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
     for(jk=1; jk <=nlstate ; jk++){  {
       if(pos>=1.e-5)    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);       matrix by transitions matrix until convergence is reached */
       else  
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    int i, ii,j,k;
       if( i <= (int) agemax){    double min, max, maxmin, maxmax,sumnew=0.;
         if(pos>=1.e-5){    double **matprod2();
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    double **out, cov[NCOVMAX+1], **pmij();
           probs[i][jk][j1]= pp[jk]/pos;    double **newm;
           /*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 agefin, delaymax=50 ; /* Max number of years to converge */
         }  
       else    for (ii=1;ii<=nlstate+ndeath;ii++)
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      for (j=1;j<=nlstate+ndeath;j++){
       }        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }      }
     for(jk=-1; jk <=nlstate+ndeath; jk++)  
       for(m=-1; m <=nlstate+ndeath; m++)     cov[1]=1.;
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);   
     if(i <= (int) agemax)   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       fprintf(ficresp,"\n");    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     printf("\n");      newm=savm;
     }      /* Covariates have to be included here again */
     }      cov[2]=agefin;
  }      
   dateintmean=dateintsum/k2cpt;      for (k=1; k<=cptcovn;k++) {
          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   fclose(ficresp);        /*        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]]);*/
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      }
   free_vector(pp,1,nlstate);      for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
       for (k=1; k<=cptcovprod;k++)
   /* End of Freq */        cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
 }      
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
 /************ Prevalence ********************/      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
 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)      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
 {  /* Some frequencies */      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
        
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      savm=oldm;
   double ***freq; /* Frequencies */      oldm=newm;
   double *pp;      maxmax=0.;
   double pos, k2;      for(j=1;j<=nlstate;j++){
         min=1.;
   pp=vector(1,nlstate);        max=0.;
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);        for(i=1; i<=nlstate; i++) {
            sumnew=0;
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   j1=0;          prlim[i][j]= newm[i][j]/(1-sumnew);
            max=FMAX(max,prlim[i][j]);
   j=cptcoveff;          min=FMIN(min,prlim[i][j]);
   if (cptcovn<1) {j=1;ncodemax[1]=1;}        }
          maxmin=max-min;
  for(k1=1; k1<=j;k1++){        maxmax=FMAX(maxmax,maxmin);
     for(i1=1; i1<=ncodemax[k1];i1++){      }
       j1++;      if(maxmax < ftolpl){
          return prlim;
       for (i=-1; i<=nlstate+ndeath; i++)        }
         for (jk=-1; jk<=nlstate+ndeath; jk++)      }
           for(m=agemin; m <= agemax+3; m++)  }
             freq[i][jk][m]=0;  
        /*************** transition probabilities ***************/ 
       for (i=1; i<=imx; i++) {  
         bool=1;  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
         if  (cptcovn>0) {  {
           for (z1=1; z1<=cptcoveff; z1++)    /* According to parameters values stored in x and the covariate's values stored in cov,
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])       computes the probability to be observed in state j being in state i by appying the
               bool=0;       model to the ncovmodel covariates (including constant and age).
         }       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
         if (bool==1) {       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
           for(m=firstpass; m<=lastpass; m++){       ncth covariate in the global vector x is given by the formula:
             k2=anint[m][i]+(mint[m][i]/12.);       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
             if ((k2>=dateprev1) && (k2<=dateprev2)) {       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
               if(agev[m][i]==0) agev[m][i]=agemax+1;       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
               if(agev[m][i]==1) agev[m][i]=agemax+2;       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
               freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];       Outputs ps[i][j] the probability to be observed in j being in j according to
               freq[s[m][i]][s[m+1][i]][(int)(agemax+3+1)] += weight[i];         the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
             }    */
           }    double s1, lnpijopii;
         }    /*double t34;*/
       }    int i,j,j1, nc, ii, jj;
        
         for(i=(int)agemin; i <= (int)agemax+3; i++){      for(i=1; i<= nlstate; i++){
           for(jk=1; jk <=nlstate ; jk++){        for(j=1; j<i;j++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
               pp[jk] += freq[jk][m][i];            /*lnpijopii += param[i][j][nc]*cov[nc];*/
           }            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
           for(jk=1; jk <=nlstate ; jk++){  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
             for(m=-1, pos=0; m <=0 ; m++)          }
             pos += freq[jk][m][i];          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
         }  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
                }
          for(jk=1; jk <=nlstate ; jk++){        for(j=i+1; j<=nlstate+ndeath;j++){
            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
              pp[jk] += freq[jk][m][i];            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
          }            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
            /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
          for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];          }
           ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
          for(jk=1; jk <=nlstate ; jk++){                  }
            if( i <= (int) agemax){      }
              if(pos>=1.e-5){      
                probs[i][jk][j1]= pp[jk]/pos;      for(i=1; i<= nlstate; i++){
              }        s1=0;
            }        for(j=1; j<i; j++){
          }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
                    /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }        }
     }        for(j=i+1; j<=nlstate+ndeath; j++){
   }          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
            /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
          }
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
   free_vector(pp,1,nlstate);        ps[i][i]=1./(s1+1.);
          /* Computing other pijs */
 }  /* End of Freq */        for(j=1; j<i; j++)
           ps[i][j]= exp(ps[i][j])*ps[i][i];
 /************* Waves Concatenation ***************/        for(j=i+1; j<=nlstate+ndeath; j++)
           ps[i][j]= exp(ps[i][j])*ps[i][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)        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
 {      } /* end i */
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.      
      Death is a valid wave (if date is known).      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        for(jj=1; jj<= nlstate+ndeath; jj++){
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          ps[ii][jj]=0;
      and mw[mi+1][i]. dh depends on stepm.          ps[ii][ii]=1;
      */        }
       }
   int i, mi, m;      
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  
      double sum=0., jmean=0.;*/  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   int j, k=0,jk, ju, jl;  /*         printf("ddd %lf ",ps[ii][jj]); */
   double sum=0.;  /*       } */
   jmin=1e+5;  /*       printf("\n "); */
   jmax=-1;  /*        } */
   jmean=0.;  /*        printf("\n ");printf("%lf ",cov[2]); */
   for(i=1; i<=imx; i++){         /*
     mi=0;        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     m=firstpass;        goto end;*/
     while(s[m][i] <= nlstate){      return ps;
       if(s[m][i]>=1)  }
         mw[++mi][i]=m;  
       if(m >=lastpass)  /**************** Product of 2 matrices ******************/
         break;  
       else  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
         m++;  {
     }/* end while */    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
     if (s[m][i] > nlstate){       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
       mi++;     /* Death is another wave */    /* in, b, out are matrice of pointers which should have been initialized 
       /* if(mi==0)  never been interviewed correctly before death */       before: only the contents of out is modified. The function returns
          /* Only death is a correct wave */       a pointer to pointers identical to out */
       mw[mi][i]=m;    long i, j, k;
     }    for(i=nrl; i<= nrh; i++)
       for(k=ncolol; k<=ncoloh; k++)
     wav[i]=mi;        for(j=ncl,out[i][k]=0.; j<=nch; j++)
     if(mi==0)          out[i][k] +=in[i][j]*b[j][k];
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);  
   }    return out;
   }
   for(i=1; i<=imx; i++){  
     for(mi=1; mi<wav[i];mi++){  
       if (stepm <=0)  /************* Higher Matrix Product ***************/
         dh[mi][i]=1;  
       else{  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
         if (s[mw[mi+1][i]][i] > nlstate) {  {
           if (agedc[i] < 2*AGESUP) {    /* Computes the transition matrix starting at age 'age' over 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);       'nhstepm*hstepm*stepm' months (i.e. until
           if(j==0) j=1;  /* Survives at least one month after exam */       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
           k=k+1;       nhstepm*hstepm matrices. 
           if (j >= jmax) jmax=j;       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
           if (j <= jmin) jmin=j;       (typically every 2 years instead of every month which is too big 
           sum=sum+j;       for the memory).
           /* if (j<10) printf("j=%d num=%d ",j,i); */       Model is determined by parameters x and covariates have to be 
           }       included manually here. 
         }  
         else{       */
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  
           k=k+1;    int i, j, d, h, k;
           if (j >= jmax) jmax=j;    double **out, cov[NCOVMAX+1];
           else if (j <= jmin)jmin=j;    double **newm;
           /*   if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */  
           sum=sum+j;    /* Hstepm could be zero and should return the unit matrix */
         }    for (i=1;i<=nlstate+ndeath;i++)
         jk= j/stepm;      for (j=1;j<=nlstate+ndeath;j++){
         jl= j -jk*stepm;        oldm[i][j]=(i==j ? 1.0 : 0.0);
         ju= j -(jk+1)*stepm;        po[i][j][0]=(i==j ? 1.0 : 0.0);
         if(jl <= -ju)      }
           dh[mi][i]=jk;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
         else    for(h=1; h <=nhstepm; h++){
           dh[mi][i]=jk+1;      for(d=1; d <=hstepm; d++){
         if(dh[mi][i]==0)        newm=savm;
           dh[mi][i]=1; /* At least one step */        /* Covariates have to be included here again */
       }        cov[1]=1.;
     }        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   }        for (k=1; k<=cptcovn;k++) 
   jmean=sum/k;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);        for (k=1; k<=cptcovage;k++)
  }          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
 /*********** Tricode ****************************/        for (k=1; k<=cptcovprod;k++)
 void tricode(int *Tvar, int **nbcode, int imx)          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
 {  
   int Ndum[20],ij=1, k, j, i;  
   int cptcode=0;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   cptcoveff=0;        /*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, 
   for (k=0; k<19; k++) Ndum[k]=0;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   for (k=1; k<=7; k++) ncodemax[k]=0;        savm=oldm;
         oldm=newm;
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {      }
     for (i=1; i<=imx; i++) {      for(i=1; i<=nlstate+ndeath; i++)
       ij=(int)(covar[Tvar[j]][i]);        for(j=1;j<=nlstate+ndeath;j++) {
       Ndum[ij]++;          po[i][j][h]=newm[i][j];
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
       if (ij > cptcode) cptcode=ij;        }
     }      /*printf("h=%d ",h);*/
     } /* end h */
     for (i=0; i<=cptcode; i++) {  /*     printf("\n H=%d \n",h); */
       if(Ndum[i]!=0) ncodemax[j]++;    return po;
     }  }
     ij=1;  
   
   /*************** log-likelihood *************/
     for (i=1; i<=ncodemax[j]; i++) {  double func( double *x)
       for (k=0; k<=19; k++) {  {
         if (Ndum[k] != 0) {    int i, ii, j, k, mi, d, kk;
           nbcode[Tvar[j]][ij]=k;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
           ij++;    double **out;
         }    double sw; /* Sum of weights */
         if (ij > ncodemax[j]) break;    double lli; /* Individual log likelihood */
       }      int s1, s2;
     }    double bbh, survp;
   }      long ipmx;
     /*extern weight */
  for (k=0; k<19; k++) Ndum[k]=0;    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
  for (i=1; i<=ncovmodel-2; i++) {    /*for(i=1;i<imx;i++) 
       ij=Tvar[i];      printf(" %d\n",s[4][i]);
       Ndum[ij]++;    */
     }    cov[1]=1.;
   
  ij=1;    for(k=1; k<=nlstate; k++) ll[k]=0.;
  for (i=1; i<=10; i++) {  
    if((Ndum[i]!=0) && (i<=ncov)){    if(mle==1){
      Tvaraff[ij]=i;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      ij++;        /* Computes the values of the ncovmodel covariates of the model
    }           depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
  }           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
             to be observed in j being in i according to the model.
     cptcoveff=ij-1;         */
 }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
 /*********** Health Expectancies ****************/           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
            has been calculated etc */
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)        for(mi=1; mi<= wav[i]-1; mi++){
 {          for (ii=1;ii<=nlstate+ndeath;ii++)
   /* Health expectancies */            for (j=1;j<=nlstate+ndeath;j++){
   int i, j, nhstepm, hstepm, h;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   double age, agelim,hf;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double ***p3mat;            }
            for(d=0; d<dh[mi][i]; d++){
   fprintf(ficreseij,"# Health expectancies\n");            newm=savm;
   fprintf(ficreseij,"# Age");            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   for(i=1; i<=nlstate;i++)            for (kk=1; kk<=cptcovage;kk++) {
     for(j=1; j<=nlstate;j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
       fprintf(ficreseij," %1d-%1d",i,j);            }
   fprintf(ficreseij,"\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   hstepm=1*YEARM; /*  Every j years of age (in month) */            savm=oldm;
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            oldm=newm;
           } /* end mult */
   agelim=AGESUP;        
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
     /* nhstepm age range expressed in number of stepm */          /* But now since version 0.9 we anticipate for bias at large stepm.
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     /* Typically if 20 years = 20*12/6=40 stepm */           * (in months) between two waves is not a multiple of stepm, we rounded to 
     if (stepm >= YEARM) hstepm=1;           * the nearest (and in case of equal distance, to the lowest) interval but now
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */           * we keep into memory the bias bh[mi][i] and also the previous matrix product
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
     /* Computed by stepm unit matrices, product of hstepm matrices, stored           * probability in order to take into account the bias as a fraction of the way
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);             * -stepm/2 to stepm/2 .
            * For stepm=1 the results are the same as for previous versions of Imach.
            * For stepm > 1 the results are less biased than in previous versions. 
     for(i=1; i<=nlstate;i++)           */
       for(j=1; j<=nlstate;j++)          s1=s[mw[mi][i]][i];
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){          s2=s[mw[mi+1][i]][i];
           eij[i][j][(int)age] +=p3mat[i][j][h];          bbh=(double)bh[mi][i]/(double)stepm; 
         }          /* bias bh is positive if real duration
               * is higher than the multiple of stepm and negative otherwise.
     hf=1;           */
     if (stepm >= YEARM) hf=stepm/YEARM;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     fprintf(ficreseij,"%.0f",age );          if( s2 > nlstate){ 
     for(i=1; i<=nlstate;i++)            /* i.e. if s2 is a death state and if the date of death is known 
       for(j=1; j<=nlstate;j++){               then the contribution to the likelihood is the probability to 
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);               die between last step unit time and current  step unit time, 
       }               which is also equal to probability to die before dh 
     fprintf(ficreseij,"\n");               minus probability to die before dh-stepm . 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);               In version up to 0.92 likelihood was computed
   }          as if date of death was unknown. Death was treated as any other
 }          health state: the date of the interview describes the actual state
           and not the date of a change in health state. The former idea was
 /************ Variance ******************/          to consider that at each interview the state was recorded
 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)          (healthy, disable or death) and IMaCh was corrected; but when we
 {          introduced the exact date of death then we should have modified
   /* Variance of health expectancies */          the contribution of an exact death to the likelihood. This new
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          contribution is smaller and very dependent of the step unit
   double **newm;          stepm. It is no more the probability to die between last interview
   double **dnewm,**doldm;          and month of death but the probability to survive from last
   int i, j, nhstepm, hstepm, h;          interview up to one month before death multiplied by the
   int k, cptcode;          probability to die within a month. Thanks to Chris
   double *xp;          Jackson for correcting this bug.  Former versions increased
   double **gp, **gm;          mortality artificially. The bad side is that we add another loop
   double ***gradg, ***trgradg;          which slows down the processing. The difference can be up to 10%
   double ***p3mat;          lower mortality.
   double age,agelim;            */
   int theta;            lli=log(out[s1][s2] - savm[s1][s2]);
   
    fprintf(ficresvij,"# Covariances of life expectancies\n");  
   fprintf(ficresvij,"# Age");          } else if  (s2==-2) {
   for(i=1; i<=nlstate;i++)            for (j=1,survp=0. ; j<=nlstate; j++) 
     for(j=1; j<=nlstate;j++)              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);            /*survp += out[s1][j]; */
   fprintf(ficresvij,"\n");            lli= log(survp);
           }
   xp=vector(1,npar);          
   dnewm=matrix(1,nlstate,1,npar);          else if  (s2==-4) { 
   doldm=matrix(1,nlstate,1,nlstate);            for (j=3,survp=0. ; j<=nlstate; j++)  
                survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   hstepm=1*YEARM; /* Every year of age */            lli= log(survp); 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          } 
   agelim = AGESUP;  
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          else if  (s2==-5) { 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */            for (j=1,survp=0. ; j<=2; j++)  
     if (stepm >= YEARM) hstepm=1;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            lli= log(survp); 
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          } 
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);          
     gp=matrix(0,nhstepm,1,nlstate);          else{
     gm=matrix(0,nhstepm,1,nlstate);            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
             /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
     for(theta=1; theta <=npar; theta++){          } 
       for(i=1; i<=npar; i++){ /* Computes gradient */          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          /*if(lli ==000.0)*/
       }          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);            ipmx +=1;
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       if (popbased==1) {        } /* end of wave */
         for(i=1; i<=nlstate;i++)      } /* end of individual */
           prlim[i][i]=probs[(int)age][i][ij];    }  else if(mle==2){
       }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
              for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(j=1; j<= nlstate; j++){        for(mi=1; mi<= wav[i]-1; mi++){
         for(h=0; h<=nhstepm; h++){          for (ii=1;ii<=nlstate+ndeath;ii++)
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)            for (j=1;j<=nlstate+ndeath;j++){
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       }            }
              for(d=0; d<=dh[mi][i]; d++){
       for(i=1; i<=npar; i++) /* Computes gradient */            newm=savm;
         xp[i] = x[i] - (i==theta ?delti[theta]:0);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              for (kk=1; kk<=cptcovage;kk++) {
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
             }
       if (popbased==1) {            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));
           prlim[i][i]=probs[(int)age][i][ij];            savm=oldm;
       }            oldm=newm;
           } /* end mult */
       for(j=1; j<= nlstate; j++){        
         for(h=0; h<=nhstepm; h++){          s1=s[mw[mi][i]][i];
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)          s2=s[mw[mi+1][i]][i];
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];          bbh=(double)bh[mi][i]/(double)stepm; 
         }          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       }          ipmx +=1;
           sw += weight[i];
       for(j=1; j<= nlstate; j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         for(h=0; h<=nhstepm; h++){        } /* end of wave */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      } /* end of individual */
         }    }  else if(mle==3){  /* exponential inter-extrapolation */
     } /* End theta */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
     for(h=0; h<=nhstepm; h++)            for (j=1;j<=nlstate+ndeath;j++){
       for(j=1; j<=nlstate;j++)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for(theta=1; theta <=npar; theta++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           trgradg[h][j][theta]=gradg[h][theta][j];            }
           for(d=0; d<dh[mi][i]; d++){
     for(i=1;i<=nlstate;i++)            newm=savm;
       for(j=1;j<=nlstate;j++)            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         vareij[i][j][(int)age] =0.;            for (kk=1; kk<=cptcovage;kk++) {
     for(h=0;h<=nhstepm;h++){              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for(k=0;k<=nhstepm;k++){            }
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);                         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;
             vareij[i][j][(int)age] += doldm[i][j];          } /* end mult */
       }        
     }          s1=s[mw[mi][i]][i];
     h=1;          s2=s[mw[mi+1][i]][i];
     if (stepm >= YEARM) h=stepm/YEARM;          bbh=(double)bh[mi][i]/(double)stepm; 
     fprintf(ficresvij,"%.0f ",age );          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 */
     for(i=1; i<=nlstate;i++)          ipmx +=1;
       for(j=1; j<=nlstate;j++){          sw += weight[i];
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        } /* end of wave */
     fprintf(ficresvij,"\n");      } /* end of individual */
     free_matrix(gp,0,nhstepm,1,nlstate);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     free_matrix(gm,0,nhstepm,1,nlstate);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        for(mi=1; mi<= wav[i]-1; mi++){
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (ii=1;ii<=nlstate+ndeath;ii++)
   } /* End age */            for (j=1;j<=nlstate+ndeath;j++){
                oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_vector(xp,1,npar);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   free_matrix(doldm,1,nlstate,1,npar);            }
   free_matrix(dnewm,1,nlstate,1,nlstate);          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
 }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             for (kk=1; kk<=cptcovage;kk++) {
 /************ Variance of prevlim ******************/              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)            }
 {          
   /* Variance of prevalence limit */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double **newm;            savm=oldm;
   double **dnewm,**doldm;            oldm=newm;
   int i, j, nhstepm, hstepm;          } /* end mult */
   int k, cptcode;        
   double *xp;          s1=s[mw[mi][i]][i];
   double *gp, *gm;          s2=s[mw[mi+1][i]][i];
   double **gradg, **trgradg;          if( s2 > nlstate){ 
   double age,agelim;            lli=log(out[s1][s2] - savm[s1][s2]);
   int theta;          }else{
                lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");          }
   fprintf(ficresvpl,"# Age");          ipmx +=1;
   for(i=1; i<=nlstate;i++)          sw += weight[i];
       fprintf(ficresvpl," %1d-%1d",i,i);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   fprintf(ficresvpl,"\n");  /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         } /* end of wave */
   xp=vector(1,npar);      } /* end of individual */
   dnewm=matrix(1,nlstate,1,npar);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   doldm=matrix(1,nlstate,1,nlstate);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   hstepm=1*YEARM; /* Every year of age */        for(mi=1; mi<= wav[i]-1; mi++){
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */          for (ii=1;ii<=nlstate+ndeath;ii++)
   agelim = AGESUP;            for (j=1;j<=nlstate+ndeath;j++){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     if (stepm >= YEARM) hstepm=1;            }
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          for(d=0; d<dh[mi][i]; d++){
     gradg=matrix(1,npar,1,nlstate);            newm=savm;
     gp=vector(1,nlstate);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     gm=vector(1,nlstate);            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     for(theta=1; theta <=npar; theta++){            }
       for(i=1; i<=npar; i++){ /* Computes gradient */          
         xp[i] = x[i] + (i==theta ?delti[theta]:0);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);            savm=oldm;
       for(i=1;i<=nlstate;i++)            oldm=newm;
         gp[i] = prlim[i][i];          } /* end mult */
            
       for(i=1; i<=npar; i++) /* Computes gradient */          s1=s[mw[mi][i]][i];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          s2=s[mw[mi+1][i]][i];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       for(i=1;i<=nlstate;i++)          ipmx +=1;
         gm[i] = prlim[i][i];          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       for(i=1;i<=nlstate;i++)          /*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]);*/
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        } /* end of wave */
     } /* End theta */      } /* end of individual */
     } /* End of if */
     trgradg =matrix(1,nlstate,1,npar);    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     for(j=1; j<=nlstate;j++)    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       for(theta=1; theta <=npar; theta++)    return -l;
         trgradg[j][theta]=gradg[theta][j];  }
   
     for(i=1;i<=nlstate;i++)  /*************** log-likelihood *************/
       varpl[i][(int)age] =0.;  double funcone( double *x)
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);  {
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    /* Same as likeli but slower because of a lot of printf and if */
     for(i=1;i<=nlstate;i++)    int i, ii, j, k, mi, d, kk;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     double **out;
     fprintf(ficresvpl,"%.0f ",age );    double lli; /* Individual log likelihood */
     for(i=1; i<=nlstate;i++)    double llt;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));    int s1, s2;
     fprintf(ficresvpl,"\n");    double bbh, survp;
     free_vector(gp,1,nlstate);    /*extern weight */
     free_vector(gm,1,nlstate);    /* We are differentiating ll according to initial status */
     free_matrix(gradg,1,npar,1,nlstate);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     free_matrix(trgradg,1,nlstate,1,npar);    /*for(i=1;i<imx;i++) 
   } /* End age */      printf(" %d\n",s[4][i]);
     */
   free_vector(xp,1,npar);    cov[1]=1.;
   free_matrix(doldm,1,nlstate,1,npar);  
   free_matrix(dnewm,1,nlstate,1,nlstate);    for(k=1; k<=nlstate; k++) ll[k]=0.;
   
 }    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
 /************ Variance of one-step probabilities  ******************/      for(mi=1; mi<= wav[i]-1; mi++){
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij)        for (ii=1;ii<=nlstate+ndeath;ii++)
 {          for (j=1;j<=nlstate+ndeath;j++){
   int i, j;            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   int k=0, cptcode;            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   double **dnewm,**doldm;          }
   double *xp;        for(d=0; d<dh[mi][i]; d++){
   double *gp, *gm;          newm=savm;
   double **gradg, **trgradg;          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double age,agelim, cov[NCOVMAX];          for (kk=1; kk<=cptcovage;kk++) {
   int theta;            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   char fileresprob[FILENAMELENGTH];          }
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   strcpy(fileresprob,"prob");                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   strcat(fileresprob,fileres);          savm=oldm;
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {          oldm=newm;
     printf("Problem with resultfile: %s\n", fileresprob);        } /* end mult */
   }        
   printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob);        s1=s[mw[mi][i]][i];
          s2=s[mw[mi+1][i]][i];
         bbh=(double)bh[mi][i]/(double)stepm; 
   xp=vector(1,npar);        /* bias is positive if real duration
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);         * is higher than the multiple of stepm and negative otherwise.
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));         */
          if( s2 > nlstate && (mle <5) ){  /* Jackson */
   cov[1]=1;          lli=log(out[s1][s2] - savm[s1][s2]);
   for (age=bage; age<=fage; age ++){        } else if  (s2==-2) {
     cov[2]=age;          for (j=1,survp=0. ; j<=nlstate; j++) 
     gradg=matrix(1,npar,1,9);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     trgradg=matrix(1,9,1,npar);          lli= log(survp);
     gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));        }else if (mle==1){
     gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
            } else if(mle==2){
     for(theta=1; theta <=npar; theta++){          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
       for(i=1; i<=npar; i++)        } else if(mle==3){  /* exponential inter-extrapolation */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          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 */
       pmij(pmmij,cov,ncovmodel,xp,nlstate);          lli=log(out[s1][s2]); /* Original formula */
            } else{  /* mle=0 back to 1 */
       k=0;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       for(i=1; i<= (nlstate+ndeath); i++){          /*lli=log(out[s1][s2]); */ /* Original formula */
         for(j=1; j<=(nlstate+ndeath);j++){        } /* End of if */
            k=k+1;        ipmx +=1;
           gp[k]=pmmij[i][j];        sw += weight[i];
         }        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
         if(globpr){
       for(i=1; i<=npar; i++)          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
         xp[i] = x[i] - (i==theta ?delti[theta]:0);   %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]);
       pmij(pmmij,cov,ncovmodel,xp,nlstate);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       k=0;            llt +=ll[k]*gipmx/gsw;
       for(i=1; i<=(nlstate+ndeath); i++){            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
         for(j=1; j<=(nlstate+ndeath);j++){          }
           k=k+1;          fprintf(ficresilk," %10.6f\n", -llt);
           gm[k]=pmmij[i][j];        }
         }      } /* end of wave */
       }    } /* end of individual */
          for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
        for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
            gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     }    if(globpr==0){ /* First time we count the contributions and weights */
       gipmx=ipmx;
      for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)      gsw=sw;
       for(theta=1; theta <=npar; theta++)    }
       trgradg[j][theta]=gradg[theta][j];    return -l;
    }
      matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);  
      matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);  
   /*************** function likelione ***********/
      pmij(pmmij,cov,ncovmodel,x,nlstate);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
   {
      k=0;    /* This routine should help understanding what is done with 
      for(i=1; i<=(nlstate+ndeath); i++){       the selection of individuals/waves and
        for(j=1; j<=(nlstate+ndeath);j++){       to check the exact contribution to the likelihood.
          k=k+1;       Plotting could be done.
          gm[k]=pmmij[i][j];     */
         }    int k;
      }  
          if(*globpri !=0){ /* Just counts and sums, no printings */
      /*printf("\n%d ",(int)age);      strcpy(fileresilk,"ilk"); 
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      strcat(fileresilk,fileres);
              if((ficresilk=fopen(fileresilk,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", fileresilk);
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
      }*/      }
       fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
   fprintf(ficresprob,"\n%d ",(int)age);      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
       /*  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 (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){      for(k=1; k<=nlstate; k++) 
     if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
 if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
   }    }
   
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));    *fretone=(*funcone)(p);
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));    if(*globpri !=0){
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      fclose(ficresilk);
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
 }      fflush(fichtm); 
  free_vector(xp,1,npar);    } 
 fclose(ficresprob);    return;
  exit(0);  }
 }  
   
 /***********************************************/  /*********** Maximum Likelihood Estimation ***************/
 /**************** Main Program *****************/  
 /***********************************************/  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
   {
 /*int main(int argc, char *argv[])*/    int i,j, iter;
 int main()    double **xi;
 {    double fret;
     double fretone; /* Only one call to likelihood */
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;    /*  char filerespow[FILENAMELENGTH];*/
   double agedeb, agefin,hf;    xi=matrix(1,npar,1,npar);
   double agemin=1.e20, agemax=-1.e20;    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++)
   double fret;        xi[i][j]=(i==j ? 1.0 : 0.0);
   double **xi,tmp,delta;    printf("Powell\n");  fprintf(ficlog,"Powell\n");
     strcpy(filerespow,"pow"); 
   double dum; /* Dummy variable */    strcat(filerespow,fileres);
   double ***p3mat;    if((ficrespow=fopen(filerespow,"w"))==NULL) {
   int *indx;      printf("Problem with resultfile: %s\n", filerespow);
   char line[MAXLINE], linepar[MAXLINE];      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
   char title[MAXLINE];    }
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];    fprintf(ficrespow,"# Powell\n# iter -2*LL");
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], fileresf[FILENAMELENGTH];    for (i=1;i<=nlstate;i++)
   char filerest[FILENAMELENGTH];      for(j=1;j<=nlstate+ndeath;j++)
   char fileregp[FILENAMELENGTH];        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
   char popfile[FILENAMELENGTH];    fprintf(ficrespow,"\n");
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];  
   int firstobs=1, lastobs=10;    powell(p,xi,npar,ftol,&iter,&fret,func);
   int sdeb, sfin; /* Status at beginning and end */  
   int c,  h , cpt,l;    free_matrix(xi,1,npar,1,npar);
   int ju,jl, mi;    fclose(ficrespow);
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   int mobilav=0,popforecast=0;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   int hstepm, nhstepm;  
   int *popage;/*boolprev=0 if date and zero if wave*/  }
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2;  
   /**** Computes Hessian and covariance matrix ***/
   double bage, fage, age, agelim, agebase;  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
   double ftolpl=FTOL;  {
   double **prlim;    double  **a,**y,*x,pd;
   double *severity;    double **hess;
   double ***param; /* Matrix of parameters */    int i, j,jk;
   double  *p;    int *indx;
   double **matcov; /* Matrix of covariance */  
   double ***delti3; /* Scale */    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   double *delti; /* Scale */    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   double ***eij, ***vareij;    void lubksb(double **a, int npar, int *indx, double b[]) ;
   double **varpl; /* Variances of prevalence limits by age */    void ludcmp(double **a, int npar, int *indx, double *d) ;
   double *epj, vepp;    double gompertz(double p[]);
   double kk1, kk2;    hess=matrix(1,npar,1,npar);
   double *popeffectif,*popcount;  
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,jprojmean,mprojmean,anprojmean, calagedate;    printf("\nCalculation of the hessian matrix. Wait...\n");
   double yp,yp1,yp2;    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     for (i=1;i<=npar;i++){
   char version[80]="Imach version 64b, May 2001, INED-EUROREVES ";      printf("%d",i);fflush(stdout);
   char *alph[]={"a","a","b","c","d","e"}, str[4];      fprintf(ficlog,"%d",i);fflush(ficlog);
      
        hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   char z[1]="c", occ;      
 #include <sys/time.h>      /*  printf(" %f ",p[i]);
 #include <time.h>          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    }
      
   /* long total_usecs;    for (i=1;i<=npar;i++) {
   struct timeval start_time, end_time;      for (j=1;j<=npar;j++)  {
          if (j>i) { 
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */          printf(".%d%d",i,j);fflush(stdout);
           fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
           hess[i][j]=hessij(p,delti,i,j,func,npar);
   printf("\nIMACH, Version 0.7");          
   printf("\nEnter the parameter file name: ");          hess[j][i]=hess[i][j];    
           /*printf(" %lf ",hess[i][j]);*/
 #ifdef windows        }
   scanf("%s",pathtot);      }
   getcwd(pathcd, size);    }
   /*cygwin_split_path(pathtot,path,optionfile);    printf("\n");
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    fprintf(ficlog,"\n");
   /* cutv(path,optionfile,pathtot,'\\');*/  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
 split(pathtot, path,optionfile);    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   chdir(path);    
   replace(pathc,path);    a=matrix(1,npar,1,npar);
 #endif    y=matrix(1,npar,1,npar);
 #ifdef unix    x=vector(1,npar);
   scanf("%s",optionfile);    indx=ivector(1,npar);
 #endif    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
 /*-------- arguments in the command line --------*/    ludcmp(a,npar,indx,&pd);
   
   strcpy(fileres,"r");    for (j=1;j<=npar;j++) {
   strcat(fileres, optionfile);      for (i=1;i<=npar;i++) x[i]=0;
       x[j]=1;
   /*---------arguments file --------*/      lubksb(a,npar,indx,x);
       for (i=1;i<=npar;i++){ 
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        matcov[i][j]=x[i];
     printf("Problem with optionfile %s\n",optionfile);      }
     goto end;    }
   }  
     printf("\n#Hessian matrix#\n");
   strcpy(filereso,"o");    fprintf(ficlog,"\n#Hessian matrix#\n");
   strcat(filereso,fileres);    for (i=1;i<=npar;i++) { 
   if((ficparo=fopen(filereso,"w"))==NULL) {      for (j=1;j<=npar;j++) { 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        printf("%.3e ",hess[i][j]);
   }        fprintf(ficlog,"%.3e ",hess[i][j]);
       }
   /* Reads comments: lines beginning with '#' */      printf("\n");
   while((c=getc(ficpar))=='#' && c!= EOF){      fprintf(ficlog,"\n");
     ungetc(c,ficpar);    }
     fgets(line, MAXLINE, ficpar);  
     puts(line);    /* Recompute Inverse */
     fputs(line,ficparo);    for (i=1;i<=npar;i++)
   }      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   ungetc(c,ficpar);    ludcmp(a,npar,indx,&pd);
   
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    /*  printf("\n#Hessian matrix recomputed#\n");
   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);    for (j=1;j<=npar;j++) {
 while((c=getc(ficpar))=='#' && c!= EOF){      for (i=1;i<=npar;i++) x[i]=0;
     ungetc(c,ficpar);      x[j]=1;
     fgets(line, MAXLINE, ficpar);      lubksb(a,npar,indx,x);
     puts(line);      for (i=1;i<=npar;i++){ 
     fputs(line,ficparo);        y[i][j]=x[i];
   }        printf("%.3e ",y[i][j]);
   ungetc(c,ficpar);        fprintf(ficlog,"%.3e ",y[i][j]);
        }
          printf("\n");
   covar=matrix(0,NCOVMAX,1,n);      fprintf(ficlog,"\n");
   cptcovn=0;    }
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    */
   
   ncovmodel=2+cptcovn;    free_matrix(a,1,npar,1,npar);
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */    free_matrix(y,1,npar,1,npar);
      free_vector(x,1,npar);
   /* Read guess parameters */    free_ivector(indx,1,npar);
   /* Reads comments: lines beginning with '#' */    free_matrix(hess,1,npar,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);  }
     puts(line);  
     fputs(line,ficparo);  /*************** hessian matrix ****************/
   }  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   ungetc(c,ficpar);  {
      int i;
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    int l=1, lmax=20;
     for(i=1; i <=nlstate; i++)    double k1,k2;
     for(j=1; j <=nlstate+ndeath-1; j++){    double p2[MAXPARM+1]; /* identical to x */
       fscanf(ficpar,"%1d%1d",&i1,&j1);    double res;
       fprintf(ficparo,"%1d%1d",i1,j1);    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
       printf("%1d%1d",i,j);    double fx;
       for(k=1; k<=ncovmodel;k++){    int k=0,kmax=10;
         fscanf(ficpar," %lf",&param[i][j][k]);    double l1;
         printf(" %lf",param[i][j][k]);  
         fprintf(ficparo," %lf",param[i][j][k]);    fx=func(x);
       }    for (i=1;i<=npar;i++) p2[i]=x[i];
       fscanf(ficpar,"\n");    for(l=0 ; l <=lmax; l++){
       printf("\n");      l1=pow(10,l);
       fprintf(ficparo,"\n");      delts=delt;
     }      for(k=1 ; k <kmax; k=k+1){
          delt = delta*(l1*k);
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;        p2[theta]=x[theta] +delt;
         k1=func(p2)-fx;
   p=param[1][1];        p2[theta]=x[theta]-delt;
          k2=func(p2)-fx;
   /* Reads comments: lines beginning with '#' */        /*res= (k1-2.0*fx+k2)/delt/delt; */
   while((c=getc(ficpar))=='#' && c!= EOF){        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
     ungetc(c,ficpar);        
     fgets(line, MAXLINE, ficpar);  #ifdef DEBUGHESS
     puts(line);        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);
     fputs(line,ficparo);        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
   }  #endif
   ungetc(c,ficpar);        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          k=kmax;
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */        }
   for(i=1; i <=nlstate; i++){        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     for(j=1; j <=nlstate+ndeath-1; j++){          k=kmax; l=lmax*10.;
       fscanf(ficpar,"%1d%1d",&i1,&j1);        }
       printf("%1d%1d",i,j);        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
       fprintf(ficparo,"%1d%1d",i1,j1);          delts=delt;
       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]);    delti[theta]=delts;
       }    return res; 
       fscanf(ficpar,"\n");    
       printf("\n");  }
       fprintf(ficparo,"\n");  
     }  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   }  {
   delti=delti3[1][1];    int i;
      int l=1, l1, lmax=20;
   /* Reads comments: lines beginning with '#' */    double k1,k2,k3,k4,res,fx;
   while((c=getc(ficpar))=='#' && c!= EOF){    double p2[MAXPARM+1];
     ungetc(c,ficpar);    int k;
     fgets(line, MAXLINE, ficpar);  
     puts(line);    fx=func(x);
     fputs(line,ficparo);    for (k=1; k<=2; k++) {
   }      for (i=1;i<=npar;i++) p2[i]=x[i];
   ungetc(c,ficpar);      p2[thetai]=x[thetai]+delti[thetai]/k;
        p2[thetaj]=x[thetaj]+delti[thetaj]/k;
   matcov=matrix(1,npar,1,npar);      k1=func(p2)-fx;
   for(i=1; i <=npar; i++){    
     fscanf(ficpar,"%s",&str);      p2[thetai]=x[thetai]+delti[thetai]/k;
     printf("%s",str);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     fprintf(ficparo,"%s",str);      k2=func(p2)-fx;
     for(j=1; j <=i; j++){    
       fscanf(ficpar," %le",&matcov[i][j]);      p2[thetai]=x[thetai]-delti[thetai]/k;
       printf(" %.5le",matcov[i][j]);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       fprintf(ficparo," %.5le",matcov[i][j]);      k3=func(p2)-fx;
     }    
     fscanf(ficpar,"\n");      p2[thetai]=x[thetai]-delti[thetai]/k;
     printf("\n");      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     fprintf(ficparo,"\n");      k4=func(p2)-fx;
   }      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   for(i=1; i <=npar; i++)  #ifdef DEBUG
     for(j=i+1;j<=npar;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);
       matcov[i][j]=matcov[j][i];      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
      #endif
   printf("\n");    }
     return res;
   }
     /*-------- data file ----------*/  
     if((ficres =fopen(fileres,"w"))==NULL) {  /************** Inverse of matrix **************/
       printf("Problem with resultfile: %s\n", fileres);goto end;  void ludcmp(double **a, int n, int *indx, double *d) 
     }  { 
     fprintf(ficres,"#%s\n",version);    int i,imax,j,k; 
        double big,dum,sum,temp; 
     if((fic=fopen(datafile,"r"))==NULL)    {    double *vv; 
       printf("Problem with datafile: %s\n", datafile);goto end;   
     }    vv=vector(1,n); 
     *d=1.0; 
     n= lastobs;    for (i=1;i<=n;i++) { 
     severity = vector(1,maxwav);      big=0.0; 
     outcome=imatrix(1,maxwav+1,1,n);      for (j=1;j<=n;j++) 
     num=ivector(1,n);        if ((temp=fabs(a[i][j])) > big) big=temp; 
     moisnais=vector(1,n);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     annais=vector(1,n);      vv[i]=1.0/big; 
     moisdc=vector(1,n);    } 
     andc=vector(1,n);    for (j=1;j<=n;j++) { 
     agedc=vector(1,n);      for (i=1;i<j;i++) { 
     cod=ivector(1,n);        sum=a[i][j]; 
     weight=vector(1,n);        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */        a[i][j]=sum; 
     mint=matrix(1,maxwav,1,n);      } 
     anint=matrix(1,maxwav,1,n);      big=0.0; 
     s=imatrix(1,maxwav+1,1,n);      for (i=j;i<=n;i++) { 
     adl=imatrix(1,maxwav+1,1,n);            sum=a[i][j]; 
     tab=ivector(1,NCOVMAX);        for (k=1;k<j;k++) 
     ncodemax=ivector(1,8);          sum -= a[i][k]*a[k][j]; 
         a[i][j]=sum; 
     i=1;        if ( (dum=vv[i]*fabs(sum)) >= big) { 
     while (fgets(line, MAXLINE, fic) != NULL)    {          big=dum; 
       if ((i >= firstobs) && (i <=lastobs)) {          imax=i; 
                } 
         for (j=maxwav;j>=1;j--){      } 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);      if (j != imax) { 
           strcpy(line,stra);        for (k=1;k<=n;k++) { 
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          dum=a[imax][k]; 
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          a[imax][k]=a[j][k]; 
         }          a[j][k]=dum; 
                } 
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);        *d = -(*d); 
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        vv[imax]=vv[j]; 
       } 
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);      indx[j]=imax; 
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      if (a[j][j] == 0.0) a[j][j]=TINY; 
       if (j != n) { 
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        dum=1.0/(a[j][j]); 
         for (j=ncov;j>=1;j--){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);      } 
         }    } 
         num[i]=atol(stra);    free_vector(vv,1,n);  /* Doesn't work */
          ;
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){  } 
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/  
   void lubksb(double **a, int n, int *indx, double b[]) 
         i=i+1;  { 
       }    int i,ii=0,ip,j; 
     }    double sum; 
     /* printf("ii=%d", ij);   
        scanf("%d",i);*/    for (i=1;i<=n;i++) { 
   imx=i-1; /* Number of individuals */      ip=indx[i]; 
       sum=b[ip]; 
   /* for (i=1; i<=imx; i++){      b[ip]=b[i]; 
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;      if (ii) 
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;      else if (sum) ii=i; 
     }      b[i]=sum; 
     } 
     for (i=1; i<=imx; i++)    for (i=n;i>=1;i--) { 
     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]));*/      sum=b[i]; 
       for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   /* Calculation of the number of parameter from char model*/      b[i]=sum/a[i][i]; 
   Tvar=ivector(1,15);    } 
   Tprod=ivector(1,15);  } 
   Tvaraff=ivector(1,15);  
   Tvard=imatrix(1,15,1,2);  void pstamp(FILE *fichier)
   Tage=ivector(1,15);        {
        fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   if (strlen(model) >1){  }
     j=0, j1=0, k1=1, k2=1;  
     j=nbocc(model,'+');  /************ Frequencies ********************/
     j1=nbocc(model,'*');  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[])
     cptcovn=j+1;  {  /* Some frequencies */
     cptcovprod=j1;    
        int i, m, jk, k1,i1, j1, bool, z1,j;
        int first;
     strcpy(modelsav,model);    double ***freq; /* Frequencies */
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    double *pp, **prop;
       printf("Error. Non available option model=%s ",model);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
       goto end;    char fileresp[FILENAMELENGTH];
     }    
        pp=vector(1,nlstate);
     for(i=(j+1); i>=1;i--){    prop=matrix(1,nlstate,iagemin,iagemax+3);
       cutv(stra,strb,modelsav,'+');    strcpy(fileresp,"p");
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    strcat(fileresp,fileres);
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/    if((ficresp=fopen(fileresp,"w"))==NULL) {
       /*scanf("%d",i);*/      printf("Problem with prevalence resultfile: %s\n", fileresp);
       if (strchr(strb,'*')) {      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
         cutv(strd,strc,strb,'*');      exit(0);
         if (strcmp(strc,"age")==0) {    }
           cptcovprod--;    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
           cutv(strb,stre,strd,'V');    j1=0;
           Tvar[i]=atoi(stre);    
           cptcovage++;    j=cptcoveff;
             Tage[cptcovage]=i;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
             /*printf("stre=%s ", stre);*/  
         }    first=1;
         else if (strcmp(strd,"age")==0) {  
           cptcovprod--;    for(k1=1; k1<=j;k1++){
           cutv(strb,stre,strc,'V');      for(i1=1; i1<=ncodemax[k1];i1++){
           Tvar[i]=atoi(stre);        j1++;
           cptcovage++;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           Tage[cptcovage]=i;          scanf("%d", i);*/
         }        for (i=-5; i<=nlstate+ndeath; i++)  
         else {          for (jk=-5; jk<=nlstate+ndeath; jk++)  
           cutv(strb,stre,strc,'V');            for(m=iagemin; m <= iagemax+3; m++)
           Tvar[i]=ncov+k1;              freq[i][jk][m]=0;
           cutv(strb,strc,strd,'V');  
           Tprod[k1]=i;      for (i=1; i<=nlstate; i++)  
           Tvard[k1][1]=atoi(strc);        for(m=iagemin; m <= iagemax+3; m++)
           Tvard[k1][2]=atoi(stre);          prop[i][m]=0;
           Tvar[cptcovn+k2]=Tvard[k1][1];        
           Tvar[cptcovn+k2+1]=Tvard[k1][2];        dateintsum=0;
           for (k=1; k<=lastobs;k++)        k2cpt=0;
             covar[ncov+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];        for (i=1; i<=imx; i++) {
           k1++;          bool=1;
           k2=k2+2;          if  (cptcovn>0) {
         }            for (z1=1; z1<=cptcoveff; z1++) 
       }              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
       else {                bool=0;
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          }
        /*  scanf("%d",i);*/          if (bool==1){
       cutv(strd,strc,strb,'V');            for(m=firstpass; m<=lastpass; m++){
       Tvar[i]=atoi(strc);              k2=anint[m][i]+(mint[m][i]/12.);
       }              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
       strcpy(modelsav,stra);                  if(agev[m][i]==0) agev[m][i]=iagemax+1;
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         scanf("%d",i);*/                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
     }                if (m<lastpass) {
 }                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                    freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
   /*printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);                }
   printf("cptcovprod=%d ", cptcovprod);                
   scanf("%d ",i);*/                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
     fclose(fic);                  dateintsum=dateintsum+k2;
                   k2cpt++;
     /*  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);         
         /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
    for (i=1; i<=imx; i++)        pstamp(ficresp);
      for(m=2; (m<= maxwav); m++)        if  (cptcovn>0) {
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){          fprintf(ficresp, "\n#********** Variable "); 
          anint[m][i]=9999;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
          s[m][i]=-1;          fprintf(ficresp, "**********\n#");
        }        }
            for(i=1; i<=nlstate;i++) 
     for (i=1; i<=imx; i++)  {          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);        fprintf(ficresp, "\n");
       for(m=1; (m<= maxwav); m++){        
         if(s[m][i] >0){        for(i=iagemin; i <= iagemax+3; i++){
           if (s[m][i] == nlstate+1) {          if(i==iagemax+3){
             if(agedc[i]>0)            fprintf(ficlog,"Total");
               if(moisdc[i]!=99 && andc[i]!=9999)          }else{
               agev[m][i]=agedc[i];            if(first==1){
             else {              first=0;
               if (andc[i]!=9999){              printf("See log file for details...\n");
               printf("Warning negative age at death: %d line:%d\n",num[i],i);            }
               agev[m][i]=-1;            fprintf(ficlog,"Age %d", i);
               }          }
             }          for(jk=1; jk <=nlstate ; jk++){
           }            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
           else if(s[m][i] !=9){ /* Should no more exist */              pp[jk] += freq[jk][m][i]; 
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);          }
             if(mint[m][i]==99 || anint[m][i]==9999)          for(jk=1; jk <=nlstate ; jk++){
               agev[m][i]=1;            for(m=-1, pos=0; m <=0 ; m++)
             else if(agev[m][i] <agemin){              pos += freq[jk][m][i];
               agemin=agev[m][i];            if(pp[jk]>=1.e-10){
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/              if(first==1){
             }                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             else if(agev[m][i] >agemax){              }
               agemax=agev[m][i];              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/            }else{
             }              if(first==1)
             /*agev[m][i]=anint[m][i]-annais[i];*/                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             /*   agev[m][i] = age[i]+2*m;*/              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
           }            }
           else { /* =9 */          }
             agev[m][i]=1;  
             s[m][i]=-1;          for(jk=1; jk <=nlstate ; jk++){
           }            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
         }              pp[jk] += freq[jk][m][i];
         else /*= 0 Unknown */          }       
           agev[m][i]=1;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
       }            pos += pp[jk];
                posprop += prop[jk][i];
     }          }
     for (i=1; i<=imx; i++)  {          for(jk=1; jk <=nlstate ; jk++){
       for(m=1; (m<= maxwav); m++){            if(pos>=1.e-5){
         if (s[m][i] > (nlstate+ndeath)) {              if(first==1)
           printf("Error: Wrong value in nlstate or ndeath\n");                  printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
           goto end;              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
         }            }else{
       }              if(first==1)
     }                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);            }
             if( i <= iagemax){
     free_vector(severity,1,maxwav);              if(pos>=1.e-5){
     free_imatrix(outcome,1,maxwav+1,1,n);                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
     free_vector(moisnais,1,n);                /*probs[i][jk][j1]= pp[jk]/pos;*/
     free_vector(annais,1,n);                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     /* free_matrix(mint,1,maxwav,1,n);              }
        free_matrix(anint,1,maxwav,1,n);*/              else
     free_vector(moisdc,1,n);                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
     free_vector(andc,1,n);            }
           }
              
     wav=ivector(1,imx);          for(jk=-1; jk <=nlstate+ndeath; jk++)
     dh=imatrix(1,lastpass-firstpass+1,1,imx);            for(m=-1; m <=nlstate+ndeath; m++)
     mw=imatrix(1,lastpass-firstpass+1,1,imx);              if(freq[jk][m][i] !=0 ) {
                  if(first==1)
     /* Concatenates waves */                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
           if(i <= iagemax)
       Tcode=ivector(1,100);            fprintf(ficresp,"\n");
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);          if(first==1)
       ncodemax[1]=1;            printf("Others in log...\n");
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);          fprintf(ficlog,"\n");
              }
    codtab=imatrix(1,100,1,10);      }
    h=0;    }
    m=pow(2,cptcoveff);    dateintmean=dateintsum/k2cpt; 
     
    for(k=1;k<=cptcoveff; k++){    fclose(ficresp);
      for(i=1; i <=(m/pow(2,k));i++){    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
        for(j=1; j <= ncodemax[k]; j++){    free_vector(pp,1,nlstate);
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
            h++;    /* End of Freq */
            if (h>m) h=1;codtab[h][k]=j;  }
          }  
        }  /************ Prevalence ********************/
      }  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
    }  {  
        /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
    /* Calculates basic frequencies. Computes observed prevalence at single age       in each health status at the date of interview (if between dateprev1 and dateprev2).
        and prints on file fileres'p'. */       We still use firstpass and lastpass as another selection.
     */
       
        int i, m, jk, k1, i1, j1, bool, z1,j;
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double ***freq; /* Frequencies */
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double *pp, **prop;
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double pos,posprop; 
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    double  y2; /* in fractional years */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    int iagemin, iagemax;
        
     /* For Powell, parameters are in a vector p[] starting at p[1]    iagemin= (int) agemin;
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */    iagemax= (int) agemax;
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */    /*pp=vector(1,nlstate);*/
     prop=matrix(1,nlstate,iagemin,iagemax+3); 
     if(mle==1){    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    j1=0;
     }    
        j=cptcoveff;
     /*--------- results files --------------*/    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);    
      for(k1=1; k1<=j;k1++){
       for(i1=1; i1<=ncodemax[k1];i1++){
    jk=1;        j1++;
    fprintf(ficres,"# Parameters\n");        
    printf("# Parameters\n");        for (i=1; i<=nlstate; i++)  
    for(i=1,jk=1; i <=nlstate; i++){          for(m=iagemin; m <= iagemax+3; m++)
      for(k=1; k <=(nlstate+ndeath); k++){            prop[i][m]=0.0;
        if (k != i)       
          {        for (i=1; i<=imx; i++) { /* Each individual */
            printf("%d%d ",i,k);          bool=1;
            fprintf(ficres,"%1d%1d ",i,k);          if  (cptcovn>0) {
            for(j=1; j <=ncovmodel; j++){            for (z1=1; z1<=cptcoveff; z1++) 
              printf("%f ",p[jk]);              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
              fprintf(ficres,"%f ",p[jk]);                bool=0;
              jk++;          } 
            }          if (bool==1) { 
            printf("\n");            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
            fprintf(ficres,"\n");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
          }              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
      }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
    }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
  if(mle==1){                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
     /* Computing hessian and covariance matrix */                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     ftolhess=ftol; /* Usually correct */                  /*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]]);*/
     hesscov(matcov, p, npar, delti, ftolhess, func);                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
  }                  prop[s[m][i]][iagemax+3] += weight[i]; 
     fprintf(ficres,"# Scales\n");                } 
     printf("# Scales\n");              }
      for(i=1,jk=1; i <=nlstate; i++){            } /* end selection of waves */
       for(j=1; j <=nlstate+ndeath; j++){          }
         if (j!=i) {        }
           fprintf(ficres,"%1d%1d",i,j);        for(i=iagemin; i <= iagemax+3; i++){  
           printf("%1d%1d",i,j);          
           for(k=1; k<=ncovmodel;k++){          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             printf(" %.5e",delti[jk]);            posprop += prop[jk][i]; 
             fprintf(ficres," %.5e",delti[jk]);          } 
             jk++;  
           }          for(jk=1; jk <=nlstate ; jk++){     
           printf("\n");            if( i <=  iagemax){ 
           fprintf(ficres,"\n");              if(posprop>=1.e-5){ 
         }                probs[i][jk][j1]= prop[jk][i]/posprop;
       }              } else
      }                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
                } 
     k=1;          }/* end jk */ 
     fprintf(ficres,"# Covariance\n");        }/* end i */ 
     printf("# Covariance\n");      } /* end i1 */
     for(i=1;i<=npar;i++){    } /* end k1 */
       /*  if (k>nlstate) k=1;    
       i1=(i-1)/(ncovmodel*nlstate)+1;    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    /*free_vector(pp,1,nlstate);*/
       printf("%s%d%d",alph[k],i1,tab[i]);*/    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
       fprintf(ficres,"%3d",i);  }  /* End of prevalence */
       printf("%3d",i);  
       for(j=1; j<=i;j++){  /************* Waves Concatenation ***************/
         fprintf(ficres," %.5e",matcov[i][j]);  
         printf(" %.5e",matcov[i][j]);  void  concatwav(int wav[], int **dh, int **bh,  int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
       }  {
       fprintf(ficres,"\n");    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
       printf("\n");       Death is a valid wave (if date is known).
       k++;       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
     }       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
           and mw[mi+1][i]. dh depends on stepm.
     while((c=getc(ficpar))=='#' && c!= EOF){       */
       ungetc(c,ficpar);  
       fgets(line, MAXLINE, ficpar);    int i, mi, m;
       puts(line);    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
       fputs(line,ficparo);       double sum=0., jmean=0.;*/
     }    int first;
     ungetc(c,ficpar);    int j, k=0,jk, ju, jl;
      double sum=0.;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    first=0;
        jmin=1e+5;
     if (fage <= 2) {    jmax=-1;
       bage = agemin;    jmean=0.;
       fage = agemax;    for(i=1; i<=imx; i++){
     }      mi=0;
       m=firstpass;
     fprintf(ficres,"# agemin agemax for life expectancy.\n");      while(s[m][i] <= nlstate){
         if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);          mw[++mi][i]=m;
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);        if(m >=lastpass)
            break;
     while((c=getc(ficpar))=='#' && c!= EOF){        else
     ungetc(c,ficpar);          m++;
     fgets(line, MAXLINE, ficpar);      }/* end while */
     puts(line);      if (s[m][i] > nlstate){
     fputs(line,ficparo);        mi++;     /* Death is another wave */
   }        /* if(mi==0)  never been interviewed correctly before death */
   ungetc(c,ficpar);           /* Only death is a correct wave */
          mw[mi][i]=m;
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mob_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);      }
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);  
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mob_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);      wav[i]=mi;
            if(mi==0){
   while((c=getc(ficpar))=='#' && c!= EOF){        nbwarn++;
     ungetc(c,ficpar);        if(first==0){
     fgets(line, MAXLINE, ficpar);          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
     puts(line);          first=1;
     fputs(line,ficparo);        }
   }        if(first==1){
   ungetc(c,ficpar);          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
          }
       } /* end mi==0 */
    dateprev1=anprev1+mprev1/12.+jprev1/365.;    } /* End individuals */
    dateprev2=anprev2+mprev2/12.+jprev2/365.;  
     for(i=1; i<=imx; i++){
   fscanf(ficpar,"pop_based=%d\n",&popbased);      for(mi=1; mi<wav[i];mi++){
    fprintf(ficparo,"pop_based=%d\n",popbased);          if (stepm <=0)
    fprintf(ficres,"pop_based=%d\n",popbased);            dh[mi][i]=1;
         else{
   while((c=getc(ficpar))=='#' && c!= EOF){          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
     ungetc(c,ficpar);            if (agedc[i] < 2*AGESUP) {
     fgets(line, MAXLINE, ficpar);              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
     puts(line);              if(j==0) j=1;  /* Survives at least one month after exam */
     fputs(line,ficparo);              else if(j<0){
   }                nberr++;
   ungetc(c,ficpar);                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
   fscanf(ficpar,"popforecast=%d popfile=%s starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf\n",&popforecast,popfile,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2);                j=1; /* Temporary Dangerous patch */
 fprintf(ficparo,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);                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(ficres,"popforecast=%d popfile=%s starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf\n",popforecast,popfile,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2);                fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                 fprintf(ficlog,"   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2);              }
               k=k+1;
  /*------------ gnuplot -------------*/              if (j >= jmax){
 chdir(pathcd);                jmax=j;
   if((ficgp=fopen("graph.plt","w"))==NULL) {                ijmax=i;
     printf("Problem with file graph.gp");goto end;              }
   }              if (j <= jmin){
 #ifdef windows                jmin=j;
   fprintf(ficgp,"cd \"%s\" \n",pathc);                ijmin=i;
 #endif              }
 m=pow(2,cptcoveff);              sum=sum+j;
                /*if (j<0) printf("j=%d num=%d \n",j,i);*/
  /* 1eme*/              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
   for (cpt=1; cpt<= nlstate ; cpt ++) {            }
    for (k1=1; k1<= m ; k1 ++) {          }
           else{
 #ifdef windows            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);  /*        if (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]); */
 #endif  
 #ifdef unix            k=k+1;
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);            if (j >= jmax) {
 #endif              jmax=j;
               ijmax=i;
 for (i=1; i<= nlstate ; i ++) {            }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            else if (j <= jmin){
   else fprintf(ficgp," \%%*lf (\%%*lf)");              jmin=j;
 }              ijmin=i;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);            }
     for (i=1; i<= nlstate ; i ++) {            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            /*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]);*/
   else fprintf(ficgp," \%%*lf (\%%*lf)");            if(j<0){
 }              nberr++;
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);              printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
      for (i=1; i<= nlstate ; i ++) {              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            sum=sum+j;
 }            }
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));          jk= j/stepm;
 #ifdef unix          jl= j -jk*stepm;
 fprintf(ficgp,"\nset ter gif small size 400,300");          ju= j -(jk+1)*stepm;
 #endif          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);            if(jl==0){
    }              dh[mi][i]=jk;
   }              bh[mi][i]=0;
   /*2 eme*/            }else{ /* We want a negative bias in order to only have interpolation ie
                     * to avoid the price of an extra matrix product in likelihood */
   for (k1=1; k1<= m ; k1 ++) {              dh[mi][i]=jk+1;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);              bh[mi][i]=ju;
                }
     for (i=1; i<= nlstate+1 ; i ++) {          }else{
       k=2*i;            if(jl <= -ju){
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);              dh[mi][i]=jk;
       for (j=1; j<= nlstate+1 ; j ++) {              bh[mi][i]=jl;       /* bias is positive if real duration
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                                   * is higher than the multiple of stepm and negative otherwise.
   else fprintf(ficgp," \%%*lf (\%%*lf)");                                   */
 }              }
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");            else{
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);              dh[mi][i]=jk+1;
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);              bh[mi][i]=ju;
       for (j=1; j<= nlstate+1 ; j ++) {            }
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");            if(dh[mi][i]==0){
         else fprintf(ficgp," \%%*lf (\%%*lf)");              dh[mi][i]=1; /* At least one step */
 }                bh[mi][i]=ju; /* At least one step */
       fprintf(ficgp,"\" t\"\" w l 0,");              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            }
       for (j=1; j<= nlstate+1 ; j ++) {          } /* end if mle */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        }
   else fprintf(ficgp," \%%*lf (\%%*lf)");      } /* end wave */
 }      }
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    jmean=sum/k;
       else fprintf(ficgp,"\" t\"\" w l 0,");    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);
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);   }
   }  
    /*********** Tricode ****************************/
   /*3eme*/  void tricode(int *Tvar, int **nbcode, int imx)
   {
   for (k1=1; k1<= m ; k1 ++) {    /* Uses cptcovn+2*cptcovprod as the number of covariates */
     for (cpt=1; cpt<= nlstate ; cpt ++) {    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
       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);    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
       for (i=1; i< nlstate ; i ++) {    int modmaxcovj=0; /* Modality max of covariates j */
         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);    cptcoveff=0; 
       }   
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    for (k=0; k<maxncov; k++) Ndum[k]=0;
     }    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
   }  
      for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
   /* CV preval stat */      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
   for (k1=1; k1<= m ; k1 ++) {                                 modality of this covariate Vj*/ 
     for (cpt=1; cpt<nlstate ; cpt ++) {        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
       k=3;                                        modality of the nth covariate of individual i. */
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
       for (i=1; i< nlstate ; i ++)        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         fprintf(ficgp,"+$%d",k+i+1);        if (ij > modmaxcovj) modmaxcovj=ij; 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);        /* getting the maximum value of the modality of the covariate
                 (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
       l=3+(nlstate+ndeath)*cpt;           female is 1, then modmaxcovj=1.*/
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);      }
       for (i=1; i< nlstate ; i ++) {      /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
         l=3+(nlstate+ndeath)*cpt;      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each modality of model-cov j */
         fprintf(ficgp,"+$%d",l+i+1);        if( Ndum[i] != 0 )
       }          ncodemax[j]++; 
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);          /* Number of modalities of the j th covariate. In fact
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);           ncodemax[j]=2 (dichotom. variables only) but it could be more for
     }           historical reasons */
   }        } /* Ndum[-1] number of undefined modalities */
   
   /* proba elementaires */      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
    for(i=1,jk=1; i <=nlstate; i++){      ij=1; 
     for(k=1; k <=(nlstate+ndeath); k++){      for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
       if (k != i) {        for (k=0; k<= modmaxcovj; k++) { /* k=-1 ? NCOVMAX*//* maxncov or modmaxcovj */
         for(j=1; j <=ncovmodel; j++){          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
           /*fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);*/            nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
           /*fprintf(ficgp,"%s",alph[1]);*/                                       k is a modality. If we have model=V1+V1*sex 
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
           jk++;            ij++;
           fprintf(ficgp,"\n");          }
         }          if (ij > ncodemax[j]) break; 
       }        }  /* end of loop on */
     }      } /* end of loop on modality */ 
     }    } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
     
   for(jk=1; jk <=m; jk++) {    for (k=0; k< maxncov; k++) Ndum[k]=0;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);    
    i=1;    for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
    for(k2=1; k2<=nlstate; k2++) {     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
      k3=i;     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
      for(k=1; k<=(nlstate+ndeath); k++) {     Ndum[ij]++;
        if (k != k2){   }
         fprintf(ficgp," exp(p%d+p%d*x",i,i+1);  
 ij=1;   ij=1;
         for(j=3; j <=ncovmodel; j++) {   for (i=1; i<= maxncov; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
           if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {     if((Ndum[i]!=0) && (i<=ncovcol)){
             fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);       Tvaraff[ij]=i; /*For printing */
             ij++;       ij++;
           }     }
           else   }
           fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);   ij--;
         }   cptcoveff=ij; /*Number of simple covariates*/
           fprintf(ficgp,")/(1");  }
          
         for(k1=1; k1 <=nlstate; k1++){    /*********** Health Expectancies ****************/
           fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);  
 ij=1;  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
           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]]]);    /* Health expectancies, no variances */
             ij++;    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
           }    int nhstepma, nstepma; /* Decreasing with age */
           else    double age, agelim, hf;
             fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    double ***p3mat;
           }    double eip;
           fprintf(ficgp,")");  
         }    pstamp(ficreseij);
         fprintf(ficgp,") t \"p%d%d\" ", k2,k);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
         if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    fprintf(ficreseij,"# Age");
         i=i+ncovmodel;    for(i=1; i<=nlstate;i++){
        }      for(j=1; j<=nlstate;j++){
      }        fprintf(ficreseij," e%1d%1d ",i,j);
    }      }
    fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      fprintf(ficreseij," e%1d. ",i);
   }    }
        fprintf(ficreseij,"\n");
   fclose(ficgp);  
        
 chdir(path);    if(estepm < stepm){
          printf ("Problem %d lower than %d\n",estepm, stepm);
     free_ivector(wav,1,imx);    }
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    else  hstepm=estepm;   
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      /* We compute the life expectancy from trapezoids spaced every estepm months
     free_ivector(num,1,n);     * This is mainly to measure the difference between two models: for example
     free_vector(agedc,1,n);     * if stepm=24 months pijx are given only every 2 years and by summing them
     /*free_matrix(covar,1,NCOVMAX,1,n);*/     * we are calculating an estimate of the Life Expectancy assuming a linear 
     fclose(ficparo);     * progression in between and thus overestimating or underestimating according
     fclose(ficres);     * to the curvature of the survival function. If, for the same date, we 
     /*  }*/     * estimate the model with stepm=1 month, we can keep estepm to 24 months
         * to compare the new estimate of Life expectancy with the same linear 
    /*________fin mle=1_________*/     * 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 */
     /* No more information from the sample is required now */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   /* Reads comments: lines beginning with '#' */       nhstepm is the number of hstepm from age to agelim 
   while((c=getc(ficpar))=='#' && c!= EOF){       nstepm is the number of stepm from age to agelin. 
     ungetc(c,ficpar);       Look at hpijx to understand the reason of that which relies in memory size
     fgets(line, MAXLINE, ficpar);       and note for a fixed period like estepm months */
     puts(line);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
     fputs(line,ficparo);       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
   ungetc(c,ficpar);       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.
   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);    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);  
 /*--------- index.htm --------*/    agelim=AGESUP;
     /* If stepm=6 months */
   strcpy(optionfilehtm,optionfile);      /* Computed by stepm unit matrices, product of hstepm matrices, stored
   strcat(optionfilehtm,".htm");         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {      
     printf("Problem with %s \n",optionfilehtm);goto end;  /* nhstepm age range expressed in number of stepm */
   }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
  fprintf(fichtm,"<body><ul> <font size=\"6\">Imach, Version 0.7 </font> <hr size=\"2\" color=\"#EC5E5E\">    /* if (stepm >= YEARM) hstepm=1;*/
 Titre=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
 Total number of observations=%d <br>    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>  
 <hr  size=\"2\" color=\"#EC5E5E\">    for (age=bage; age<=fage; age ++){ 
 <li>Outputs files<br><br>\n      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>      /* if (stepm >= YEARM) hstepm=1;*/
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>  
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>      /* If stepm=6 months */
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>      /* Computed by stepm unit matrices, product of hstepma matrices, stored
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>      
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br>      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
         - Prevalences and population forecasting: <a href=\"f%s\">f%s</a> <br>      
 <br>",title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       
  fprintf(fichtm," <li>Graphs</li><p>");      printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
  m=cptcoveff;      
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
  j1=0;        for(j=1; j<=nlstate;j++)
  for(k1=1; k1<=m;k1++){          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
    for(i1=1; i1<=ncodemax[k1];i1++){            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
        j1++;            
        if (cptcovn > 0) {            /* 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(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[j1][cpt]]);  
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      fprintf(ficreseij,"%3.0f",age );
        }      for(i=1; i<=nlstate;i++){
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>        eip=0;
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);            for(j=1; j<=nlstate;j++){
        for(cpt=1; cpt<nlstate;cpt++){          eip +=eij[i][j][(int)age];
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        }
        }        fprintf(ficreseij,"%9.4f", eip );
     for(cpt=1; cpt<=nlstate;cpt++) {      }
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident      fprintf(ficreseij,"\n");
 interval) in state (%d): v%s%d%d.gif <br>      
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);      }
      }    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
      for(cpt=1; cpt<=nlstate;cpt++) {    printf("\n");
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    fprintf(ficlog,"\n");
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    
      }  }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and  
 health expectancies in states (1) and (2): e%s%d.gif<br>  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[] )
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);  
 fprintf(fichtm,"\n</body>");  {
    }    /* Covariances of health expectancies eij and of total life expectancies according
  }     to initial status i, ei. .
 fclose(fichtm);    */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   /*--------------- Prevalence limit --------------*/    int nhstepma, nstepma; /* Decreasing with age */
      double age, agelim, hf;
   strcpy(filerespl,"pl");    double ***p3matp, ***p3matm, ***varhe;
   strcat(filerespl,fileres);    double **dnewm,**doldm;
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    double *xp, *xm;
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    double **gp, **gm;
   }    double ***gradg, ***trgradg;
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    int theta;
   fprintf(ficrespl,"#Prevalence limit\n");  
   fprintf(ficrespl,"#Age ");    double eip, vip;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  
   fprintf(ficrespl,"\n");    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
      xp=vector(1,npar);
   prlim=matrix(1,nlstate,1,nlstate);    xm=vector(1,npar);
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    dnewm=matrix(1,nlstate*nlstate,1,npar);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    pstamp(ficresstdeij);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
   k=0;    fprintf(ficresstdeij,"# Age");
   agebase=agemin;    for(i=1; i<=nlstate;i++){
   agelim=agemax;      for(j=1; j<=nlstate;j++)
   ftolpl=1.e-10;        fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   i1=cptcoveff;      fprintf(ficresstdeij," e%1d. ",i);
   if (cptcovn < 1){i1=1;}    }
     fprintf(ficresstdeij,"\n");
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    pstamp(ficrescveij);
         k=k+1;    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    fprintf(ficrescveij,"# Age");
         fprintf(ficrespl,"\n#******");    for(i=1; i<=nlstate;i++)
         for(j=1;j<=cptcoveff;j++)      for(j=1; j<=nlstate;j++){
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);        cptj= (j-1)*nlstate+i;
         fprintf(ficrespl,"******\n");        for(i2=1; i2<=nlstate;i2++)
                  for(j2=1; j2<=nlstate;j2++){
         for (age=agebase; age<=agelim; age++){            cptj2= (j2-1)*nlstate+i2;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            if(cptj2 <= cptj)
           fprintf(ficrespl,"%.0f",age );              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           for(i=1; i<=nlstate;i++)          }
           fprintf(ficrespl," %.5f", prlim[i][i]);      }
           fprintf(ficrespl,"\n");    fprintf(ficrescveij,"\n");
         }    
       }    if(estepm < stepm){
     }      printf ("Problem %d lower than %d\n",estepm, stepm);
   fclose(ficrespl);    }
     else  hstepm=estepm;   
   /*------------- h Pij x at various ages ------------*/    /* We compute the life expectancy from trapezoids spaced every estepm months
       * This is mainly to measure the difference between two models: for example
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);     * if stepm=24 months pijx are given only every 2 years and by summing them
   if((ficrespij=fopen(filerespij,"w"))==NULL) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;     * progression in between and thus overestimating or underestimating according
   }     * to the curvature of the survival function. If, for the same date, we 
   printf("Computing pij: result on file '%s' \n", filerespij);     * estimate the model with stepm=1 month, we can keep estepm to 24 months
       * to compare the new estimate of Life expectancy with the same linear 
   stepsize=(int) (stepm+YEARM-1)/YEARM;     * hypothesis. A more precise result, taking into account a more precise
   /*if (stepm<=24) stepsize=2;*/     * curvature will be obtained if estepm is as small as stepm. */
   
   agelim=AGESUP;    /* For example we decided to compute the life expectancy with the smallest unit */
   hstepm=stepsize*YEARM; /* Every year of age */    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */       nhstepm is the number of hstepm from age to agelim 
         nstepm is the number of stepm from age to agelin. 
   k=0;       Look at hpijx to understand the reason of that which relies in memory size
   for(cptcov=1;cptcov<=i1;cptcov++){       and note for a fixed period like estepm months */
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
       k=k+1;       survival function given by stepm (the optimization length). Unfortunately it
         fprintf(ficrespij,"\n#****** ");       means that if the survival funtion is printed only each two years of age and if
         for(j=1;j<=cptcoveff;j++)       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);       results. So we changed our mind and took the option of the best precision.
         fprintf(ficrespij,"******\n");    */
            hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    /* If stepm=6 months */
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    /* nhstepm age range expressed in number of stepm */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    agelim=AGESUP;
           oldm=oldms;savm=savms;    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           fprintf(ficrespij,"# Age");    /* if (stepm >= YEARM) hstepm=1;*/
           for(i=1; i<=nlstate;i++)    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
             for(j=1; j<=nlstate+ndeath;j++)    
               fprintf(ficrespij," %1d-%1d",i,j);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           fprintf(ficrespij,"\n");    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           for (h=0; h<=nhstepm; h++){    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
             for(i=1; i<=nlstate;i++)    gp=matrix(0,nhstepm,1,nlstate*nlstate);
               for(j=1; j<=nlstate+ndeath;j++)    gm=matrix(0,nhstepm,1,nlstate*nlstate);
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);  
             fprintf(ficrespij,"\n");    for (age=bage; age<=fage; age ++){ 
           }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
           fprintf(ficrespij,"\n");      /* if (stepm >= YEARM) hstepm=1;*/
         }      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
     }  
   }      /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
   /* varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k);*/         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   fclose(ficrespij);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
   /*---------- Forecasting ------------------*/      /* Computing  Variances of health expectancies */
   calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          decrease memory allocation */
   prevalence(agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);      for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
   strcpy(fileresf,"f");          xm[i] = x[i] - (i==theta ?delti[theta]:0);
   strcat(fileresf,fileres);        }
   if((ficresf=fopen(fileresf,"w"))==NULL) {        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
     printf("Problem with forecast resultfile: %s\n", fileresf);goto end;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
   }    
   printf("Computing forecasting: result on file '%s' \n", fileresf);        for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate; i++){
   free_matrix(mint,1,maxwav,1,n);            for(h=0; h<=nhstepm-1; h++){
   free_matrix(anint,1,maxwav,1,n);              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
   free_matrix(agev,1,maxwav,1,imx);              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
   /* Mobile average */            }
           }
   if (cptcoveff==0) ncodemax[cptcoveff]=1;        }
        
   if (mobilav==1) {        for(ij=1; ij<= nlstate*nlstate; ij++)
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          for(h=0; h<=nhstepm-1; h++){
     for (agedeb=bage+3; agedeb<=fage-2; agedeb++)            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
       for (i=1; i<=nlstate;i++)          }
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)      }/* End theta */
           mobaverage[(int)agedeb][i][cptcod]=0.;      
          
     for (agedeb=bage+4; agedeb<=fage; agedeb++){      for(h=0; h<=nhstepm-1; h++)
       for (i=1; i<=nlstate;i++){        for(j=1; j<=nlstate*nlstate;j++)
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){          for(theta=1; theta <=npar; theta++)
           for (cpt=0;cpt<=4;cpt++){            trgradg[h][j][theta]=gradg[h][theta][j];
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];      
           }  
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;       for(ij=1;ij<=nlstate*nlstate;ij++)
         }        for(ji=1;ji<=nlstate*nlstate;ji++)
       }          varhe[ij][ji][(int)age] =0.;
     }    
   }       printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   stepsize=(int) (stepm+YEARM-1)/YEARM;       for(h=0;h<=nhstepm-1;h++){
   if (stepm<=12) stepsize=1;        for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
   agelim=AGESUP;          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
   /*hstepm=stepsize*YEARM; *//* Every year of age */          for(ij=1;ij<=nlstate*nlstate;ij++)
   hstepm=1;            for(ji=1;ji<=nlstate*nlstate;ji++)
   hstepm=hstepm/stepm; /* Typically 2 years, = 2 years/6 months = 4 */              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
   yp1=modf(dateintmean,&yp);        }
   anprojmean=yp;      }
   yp2=modf((yp1*12),&yp);  
   mprojmean=yp;      /* Computing expectancies */
   yp1=modf((yp2*30.5),&yp);      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   jprojmean=yp;      for(i=1; i<=nlstate;i++)
   if(jprojmean==0) jprojmean=1;        for(j=1; j<=nlstate;j++)
   if(mprojmean==0) jprojmean=1;          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;
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);            
             /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   if (popforecast==1) {  
     if((ficpop=fopen(popfile,"r"))==NULL)    {          }
       printf("Problem with population file : %s\n",popfile);goto end;  
     }      fprintf(ficresstdeij,"%3.0f",age );
     popage=ivector(0,AGESUP);      for(i=1; i<=nlstate;i++){
     popeffectif=vector(0,AGESUP);        eip=0.;
     popcount=vector(0,AGESUP);        vip=0.;
         for(j=1; j<=nlstate;j++){
     i=1;            eip += eij[i][j][(int)age];
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF)          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];
         i=i+1;          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
       }        }
     imx=i;        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
          }
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];      fprintf(ficresstdeij,"\n");
   }  
       fprintf(ficrescveij,"%3.0f",age );
   for(cptcov=1;cptcov<=i1;cptcov++){      for(i=1; i<=nlstate;i++)
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        for(j=1; j<=nlstate;j++){
       k=k+1;          cptj= (j-1)*nlstate+i;
       fprintf(ficresf,"\n#******");          for(i2=1; i2<=nlstate;i2++)
       for(j=1;j<=cptcoveff;j++) {            for(j2=1; j2<=nlstate;j2++){
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              cptj2= (j2-1)*nlstate+i2;
       }              if(cptj2 <= cptj)
       fprintf(ficresf,"******\n");                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
       fprintf(ficresf,"# StartingAge FinalAge");            }
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);        }
       if (popforecast==1)  fprintf(ficresf," [Population]");      fprintf(ficrescveij,"\n");
       
       for (cpt=0; cpt<=5;cpt++) {    }
         fprintf(ficresf,"\n");    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);      free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
       for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(bage-((int)calagedate %12)/12.); agedeb--){ /* If stepm=6 months */    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
         nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
         nhstepm = nhstepm/hstepm;    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         /*printf("agedeb=%.lf stepm=%d hstepm=%d nhstepm=%d \n",agedeb,stepm,hstepm,nhstepm);*/    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
         p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    fprintf(ficlog,"\n");
         oldm=oldms;savm=savms;  
         hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);      free_vector(xm,1,npar);
                    free_vector(xp,1,npar);
         for (h=0; h<=nhstepm; h++){    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
           if (h==(int) (calagedate+YEARM*cpt)) {    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
             fprintf(ficresf,"\n %.f ",agedeb+h*hstepm/YEARM*stepm);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
           }  }
           for(j=1; j<=nlstate+ndeath;j++) {  
             kk1=0.;kk2=0;  /************ Variance ******************/
             for(i=1; i<=nlstate;i++) {          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[])
               if (mobilav==1)  {
                 kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    /* Variance of health expectancies */
               else {    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
                 kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    /* double **newm;*/
                 /* fprintf(ficresf," p3=%.3f p=%.3f ", p3mat[i][j][h], probs[(int)(agedeb)+1][i][cptcod]);*/    double **dnewm,**doldm;
               }    double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
               if (popforecast==1) kk2=kk1*popeffectif[(int)agedeb];    int k, cptcode;
             }    double *xp;
              double **gp, **gm;  /* for var eij */
             if (h==(int)(calagedate+12*cpt)){    double ***gradg, ***trgradg; /*for var eij */
               fprintf(ficresf," %.3f", kk1);    double **gradgp, **trgradgp; /* for var p point j */
                  double *gpp, *gmp; /* for var p point j */
               if (popforecast==1) fprintf(ficresf," [%.f]", kk2);    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
             }    double ***p3mat;
           }    double age,agelim, hf;
         }    double ***mobaverage;
         free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    int theta;
       }    char digit[4];
       }    char digitp[25];
     }  
   }    char fileresprobmorprev[FILENAMELENGTH];
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   if (popforecast==1) {    if(popbased==1){
     free_ivector(popage,0,AGESUP);      if(mobilav!=0)
     free_vector(popeffectif,0,AGESUP);        strcpy(digitp,"-populbased-mobilav-");
     free_vector(popcount,0,AGESUP);      else strcpy(digitp,"-populbased-nomobil-");
   }    }
   free_imatrix(s,1,maxwav+1,1,n);    else 
   free_vector(weight,1,n);      strcpy(digitp,"-stablbased-");
   fclose(ficresf);  
   /*---------- Health expectancies and variances ------------*/    if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   strcpy(filerest,"t");      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
   strcat(filerest,fileres);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   if((ficrest=fopen(filerest,"w"))==NULL) {        printf(" Error in movingaverage mobilav=%d\n",mobilav);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      }
   }    }
   printf("Computing Total LEs with variances: file '%s' \n", filerest);  
     strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
   strcpy(filerese,"e");    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   strcat(filerese,fileres);    strcat(fileresprobmorprev,digit); /* Tvar to be done */
   if((ficreseij=fopen(filerese,"w"))==NULL) {    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    strcat(fileresprobmorprev,fileres);
   }    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
  strcpy(fileresv,"v");    }
   strcat(fileresv,fileres);    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {   
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   }    pstamp(ficresprobmorprev);
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   k=0;    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   for(cptcov=1;cptcov<=i1;cptcov++){      fprintf(ficresprobmorprev," p.%-d SE",j);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      for(i=1; i<=nlstate;i++)
       k=k+1;        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
       fprintf(ficrest,"\n#****** ");    }  
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresprobmorprev,"\n");
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    fprintf(ficgp,"\n# Routine varevsij");
       fprintf(ficrest,"******\n");    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
       fprintf(ficreseij,"\n#****** ");    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
       for(j=1;j<=cptcoveff;j++)  /*   } */
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
       fprintf(ficreseij,"******\n");    pstamp(ficresvij);
     fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
       fprintf(ficresvij,"\n#****** ");    if(popbased==1)
       for(j=1;j<=cptcoveff;j++)      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);    else
       fprintf(ficresvij,"******\n");      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    for(i=1; i<=nlstate;i++)
       oldm=oldms;savm=savms;      for(j=1; j<=nlstate;j++)
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);          fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);    fprintf(ficresvij,"\n");
       oldm=oldms;savm=savms;  
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    xp=vector(1,npar);
          dnewm=matrix(1,nlstate,1,npar);
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    doldm=matrix(1,nlstate,1,nlstate);
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
       fprintf(ficrest,"\n");    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
          
       hf=1;    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
       if (stepm >= YEARM) hf=stepm/YEARM;    gpp=vector(nlstate+1,nlstate+ndeath);
       epj=vector(1,nlstate+1);    gmp=vector(nlstate+1,nlstate+ndeath);
       for(age=bage; age <=fage ;age++){    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    
         if (popbased==1) {    if(estepm < stepm){
           for(i=1; i<=nlstate;i++)      printf ("Problem %d lower than %d\n",estepm, stepm);
             prlim[i][i]=probs[(int)age][i][k];    }
         }    else  hstepm=estepm;   
            /* For example we decided to compute the life expectancy with the smallest unit */
         fprintf(ficrest," %.0f",age);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){       nhstepm is the number of hstepm from age to agelim 
           for(i=1, epj[j]=0.;i <=nlstate;i++) {       nstepm is the number of stepm from age to agelin. 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];       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
           epj[nlstate+1] +=epj[j];       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
         for(i=1, vepp=0.;i <=nlstate;i++)       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           for(j=1;j <=nlstate;j++)       results. So we changed our mind and took the option of the best precision.
             vepp += vareij[i][j][(int)age];    */
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         for(j=1;j <=nlstate;j++){    agelim = AGESUP;
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
         }      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
         fprintf(ficrest,"\n");      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       }      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
   }      gp=matrix(0,nhstepm,1,nlstate);
              gm=matrix(0,nhstepm,1,nlstate);
          
   
       for(theta=1; theta <=npar; theta++){
  fclose(ficreseij);        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
  fclose(ficresvij);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   fclose(ficrest);        }
   fclose(ficpar);        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   free_vector(epj,1,nlstate+1);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   /*  scanf("%d ",i); */  
         if (popbased==1) {
   /*------- Variance limit prevalence------*/            if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
 strcpy(fileresvpl,"vpl");              prlim[i][i]=probs[(int)age][i][ij];
   strcat(fileresvpl,fileres);          }else{ /* mobilav */ 
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {            for(i=1; i<=nlstate;i++)
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);              prlim[i][i]=mobaverage[(int)age][i][ij];
     exit(0);          }
   }        }
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    
         for(j=1; j<= nlstate; j++){
  k=0;          for(h=0; h<=nhstepm; h++){
  for(cptcov=1;cptcov<=i1;cptcov++){            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
      k=k+1;          }
      fprintf(ficresvpl,"\n#****** ");        }
      for(j=1;j<=cptcoveff;j++)        /* This for computing probability of death (h=1 means
        fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);           computed over hstepm matrices product = hstepm*stepm months) 
      fprintf(ficresvpl,"******\n");           as a weighted average of prlim.
              */
      varpl=matrix(1,nlstate,(int) bage, (int) fage);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
      oldm=oldms;savm=savms;          for(i=1,gpp[j]=0.; i<= nlstate; i++)
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);            gpp[j] += prlim[i][i]*p3mat[i][j][1];
    }        }    
  }        /* end probability of death */
   
   fclose(ficresvpl);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
   /*---------- End : free ----------------*/        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);        if (popbased==1) {
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);          if(mobilav ==0){
              for(i=1; i<=nlstate;i++)
                prlim[i][i]=probs[(int)age][i][ij];
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);          }else{ /* mobilav */ 
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);            for(i=1; i<=nlstate;i++)
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);              prlim[i][i]=mobaverage[(int)age][i][ij];
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);          }
          }
   free_matrix(matcov,1,npar,1,npar);  
   free_vector(delti,1,npar);        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
            for(h=0; h<=nhstepm; h++){
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
   printf("End of Imach\n");          }
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */        }
          /* This for computing probability of death (h=1 means
   /* 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);*/           computed over hstepm matrices product = hstepm*stepm months) 
   /*printf("Total time was %d uSec.\n", total_usecs);*/           as a weighted average of prlim.
   /*------ End -----------*/        */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
  end:           gmp[j] += prlim[i][i]*p3mat[i][j][1];
 #ifdef windows        }    
  chdir(pathcd);        /* end probability of death */
 #endif  
          for(j=1; j<= nlstate; j++) /* vareij */
  system("..\\gp37mgw\\wgnuplot graph.plt");          for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
 #ifdef windows          }
   while (z[0] != 'q') {  
     chdir(pathcd);        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
     printf("\nType e to edit output files, c to start again, and q for exiting: ");          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
     scanf("%s",z);        }
     if (z[0] == 'c') system("./imach");  
     else if (z[0] == 'e') {      } /* End theta */
       chdir(path);  
       system(optionfilehtm);      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
     }  
     else if (z[0] == 'q') exit(0);      for(h=0; h<=nhstepm; h++) /* veij */
   }        for(j=1; j<=nlstate;j++)
 #endif          for(theta=1; theta <=npar; theta++)
 }            trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
     double **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     
     pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
   
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     pstamp(ficresprobcov);
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     pstamp(ficresprobcor);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcor,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
     xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     fprintf(fichtm,"\n");
   
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
   standard deviations wide on each axis. <br>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   
     cov[1]=1;
     tj=cptcoveff;
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(t=1; t<=tj;t++){
       for(i1=1; i1<=ncodemax[t];i1++){ 
         j1++;
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
           gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
           gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
           free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
           free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i=i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
   
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     if ((lc2 <0) || (lc1 <0) ){
                       printf("Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Continuing by making them positive: WRONG RESULTS.\n", lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
                       fprintf(ficlog,"Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e\n", lc1, lc2, v1, v2, cv12);fflush(ficlog);
                       lc1=fabs(lc1);
                       lc2=fabs(lc2);
                     }
   
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small\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;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%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);
           fprintf(ficlog,"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);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     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*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       for(k=cptcovn; k>=1;k--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 
                                       */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=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'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=2 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1;  /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1]=atoi(strc); /* m 1 for V1*/
             Tvard[k1][2]=atoi(stre); /* n 4 for V4*/
             Tvar[cptcovn+k2]=Tvard[k1][1]; /* Tvar[(cptcovn=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovn+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovn=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
             k1++;
             k2=k2+2;
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutv(strd,strc,strb,'V');
           Tvar[k]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\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 plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read 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++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8); /* hard coded ? */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,15); 
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2); /* For V3*V2 Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,15); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     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++){ /* scans any effective covariate */
       for(i=1; i <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) {
               h=1;
               codtab[h][k]=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); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         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;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           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 */
    endfree:
     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_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.1.20  
changed lines
  Added in v.1.139


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