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version 1.52, 2002/07/19 18:49:30 version 1.130, 2009/05/26 06:44:34
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.130  2009/05/26 06:44:34  brouard
      (Module): Max Covariate is now set to 20 instead of 8. A
   This program computes Healthy Life Expectancies from    lot of cleaning with variables initialized to 0. Trying to make
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   first survey ("cross") where individuals from different ages are  
   interviewed on their health status or degree of disability (in the    Revision 1.129  2007/08/31 13:49:27  lievre
   case of a health survey which is our main interest) -2- at least a    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   second wave of interviews ("longitudinal") which measure each change  
   (if any) in individual health status.  Health expectancies are    Revision 1.128  2006/06/30 13:02:05  brouard
   computed from the time spent in each health state according to a    (Module): Clarifications on computing e.j
   model. More health states you consider, more time is necessary to reach the  
   Maximum Likelihood of the parameters involved in the model.  The    Revision 1.127  2006/04/28 18:11:50  brouard
   simplest model is the multinomial logistic model where pij is the    (Module): Yes the sum of survivors was wrong since
   probability to be observed in state j at the second wave    imach-114 because nhstepm was no more computed in the age
   conditional to be observed in state i at the first wave. Therefore    loop. Now we define nhstepma in the age loop.
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    (Module): In order to speed up (in case of numerous covariates) we
   'age' is age and 'sex' is a covariate. If you want to have a more    compute health expectancies (without variances) in a first step
   complex model than "constant and age", you should modify the program    and then all the health expectancies with variances or standard
   where the markup *Covariates have to be included here again* invites    deviation (needs data from the Hessian matrices) which slows the
   you to do it.  More covariates you add, slower the    computation.
   convergence.    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
   The advantage of this computer programme, compared to a simple  
   multinomial logistic model, is clear when the delay between waves is not    Revision 1.126  2006/04/28 17:23:28  brouard
   identical for each individual. Also, if a individual missed an    (Module): Yes the sum of survivors was wrong since
   intermediate interview, the information is lost, but taken into    imach-114 because nhstepm was no more computed in the age
   account using an interpolation or extrapolation.      loop. Now we define nhstepma in the age loop.
     Version 0.98h
   hPijx is the probability to be observed in state i at age x+h  
   conditional to the observed state i at age x. The delay 'h' can be    Revision 1.125  2006/04/04 15:20:31  lievre
   split into an exact number (nh*stepm) of unobserved intermediate    Errors in calculation of health expectancies. Age was not initialized.
   states. This elementary transition (by month or quarter trimester,    Forecasting file added.
   semester or year) is model as a multinomial logistic.  The hPx  
   matrix is simply the matrix product of nh*stepm elementary matrices    Revision 1.124  2006/03/22 17:13:53  lievre
   and the contribution of each individual to the likelihood is simply    Parameters are printed with %lf instead of %f (more numbers after the comma).
   hPijx.    The log-likelihood is printed in the log file
   
   Also this programme outputs the covariance matrix of the parameters but also    Revision 1.123  2006/03/20 10:52:43  brouard
   of the life expectancies. It also computes the prevalence limits.    * imach.c (Module): <title> changed, corresponds to .htm file
      name. <head> headers where missing.
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).  
            Institut national d'études démographiques, Paris.    * imach.c (Module): Weights can have a decimal point as for
   This software have been partly granted by Euro-REVES, a concerted action    English (a comma might work with a correct LC_NUMERIC environment,
   from the European Union.    otherwise the weight is truncated).
   It is copyrighted identically to a GNU software product, ie programme and    Modification of warning when the covariates values are not 0 or
   software can be distributed freely for non commercial use. Latest version    1.
   can be accessed at http://euroreves.ined.fr/imach .    Version 0.98g
   **********************************************************************/  
      Revision 1.122  2006/03/20 09:45:41  brouard
 #include <math.h>    (Module): Weights can have a decimal point as for
 #include <stdio.h>    English (a comma might work with a correct LC_NUMERIC environment,
 #include <stdlib.h>    otherwise the weight is truncated).
 #include <unistd.h>    Modification of warning when the covariates values are not 0 or
     1.
 #define MAXLINE 256    Version 0.98g
 #define GNUPLOTPROGRAM "gnuplot"  
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    Revision 1.121  2006/03/16 17:45:01  lievre
 #define FILENAMELENGTH 80    * imach.c (Module): Comments concerning covariates added
 /*#define DEBUG*/  
 #define windows    * imach.c (Module): refinements in the computation of lli if
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    status=-2 in order to have more reliable computation if stepm is
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */    not 1 month. Version 0.98f
   
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    Revision 1.120  2006/03/16 15:10:38  lievre
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
 #define NINTERVMAX 8    not 1 month. Version 0.98f
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    Revision 1.119  2006/03/15 17:42:26  brouard
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): Bug if status = -2, the loglikelihood was
 #define MAXN 20000    computed as likelihood omitting the logarithm. Version O.98e
 #define YEARM 12. /* Number of months per year */  
 #define AGESUP 130    Revision 1.118  2006/03/14 18:20:07  brouard
 #define AGEBASE 40    (Module): varevsij Comments added explaining the second
 #ifdef windows    table of variances if popbased=1 .
 #define DIRSEPARATOR '\\'    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define ODIRSEPARATOR '/'    (Module): Function pstamp added
 #else    (Module): Version 0.98d
 #define DIRSEPARATOR '/'  
 #define ODIRSEPARATOR '\\'    Revision 1.117  2006/03/14 17:16:22  brouard
 #endif    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 char version[80]="Imach version 0.8i, June 2002, INED-EUROREVES ";    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 int erreur; /* Error number */    (Module): Function pstamp added
 int nvar;    (Module): Version 0.98d
 int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov;  
 int npar=NPARMAX;    Revision 1.116  2006/03/06 10:29:27  brouard
 int nlstate=2; /* Number of live states */    (Module): Variance-covariance wrong links and
 int ndeath=1; /* Number of dead states */    varian-covariance of ej. is needed (Saito).
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */  
 int popbased=0;    Revision 1.115  2006/02/27 12:17:45  brouard
     (Module): One freematrix added in mlikeli! 0.98c
 int *wav; /* Number of waves for this individuual 0 is possible */  
 int maxwav; /* Maxim number of waves */    Revision 1.114  2006/02/26 12:57:58  brouard
 int jmin, jmax; /* min, max spacing between 2 waves */    (Module): Some improvements in processing parameter
 int mle, weightopt;    filename with strsep.
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */  
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Revision 1.113  2006/02/24 14:20:24  brouard
 double jmean; /* Mean space between 2 waves */    (Module): Memory leaks checks with valgrind and:
 double **oldm, **newm, **savm; /* Working pointers to matrices */    datafile was not closed, some imatrix were not freed and on matrix
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    allocation too.
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;  
 FILE *ficlog;    Revision 1.112  2006/01/30 09:55:26  brouard
 FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 FILE *ficresprobmorprev;  
 FILE *fichtm; /* Html File */    Revision 1.111  2006/01/25 20:38:18  brouard
 FILE *ficreseij;    (Module): Lots of cleaning and bugs added (Gompertz)
 char filerese[FILENAMELENGTH];    (Module): Comments can be added in data file. Missing date values
 FILE  *ficresvij;    can be a simple dot '.'.
 char fileresv[FILENAMELENGTH];  
 FILE  *ficresvpl;    Revision 1.110  2006/01/25 00:51:50  brouard
 char fileresvpl[FILENAMELENGTH];    (Module): Lots of cleaning and bugs added (Gompertz)
 char title[MAXLINE];  
 char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];    Revision 1.109  2006/01/24 19:37:15  brouard
 char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH];    (Module): Comments (lines starting with a #) are allowed in data.
   
 char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];    Revision 1.108  2006/01/19 18:05:42  lievre
 char filelog[FILENAMELENGTH]; /* Log file */    Gnuplot problem appeared...
 char filerest[FILENAMELENGTH];    To be fixed
 char fileregp[FILENAMELENGTH];  
 char popfile[FILENAMELENGTH];    Revision 1.107  2006/01/19 16:20:37  brouard
     Test existence of gnuplot in imach path
 char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH];  
     Revision 1.106  2006/01/19 13:24:36  brouard
 #define NR_END 1    Some cleaning and links added in html output
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.105  2006/01/05 20:23:19  lievre
     *** empty log message ***
 #define NRANSI  
 #define ITMAX 200    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 #define TOL 2.0e-4    (Module): If the status is missing at the last wave but we know
     that the person is alive, then we can code his/her status as -2
 #define CGOLD 0.3819660    (instead of missing=-1 in earlier versions) and his/her
 #define ZEPS 1.0e-10    contributions to the likelihood is 1 - Prob of dying from last
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
 #define GOLD 1.618034  
 #define GLIMIT 100.0    Revision 1.103  2005/09/30 15:54:49  lievre
 #define TINY 1.0e-20    (Module): sump fixed, loop imx fixed, and simplifications.
   
 static double maxarg1,maxarg2;    Revision 1.102  2004/09/15 17:31:30  brouard
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    Add the possibility to read data file including tab characters.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.101  2004/09/15 10:38:38  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Fix on curr_time
 #define rint(a) floor(a+0.5)  
     Revision 1.100  2004/07/12 18:29:06  brouard
 static double sqrarg;    Add version for Mac OS X. Just define UNIX in Makefile
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.99  2004/06/05 08:57:40  brouard
     *** empty log message ***
 int imx;  
 int stepm;    Revision 1.98  2004/05/16 15:05:56  brouard
 /* Stepm, step in month: minimum step interpolation*/    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 estepm;    state at each age, but using a Gompertz model: log u =a + b*age .
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/    This is the basic analysis of mortality and should be done before any
     other analysis, in order to test if the mortality estimated from the
 int m,nb;    cross-longitudinal survey is different from the mortality estimated
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    from other sources like vital statistic data.
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    The same imach parameter file can be used but the option for mle should be -3.
 double dateintmean=0;  
     Agnès, who wrote this part of the code, tried to keep most of the
 double *weight;    former routines in order to include the new code within the former code.
 int **s; /* Status */  
 double *agedc, **covar, idx;    The output is very simple: only an estimate of the intercept and of
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    the slope with 95% confident intervals.
   
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Current limitations:
 double ftolhess; /* Tolerance for computing hessian */    A) Even if you enter covariates, i.e. with the
     model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
 /**************** split *************************/    B) There is no computation of Life Expectancy nor Life Table.
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )  
 {    Revision 1.97  2004/02/20 13:25:42  lievre
    char *s;                             /* pointer */    Version 0.96d. Population forecasting command line is (temporarily)
    int  l1, l2;                         /* length counters */    suppressed.
   
    l1 = strlen( path );                 /* length of path */    Revision 1.96  2003/07/15 15:38:55  brouard
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
    s= strrchr( path, DIRSEPARATOR );            /* find last / */    rewritten within the same printf. Workaround: many printfs.
    if ( s == NULL ) {                   /* no directory, so use current */  
      /*if(strrchr(path, ODIRSEPARATOR )==NULL)    Revision 1.95  2003/07/08 07:54:34  brouard
        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/    * imach.c (Repository):
 #if     defined(__bsd__)                /* get current working directory */    (Repository): Using imachwizard code to output a more meaningful covariance
       extern char       *getwd( );    matrix (cov(a12,c31) instead of numbers.
   
       if ( getwd( dirc ) == NULL ) {    Revision 1.94  2003/06/27 13:00:02  brouard
 #else    Just cleaning
       extern char       *getcwd( );  
     Revision 1.93  2003/06/25 16:33:55  brouard
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {    (Module): On windows (cygwin) function asctime_r doesn't
 #endif    exist so I changed back to asctime which exists.
          return( GLOCK_ERROR_GETCWD );    (Module): Version 0.96b
       }  
       strcpy( name, path );             /* we've got it */    Revision 1.92  2003/06/25 16:30:45  brouard
    } else {                             /* strip direcotry from path */    (Module): On windows (cygwin) function asctime_r doesn't
       s++;                              /* after this, the filename */    exist so I changed back to asctime which exists.
       l2 = strlen( s );                 /* length of filename */  
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.91  2003/06/25 15:30:29  brouard
       strcpy( name, s );                /* save file name */    * imach.c (Repository): Duplicated warning errors corrected.
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    (Repository): Elapsed time after each iteration is now output. It
       dirc[l1-l2] = 0;                  /* add zero */    helps to forecast when convergence will be reached. Elapsed time
    }    is stamped in powell.  We created a new html file for the graphs
    l1 = strlen( dirc );                 /* length of directory */    concerning matrix of covariance. It has extension -cov.htm.
 #ifdef windows  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    Revision 1.90  2003/06/24 12:34:15  brouard
 #else    (Module): Some bugs corrected for windows. Also, when
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }    mle=-1 a template is output in file "or"mypar.txt with the design
 #endif    of the covariance matrix to be input.
    s = strrchr( name, '.' );            /* find last / */  
    s++;    Revision 1.89  2003/06/24 12:30:52  brouard
    strcpy(ext,s);                       /* save extension */    (Module): Some bugs corrected for windows. Also, when
    l1= strlen( name);    mle=-1 a template is output in file "or"mypar.txt with the design
    l2= strlen( s)+1;    of the covariance matrix to be input.
    strncpy( finame, name, l1-l2);  
    finame[l1-l2]= 0;    Revision 1.88  2003/06/23 17:54:56  brouard
    return( 0 );                         /* we're done */    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
 }  
     Revision 1.87  2003/06/18 12:26:01  brouard
     Version 0.96
 /******************************************/  
     Revision 1.86  2003/06/17 20:04:08  brouard
 void replace(char *s, char*t)    (Module): Change position of html and gnuplot routines and added
 {    routine fileappend.
   int i;  
   int lg=20;    Revision 1.85  2003/06/17 13:12:43  brouard
   i=0;    * imach.c (Repository): Check when date of death was earlier that
   lg=strlen(t);    current date of interview. It may happen when the death was just
   for(i=0; i<= lg; i++) {    prior to the death. In this case, dh was negative and likelihood
     (s[i] = t[i]);    was wrong (infinity). We still send an "Error" but patch by
     if (t[i]== '\\') s[i]='/';    assuming that the date of death was just one stepm after the
   }    interview.
 }    (Repository): Because some people have very long ID (first column)
     we changed int to long in num[] and we added a new lvector for
 int nbocc(char *s, char occ)    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   int i,j=0;    (Repository): No more line truncation errors.
   int lg=20;  
   i=0;    Revision 1.84  2003/06/13 21:44:43  brouard
   lg=strlen(s);    * imach.c (Repository): Replace "freqsummary" at a correct
   for(i=0; i<= lg; i++) {    place. It differs from routine "prevalence" which may be called
   if  (s[i] == occ ) j++;    many times. Probs is memory consuming and must be used with
   }    parcimony.
   return j;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 }  
     Revision 1.83  2003/06/10 13:39:11  lievre
 void cutv(char *u,char *v, char*t, char occ)    *** empty log message ***
 {  
   /* cuts string t into u and v where u is ended by char occ excluding it    Revision 1.82  2003/06/05 15:57:20  brouard
      and v is after occ excluding it too : ex cutv(u,v,"abcdef2ghi2j",2)    Add log in  imach.c and  fullversion number is now printed.
      gives u="abcedf" and v="ghi2j" */  
   int i,lg,j,p=0;  */
   i=0;  /*
   for(j=0; j<=strlen(t)-1; j++) {     Interpolated Markov Chain
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;  
   }    Short summary of the programme:
     
   lg=strlen(t);    This program computes Healthy Life Expectancies from
   for(j=0; j<p; j++) {    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
     (u[j] = t[j]);    first survey ("cross") where individuals from different ages are
   }    interviewed on their health status or degree of disability (in the
      u[p]='\0';    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
    for(j=0; j<= lg; j++) {    (if any) in individual health status.  Health expectancies are
     if (j>=(p+1))(v[j-p-1] = t[j]);    computed from the time spent in each health state according to a
   }    model. More health states you consider, more time is necessary to reach the
 }    Maximum Likelihood of the parameters involved in the model.  The
     simplest model is the multinomial logistic model where pij is the
 /********************** nrerror ********************/    probability to be observed in state j at the second wave
     conditional to be observed in state i at the first wave. Therefore
 void nrerror(char error_text[])    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
 {    'age' is age and 'sex' is a covariate. If you want to have a more
   fprintf(stderr,"ERREUR ...\n");    complex model than "constant and age", you should modify the program
   fprintf(stderr,"%s\n",error_text);    where the markup *Covariates have to be included here again* invites
   exit(1);    you to do it.  More covariates you add, slower the
 }    convergence.
 /*********************** vector *******************/  
 double *vector(int nl, int nh)    The advantage of this computer programme, compared to a simple
 {    multinomial logistic model, is clear when the delay between waves is not
   double *v;    identical for each individual. Also, if a individual missed an
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    intermediate interview, the information is lost, but taken into
   if (!v) nrerror("allocation failure in vector");    account using an interpolation or extrapolation.  
   return v-nl+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
 /************************ free vector ******************/    split into an exact number (nh*stepm) of unobserved intermediate
 void free_vector(double*v, int nl, int nh)    states. This elementary transition (by month, quarter,
 {    semester or year) is modelled as a multinomial logistic.  The hPx
   free((FREE_ARG)(v+nl-NR_END));    matrix is simply the matrix product of nh*stepm elementary matrices
 }    and the contribution of each individual to the likelihood is simply
     hPijx.
 /************************ivector *******************************/  
 int *ivector(long nl,long nh)    Also this programme outputs the covariance matrix of the parameters but also
 {    of the life expectancies. It also computes the period (stable) prevalence. 
   int *v;    
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   if (!v) nrerror("allocation failure in ivector");             Institut national d'études démographiques, Paris.
   return v-nl+NR_END;    This software have been partly granted by Euro-REVES, a concerted action
 }    from the European Union.
     It is copyrighted identically to a GNU software product, ie programme and
 /******************free ivector **************************/    software can be distributed freely for non commercial use. Latest version
 void free_ivector(int *v, long nl, long nh)    can be accessed at http://euroreves.ined.fr/imach .
 {  
   free((FREE_ARG)(v+nl-NR_END));    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
 }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
     
 /******************* imatrix *******************************/    **********************************************************************/
 int **imatrix(long nrl, long nrh, long ncl, long nch)  /*
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    main
 {    read parameterfile
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    read datafile
   int **m;    concatwav
      freqsummary
   /* allocate pointers to rows */    if (mle >= 1)
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));      mlikeli
   if (!m) nrerror("allocation failure 1 in matrix()");    print results files
   m += NR_END;    if mle==1 
   m -= nrl;       computes hessian
      read end of parameter file: agemin, agemax, bage, fage, estepm
          begin-prev-date,...
   /* allocate rows and set pointers to them */    open gnuplot file
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    open html file
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    period (stable) prevalence
   m[nrl] += NR_END;     for age prevalim()
   m[nrl] -= ncl;    h Pij x
      variance of p varprob
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    forecasting if prevfcast==1 prevforecast call prevalence()
      health expectancies
   /* return pointer to array of pointers to rows */    Variance-covariance of DFLE
   return m;    prevalence()
 }     movingaverage()
     varevsij() 
 /****************** free_imatrix *************************/    if popbased==1 varevsij(,popbased)
 void free_imatrix(m,nrl,nrh,ncl,nch)    total life expectancies
       int **m;    Variance of period (stable) prevalence
       long nch,ncl,nrh,nrl;   end
      /* free an int matrix allocated by imatrix() */  */
 {  
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));  
 }   
   #include <math.h>
 /******************* matrix *******************************/  #include <stdio.h>
 double **matrix(long nrl, long nrh, long ncl, long nch)  #include <stdlib.h>
 {  #include <string.h>
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  #include <unistd.h>
   double **m;  
   #include <limits.h>
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #include <sys/types.h>
   if (!m) nrerror("allocation failure 1 in matrix()");  #include <sys/stat.h>
   m += NR_END;  #include <errno.h>
   m -= nrl;  extern int errno;
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  /* #include <sys/time.h> */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #include <time.h>
   m[nrl] += NR_END;  #include "timeval.h"
   m[nrl] -= ncl;  
   /* #include <libintl.h> */
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  /* #define _(String) gettext (String) */
   return m;  
 }  #define MAXLINE 256
   
 /*************************free matrix ************************/  #define GNUPLOTPROGRAM "gnuplot"
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 {  #define FILENAMELENGTH 132
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 }  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
   
 /******************* ma3x *******************************/  #define MAXPARM 30 /* Maximum number of parameters for the optimization */
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;  #define NINTERVMAX 8
   double ***m;  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));  #define NCOVMAX 20 /* Maximum number of covariates */
   if (!m) nrerror("allocation failure 1 in matrix()");  #define MAXN 20000
   m += NR_END;  #define YEARM 12. /* Number of months per year */
   m -= nrl;  #define AGESUP 130
   #define AGEBASE 40
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  #ifdef UNIX
   m[nrl] += NR_END;  #define DIRSEPARATOR '/'
   m[nrl] -= ncl;  #define CHARSEPARATOR "/"
   #define ODIRSEPARATOR '\\'
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #else
   #define DIRSEPARATOR '\\'
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #define CHARSEPARATOR "\\"
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #define ODIRSEPARATOR '/'
   m[nrl][ncl] += NR_END;  #endif
   m[nrl][ncl] -= nll;  
   for (j=ncl+1; j<=nch; j++)  /* $Id$ */
     m[nrl][j]=m[nrl][j-1]+nlay;  /* $State$ */
    
   for (i=nrl+1; i<=nrh; i++) {  char version[]="Imach version 0.98i, June 2006, INED-EUROREVES-Institut de longevite ";
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  char fullversion[]="$Revision$ $Date$"; 
     for (j=ncl+1; j<=nch; j++)  char strstart[80];
       m[i][j]=m[i][j-1]+nlay;  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
   }  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
   return m;  int nvar=0;
 }  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
   int npar=NPARMAX;
 /*************************free ma3x ************************/  int nlstate=2; /* Number of live states */
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  int ndeath=1; /* Number of dead states */
 {  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  int popbased=0;
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));  int *wav; /* Number of waves for this individuual 0 is possible */
 }  int maxwav=0; /* Maxim number of waves */
   int jmin=0, jmax=0; /* min, max spacing between 2 waves */
 /***************** f1dim *************************/  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
 extern int ncom;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
 extern double *pcom,*xicom;                     to the likelihood and the sum of weights (done by funcone)*/
 extern double (*nrfunc)(double []);  int mle=1, weightopt=0;
    int **mw; /* mw[mi][i] is number of the mi wave for this individual */
 double f1dim(double x)  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
   int j;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
   double f;  double jmean=1; /* Mean space between 2 waves */
   double *xt;  double **oldm, **newm, **savm; /* Working pointers to matrices */
    double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
   xt=vector(1,ncom);  FILE *fic,*ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  FILE *ficlog, *ficrespow;
   f=(*nrfunc)(xt);  int globpr=0; /* Global variable for printing or not */
   free_vector(xt,1,ncom);  double fretone; /* Only one call to likelihood */
   return f;  long ipmx=0; /* Number of contributions */
 }  double sw; /* Sum of weights */
   char filerespow[FILENAMELENGTH];
 /*****************brent *************************/  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  FILE *ficresilk;
 {  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
   int iter;  FILE *ficresprobmorprev;
   double a,b,d,etemp;  FILE *fichtm, *fichtmcov; /* Html File */
   double fu,fv,fw,fx;  FILE *ficreseij;
   double ftemp;  char filerese[FILENAMELENGTH];
   double p,q,r,tol1,tol2,u,v,w,x,xm;  FILE *ficresstdeij;
   double e=0.0;  char fileresstde[FILENAMELENGTH];
    FILE *ficrescveij;
   a=(ax < cx ? ax : cx);  char filerescve[FILENAMELENGTH];
   b=(ax > cx ? ax : cx);  FILE  *ficresvij;
   x=w=v=bx;  char fileresv[FILENAMELENGTH];
   fw=fv=fx=(*f)(x);  FILE  *ficresvpl;
   for (iter=1;iter<=ITMAX;iter++) {  char fileresvpl[FILENAMELENGTH];
     xm=0.5*(a+b);  char title[MAXLINE];
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
     printf(".");fflush(stdout);  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
     fprintf(ficlog,".");fflush(ficlog);  char command[FILENAMELENGTH];
 #ifdef DEBUG  int  outcmd=0;
     printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  
     fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  
 #endif  char filelog[FILENAMELENGTH]; /* Log file */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  char filerest[FILENAMELENGTH];
       *xmin=x;  char fileregp[FILENAMELENGTH];
       return fx;  char popfile[FILENAMELENGTH];
     }  
     ftemp=fu;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
     if (fabs(e) > tol1) {  
       r=(x-w)*(fx-fv);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
       q=(x-v)*(fx-fw);  struct timezone tzp;
       p=(x-v)*q-(x-w)*r;  extern int gettimeofday();
       q=2.0*(q-r);  struct tm tmg, tm, tmf, *gmtime(), *localtime();
       if (q > 0.0) p = -p;  long time_value;
       q=fabs(q);  extern long time();
       etemp=e;  char strcurr[80], strfor[80];
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  char *endptr;
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  long lval;
       else {  double dval;
         d=p/q;  
         u=x+d;  #define NR_END 1
         if (u-a < tol2 || b-u < tol2)  #define FREE_ARG char*
           d=SIGN(tol1,xm-x);  #define FTOL 1.0e-10
       }  
     } else {  #define NRANSI 
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  #define ITMAX 200 
     }  
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  #define TOL 2.0e-4 
     fu=(*f)(u);  
     if (fu <= fx) {  #define CGOLD 0.3819660 
       if (u >= x) a=x; else b=x;  #define ZEPS 1.0e-10 
       SHFT(v,w,x,u)  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
         SHFT(fv,fw,fx,fu)  
         } else {  #define GOLD 1.618034 
           if (u < x) a=u; else b=u;  #define GLIMIT 100.0 
           if (fu <= fw || w == x) {  #define TINY 1.0e-20 
             v=w;  
             w=u;  static double maxarg1,maxarg2;
             fv=fw;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
             fw=fu;  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
           } else if (fu <= fv || v == x || v == w) {    
             v=u;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
             fv=fu;  #define rint(a) floor(a+0.5)
           }  
         }  static double sqrarg;
   }  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   nrerror("Too many iterations in brent");  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
   *xmin=x;  int agegomp= AGEGOMP;
   return fx;  
 }  int imx; 
   int stepm=1;
 /****************** mnbrak ***********************/  /* Stepm, step in month: minimum step interpolation*/
   
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  int estepm;
             double (*func)(double))  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 {  
   double ulim,u,r,q, dum;  int m,nb;
   double fu;  long *num;
    int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   *fa=(*func)(*ax);  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   *fb=(*func)(*bx);  double **pmmij, ***probs;
   if (*fb > *fa) {  double *ageexmed,*agecens;
     SHFT(dum,*ax,*bx,dum)  double dateintmean=0;
       SHFT(dum,*fb,*fa,dum)  
       }  double *weight;
   *cx=(*bx)+GOLD*(*bx-*ax);  int **s; /* Status */
   *fc=(*func)(*cx);  double *agedc, **covar, idx;
   while (*fb > *fc) {  int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
     r=(*bx-*ax)*(*fb-*fc);  double *lsurv, *lpop, *tpop;
     q=(*bx-*cx)*(*fb-*fa);  
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  double ftolhess; /* Tolerance for computing hessian */
     ulim=(*bx)+GLIMIT*(*cx-*bx);  
     if ((*bx-u)*(u-*cx) > 0.0) {  /**************** split *************************/
       fu=(*func)(u);  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     } else if ((*cx-u)*(u-ulim) > 0.0) {  {
       fu=(*func)(u);    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       if (fu < *fc) {       the name of the file (name), its extension only (ext) and its first part of the name (finame)
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    */ 
           SHFT(*fb,*fc,fu,(*func)(u))    char  *ss;                            /* pointer */
           }    int   l1, l2;                         /* length counters */
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;    l1 = strlen(path );                   /* length of path */
       fu=(*func)(u);    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
     } else {    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
       u=(*cx)+GOLD*(*cx-*bx);    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       fu=(*func)(u);      strcpy( name, path );               /* we got the fullname name because no directory */
     }      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     SHFT(*ax,*bx,*cx,u)        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       SHFT(*fa,*fb,*fc,fu)      /* get current working directory */
       }      /*    extern  char* getcwd ( char *buf , int len);*/
 }      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
         return( GLOCK_ERROR_GETCWD );
 /*************** linmin ************************/      }
       /* got dirc from getcwd*/
 int ncom;      printf(" DIRC = %s \n",dirc);
 double *pcom,*xicom;    } else {                              /* strip direcotry from path */
 double (*nrfunc)(double []);      ss++;                               /* after this, the filename */
        l2 = strlen( ss );                  /* length of filename */
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 {      strcpy( name, ss );         /* save file name */
   double brent(double ax, double bx, double cx,      strncpy( dirc, path, l1 - l2 );     /* now the directory */
                double (*f)(double), double tol, double *xmin);      dirc[l1-l2] = 0;                    /* add zero */
   double f1dim(double x);      printf(" DIRC2 = %s \n",dirc);
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    }
               double *fc, double (*func)(double));    /* We add a separator at the end of dirc if not exists */
   int j;    l1 = strlen( dirc );                  /* length of directory */
   double xx,xmin,bx,ax;    if( dirc[l1-1] != DIRSEPARATOR ){
   double fx,fb,fa;      dirc[l1] =  DIRSEPARATOR;
        dirc[l1+1] = 0; 
   ncom=n;      printf(" DIRC3 = %s \n",dirc);
   pcom=vector(1,n);    }
   xicom=vector(1,n);    ss = strrchr( name, '.' );            /* find last / */
   nrfunc=func;    if (ss >0){
   for (j=1;j<=n;j++) {      ss++;
     pcom[j]=p[j];      strcpy(ext,ss);                     /* save extension */
     xicom[j]=xi[j];      l1= strlen( name);
   }      l2= strlen(ss)+1;
   ax=0.0;      strncpy( finame, name, l1-l2);
   xx=1.0;      finame[l1-l2]= 0;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    }
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  
 #ifdef DEBUG    return( 0 );                          /* we're done */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  }
   fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
 #endif  
   for (j=1;j<=n;j++) {  /******************************************/
     xi[j] *= xmin;  
     p[j] += xi[j];  void replace_back_to_slash(char *s, char*t)
   }  {
   free_vector(xicom,1,n);    int i;
   free_vector(pcom,1,n);    int lg=0;
 }    i=0;
     lg=strlen(t);
 /*************** powell ************************/    for(i=0; i<= lg; i++) {
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,      (s[i] = t[i]);
             double (*func)(double []))      if (t[i]== '\\') s[i]='/';
 {    }
   void linmin(double p[], double xi[], int n, double *fret,  }
               double (*func)(double []));  
   int i,ibig,j;  int nbocc(char *s, char occ)
   double del,t,*pt,*ptt,*xit;  {
   double fp,fptt;    int i,j=0;
   double *xits;    int lg=20;
   pt=vector(1,n);    i=0;
   ptt=vector(1,n);    lg=strlen(s);
   xit=vector(1,n);    for(i=0; i<= lg; i++) {
   xits=vector(1,n);    if  (s[i] == occ ) j++;
   *fret=(*func)(p);    }
   for (j=1;j<=n;j++) pt[j]=p[j];    return j;
   for (*iter=1;;++(*iter)) {  }
     fp=(*fret);  
     ibig=0;  void cutv(char *u,char *v, char*t, char occ)
     del=0.0;  {
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
     fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f",*iter,*fret);       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
     for (i=1;i<=n;i++)       gives u="abcedf" and v="ghi2j" */
       printf(" %d %.12f",i, p[i]);    int i,lg,j,p=0;
     fprintf(ficlog," %d %.12f",i, p[i]);    i=0;
     printf("\n");    for(j=0; j<=strlen(t)-1; j++) {
     fprintf(ficlog,"\n");      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
     for (i=1;i<=n;i++) {    }
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  
       fptt=(*fret);    lg=strlen(t);
 #ifdef DEBUG    for(j=0; j<p; j++) {
       printf("fret=%lf \n",*fret);      (u[j] = t[j]);
       fprintf(ficlog,"fret=%lf \n",*fret);    }
 #endif       u[p]='\0';
       printf("%d",i);fflush(stdout);  
       fprintf(ficlog,"%d",i);fflush(ficlog);     for(j=0; j<= lg; j++) {
       linmin(p,xit,n,fret,func);      if (j>=(p+1))(v[j-p-1] = t[j]);
       if (fabs(fptt-(*fret)) > del) {    }
         del=fabs(fptt-(*fret));  }
         ibig=i;  
       }  /********************** nrerror ********************/
 #ifdef DEBUG  
       printf("%d %.12e",i,(*fret));  void nrerror(char error_text[])
       fprintf(ficlog,"%d %.12e",i,(*fret));  {
       for (j=1;j<=n;j++) {    fprintf(stderr,"ERREUR ...\n");
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);    fprintf(stderr,"%s\n",error_text);
         printf(" x(%d)=%.12e",j,xit[j]);    exit(EXIT_FAILURE);
         fprintf(ficlog," x(%d)=%.12e",j,xit[j]);  }
       }  /*********************** vector *******************/
       for(j=1;j<=n;j++) {  double *vector(int nl, int nh)
         printf(" p=%.12e",p[j]);  {
         fprintf(ficlog," p=%.12e",p[j]);    double *v;
       }    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
       printf("\n");    if (!v) nrerror("allocation failure in vector");
       fprintf(ficlog,"\n");    return v-nl+NR_END;
 #endif  }
     }  
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  /************************ free vector ******************/
 #ifdef DEBUG  void free_vector(double*v, int nl, int nh)
       int k[2],l;  {
       k[0]=1;    free((FREE_ARG)(v+nl-NR_END));
       k[1]=-1;  }
       printf("Max: %.12e",(*func)(p));  
       fprintf(ficlog,"Max: %.12e",(*func)(p));  /************************ivector *******************************/
       for (j=1;j<=n;j++) {  int *ivector(long nl,long nh)
         printf(" %.12e",p[j]);  {
         fprintf(ficlog," %.12e",p[j]);    int *v;
       }    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       printf("\n");    if (!v) nrerror("allocation failure in ivector");
       fprintf(ficlog,"\n");    return v-nl+NR_END;
       for(l=0;l<=1;l++) {  }
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  /******************free ivector **************************/
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  void free_ivector(int *v, long nl, long nh)
           fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  {
         }    free((FREE_ARG)(v+nl-NR_END));
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  }
         fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  
       }  /************************lvector *******************************/
 #endif  long *lvector(long nl,long nh)
   {
     long *v;
       free_vector(xit,1,n);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
       free_vector(xits,1,n);    if (!v) nrerror("allocation failure in ivector");
       free_vector(ptt,1,n);    return v-nl+NR_END;
       free_vector(pt,1,n);  }
       return;  
     }  /******************free lvector **************************/
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  void free_lvector(long *v, long nl, long nh)
     for (j=1;j<=n;j++) {  {
       ptt[j]=2.0*p[j]-pt[j];    free((FREE_ARG)(v+nl-NR_END));
       xit[j]=p[j]-pt[j];  }
       pt[j]=p[j];  
     }  /******************* imatrix *******************************/
     fptt=(*func)(ptt);  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     if (fptt < fp) {       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  { 
       if (t < 0.0) {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
         linmin(p,xit,n,fret,func);    int **m; 
         for (j=1;j<=n;j++) {    
           xi[j][ibig]=xi[j][n];    /* allocate pointers to rows */ 
           xi[j][n]=xit[j];    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
         }    if (!m) nrerror("allocation failure 1 in matrix()"); 
 #ifdef DEBUG    m += NR_END; 
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    m -= nrl; 
         fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);    
         for(j=1;j<=n;j++){    
           printf(" %.12e",xit[j]);    /* allocate rows and set pointers to them */ 
           fprintf(ficlog," %.12e",xit[j]);    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
         }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
         printf("\n");    m[nrl] += NR_END; 
         fprintf(ficlog,"\n");    m[nrl] -= ncl; 
 #endif    
       }    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
     }    
   }    /* return pointer to array of pointers to rows */ 
 }    return m; 
   } 
 /**** Prevalence limit ****************/  
   /****************** free_imatrix *************************/
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  void free_imatrix(m,nrl,nrh,ncl,nch)
 {        int **m;
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit        long nch,ncl,nrh,nrl; 
      matrix by transitions matrix until convergence is reached */       /* free an int matrix allocated by imatrix() */ 
   { 
   int i, ii,j,k;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   double min, max, maxmin, maxmax,sumnew=0.;    free((FREE_ARG) (m+nrl-NR_END)); 
   double **matprod2();  } 
   double **out, cov[NCOVMAX], **pmij();  
   double **newm;  /******************* matrix *******************************/
   double agefin, delaymax=50 ; /* Max number of years to converge */  double **matrix(long nrl, long nrh, long ncl, long nch)
   {
   for (ii=1;ii<=nlstate+ndeath;ii++)    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     for (j=1;j<=nlstate+ndeath;j++){    double **m;
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
     }    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
     if (!m) nrerror("allocation failure 1 in matrix()");
    cov[1]=1.;    m += NR_END;
      m -= nrl;
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     newm=savm;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     /* Covariates have to be included here again */    m[nrl] += NR_END;
      cov[2]=agefin;    m[nrl] -= ncl;
    
       for (k=1; k<=cptcovn;k++) {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    return m;
         /*      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]]);*/    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
       }     */
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  }
       for (k=1; k<=cptcovprod;k++)  
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  /*************************free matrix ************************/
   void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/  {
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    free((FREE_ARG)(m+nrl-NR_END));
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  }
   
     savm=oldm;  /******************* ma3x *******************************/
     oldm=newm;  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
     maxmax=0.;  {
     for(j=1;j<=nlstate;j++){    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       min=1.;    double ***m;
       max=0.;  
       for(i=1; i<=nlstate; i++) {    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
         sumnew=0;    if (!m) nrerror("allocation failure 1 in matrix()");
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];    m += NR_END;
         prlim[i][j]= newm[i][j]/(1-sumnew);    m -= nrl;
         max=FMAX(max,prlim[i][j]);  
         min=FMIN(min,prlim[i][j]);    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       maxmin=max-min;    m[nrl] += NR_END;
       maxmax=FMAX(maxmax,maxmin);    m[nrl] -= ncl;
     }  
     if(maxmax < ftolpl){    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
       return prlim;  
     }    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
   }    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
 }    m[nrl][ncl] += NR_END;
     m[nrl][ncl] -= nll;
 /*************** transition probabilities ***************/    for (j=ncl+1; j<=nch; j++) 
       m[nrl][j]=m[nrl][j-1]+nlay;
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )    
 {    for (i=nrl+1; i<=nrh; i++) {
   double s1, s2;      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
   /*double t34;*/      for (j=ncl+1; j<=nch; j++) 
   int i,j,j1, nc, ii, jj;        m[i][j]=m[i][j-1]+nlay;
     }
     for(i=1; i<= nlstate; i++){    return m; 
     for(j=1; j<i;j++){    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
         /*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);*/  
       }  /*************************free ma3x ************************/
       ps[i][j]=s2;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  {
     }    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     for(j=i+1; j<=nlstate+ndeath;j++){    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    free((FREE_ARG)(m+nrl-NR_END));
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  }
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }  /*************** function subdirf ***********/
       ps[i][j]=s2;  char *subdirf(char fileres[])
     }  {
   }    /* Caution optionfilefiname is hidden */
     /*ps[3][2]=1;*/    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/"); /* Add to the right */
   for(i=1; i<= nlstate; i++){    strcat(tmpout,fileres);
      s1=0;    return tmpout;
     for(j=1; j<i; j++)  }
       s1+=exp(ps[i][j]);  
     for(j=i+1; j<=nlstate+ndeath; j++)  /*************** function subdirf2 ***********/
       s1+=exp(ps[i][j]);  char *subdirf2(char fileres[], char *preop)
     ps[i][i]=1./(s1+1.);  {
     for(j=1; j<i; j++)    
       ps[i][j]= exp(ps[i][j])*ps[i][i];    /* Caution optionfilefiname is hidden */
     for(j=i+1; j<=nlstate+ndeath; j++)    strcpy(tmpout,optionfilefiname);
       ps[i][j]= exp(ps[i][j])*ps[i][i];    strcat(tmpout,"/");
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    strcat(tmpout,preop);
   } /* end i */    strcat(tmpout,fileres);
     return tmpout;
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  }
     for(jj=1; jj<= nlstate+ndeath; jj++){  
       ps[ii][jj]=0;  /*************** function subdirf3 ***********/
       ps[ii][ii]=1;  char *subdirf3(char fileres[], char *preop, char *preop2)
     }  {
   }    
     /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){    strcat(tmpout,"/");
     for(jj=1; jj<= nlstate+ndeath; jj++){    strcat(tmpout,preop);
      printf("%lf ",ps[ii][jj]);    strcat(tmpout,preop2);
    }    strcat(tmpout,fileres);
     printf("\n ");    return tmpout;
     }  }
     printf("\n ");printf("%lf ",cov[2]);*/  
 /*  /***************** f1dim *************************/
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  extern int ncom; 
   goto end;*/  extern double *pcom,*xicom;
     return ps;  extern double (*nrfunc)(double []); 
 }   
   double f1dim(double x) 
 /**************** Product of 2 matrices ******************/  { 
     int j; 
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)    double f;
 {    double *xt; 
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times   
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    xt=vector(1,ncom); 
   /* in, b, out are matrice of pointers which should have been initialized    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
      before: only the contents of out is modified. The function returns    f=(*nrfunc)(xt); 
      a pointer to pointers identical to out */    free_vector(xt,1,ncom); 
   long i, j, k;    return f; 
   for(i=nrl; i<= nrh; i++)  } 
     for(k=ncolol; k<=ncoloh; k++)  
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  /*****************brent *************************/
         out[i][k] +=in[i][j]*b[j][k];  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
   { 
   return out;    int iter; 
 }    double a,b,d,etemp;
     double fu,fv,fw,fx;
     double ftemp;
 /************* Higher Matrix Product ***************/    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     double e=0.0; 
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )   
 {    a=(ax < cx ? ax : cx); 
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    b=(ax > cx ? ax : cx); 
      duration (i.e. until    x=w=v=bx; 
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    fw=fv=fx=(*f)(x); 
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    for (iter=1;iter<=ITMAX;iter++) { 
      (typically every 2 years instead of every month which is too big).      xm=0.5*(a+b); 
      Model is determined by parameters x and covariates have to be      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
      included manually here.      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       printf(".");fflush(stdout);
      */      fprintf(ficlog,".");fflush(ficlog);
   #ifdef DEBUG
   int i, j, d, h, k;      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   double **out, cov[NCOVMAX];      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);
   double **newm;      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   #endif
   /* Hstepm could be zero and should return the unit matrix */      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   for (i=1;i<=nlstate+ndeath;i++)        *xmin=x; 
     for (j=1;j<=nlstate+ndeath;j++){        return fx; 
       oldm[i][j]=(i==j ? 1.0 : 0.0);      } 
       po[i][j][0]=(i==j ? 1.0 : 0.0);      ftemp=fu;
     }      if (fabs(e) > tol1) { 
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */        r=(x-w)*(fx-fv); 
   for(h=1; h <=nhstepm; h++){        q=(x-v)*(fx-fw); 
     for(d=1; d <=hstepm; d++){        p=(x-v)*q-(x-w)*r; 
       newm=savm;        q=2.0*(q-r); 
       /* Covariates have to be included here again */        if (q > 0.0) p = -p; 
       cov[1]=1.;        q=fabs(q); 
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;        etemp=e; 
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];        e=d; 
       for (k=1; k<=cptcovage;k++)        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       for (k=1; k<=cptcovprod;k++)        else { 
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];          d=p/q; 
           u=x+d; 
           if (u-a < tol2 || b-u < tol2) 
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/            d=SIGN(tol1,xm-x); 
       /*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,      } else { 
                    pmij(pmmij,cov,ncovmodel,x,nlstate));        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       savm=oldm;      } 
       oldm=newm;      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
     }      fu=(*f)(u); 
     for(i=1; i<=nlstate+ndeath; i++)      if (fu <= fx) { 
       for(j=1;j<=nlstate+ndeath;j++) {        if (u >= x) a=x; else b=x; 
         po[i][j][h]=newm[i][j];        SHFT(v,w,x,u) 
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);          SHFT(fv,fw,fx,fu) 
          */          } else { 
       }            if (u < x) a=u; else b=u; 
   } /* end h */            if (fu <= fw || w == x) { 
   return po;              v=w; 
 }              w=u; 
               fv=fw; 
               fw=fu; 
 /*************** log-likelihood *************/            } else if (fu <= fv || v == x || v == w) { 
 double func( double *x)              v=u; 
 {              fv=fu; 
   int i, ii, j, k, mi, d, kk;            } 
   double l, ll[NLSTATEMAX], cov[NCOVMAX];          } 
   double **out;    } 
   double sw; /* Sum of weights */    nrerror("Too many iterations in brent"); 
   double lli; /* Individual log likelihood */    *xmin=x; 
   long ipmx;    return fx; 
   /*extern weight */  } 
   /* We are differentiating ll according to initial status */  
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  /****************** mnbrak ***********************/
   /*for(i=1;i<imx;i++)  
     printf(" %d\n",s[4][i]);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
   */              double (*func)(double)) 
   cov[1]=1.;  { 
     double ulim,u,r,q, dum;
   for(k=1; k<=nlstate; k++) ll[k]=0.;    double fu; 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){   
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    *fa=(*func)(*ax); 
     for(mi=1; mi<= wav[i]-1; mi++){    *fb=(*func)(*bx); 
       for (ii=1;ii<=nlstate+ndeath;ii++)    if (*fb > *fa) { 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);      SHFT(dum,*ax,*bx,dum) 
       for(d=0; d<dh[mi][i]; d++){        SHFT(dum,*fb,*fa,dum) 
         newm=savm;        } 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;    *cx=(*bx)+GOLD*(*bx-*ax); 
         for (kk=1; kk<=cptcovage;kk++) {    *fc=(*func)(*cx); 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    while (*fb > *fc) { 
         }      r=(*bx-*ax)*(*fb-*fc); 
              q=(*bx-*cx)*(*fb-*fa); 
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
         savm=oldm;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
         oldm=newm;      if ((*bx-u)*(u-*cx) > 0.0) { 
                fu=(*func)(u); 
              } else if ((*cx-u)*(u-ulim) > 0.0) { 
       } /* end mult */        fu=(*func)(u); 
              if (fu < *fc) { 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/            SHFT(*fb,*fc,fu,(*func)(u)) 
       ipmx +=1;            } 
       sw += weight[i];      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;        u=ulim; 
     } /* end of wave */        fu=(*func)(u); 
   } /* end of individual */      } else { 
         u=(*cx)+GOLD*(*cx-*bx); 
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];        fu=(*func)(u); 
   /* 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 */      SHFT(*ax,*bx,*cx,u) 
   return -l;        SHFT(*fa,*fb,*fc,fu) 
 }        } 
   } 
   
 /*********** Maximum Likelihood Estimation ***************/  /*************** linmin ************************/
   
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  int ncom; 
 {  double *pcom,*xicom;
   int i,j, iter;  double (*nrfunc)(double []); 
   double **xi,*delti;   
   double fret;  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   xi=matrix(1,npar,1,npar);  { 
   for (i=1;i<=npar;i++)    double brent(double ax, double bx, double cx, 
     for (j=1;j<=npar;j++)                 double (*f)(double), double tol, double *xmin); 
       xi[i][j]=(i==j ? 1.0 : 0.0);    double f1dim(double x); 
   printf("Powell\n");  fprintf(ficlog,"Powell\n");    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   powell(p,xi,npar,ftol,&iter,&fret,func);                double *fc, double (*func)(double)); 
     int j; 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    double xx,xmin,bx,ax; 
   fprintf(ficlog,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));    double fx,fb,fa;
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));   
     ncom=n; 
 }    pcom=vector(1,n); 
     xicom=vector(1,n); 
 /**** Computes Hessian and covariance matrix ***/    nrfunc=func; 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    for (j=1;j<=n;j++) { 
 {      pcom[j]=p[j]; 
   double  **a,**y,*x,pd;      xicom[j]=xi[j]; 
   double **hess;    } 
   int i, j,jk;    ax=0.0; 
   int *indx;    xx=1.0; 
     mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   double hessii(double p[], double delta, int theta, double delti[]);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   double hessij(double p[], double delti[], int i, int j);  #ifdef DEBUG
   void lubksb(double **a, int npar, int *indx, double b[]) ;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   void ludcmp(double **a, int npar, int *indx, double *d) ;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   #endif
   hess=matrix(1,npar,1,npar);    for (j=1;j<=n;j++) { 
       xi[j] *= xmin; 
   printf("\nCalculation of the hessian matrix. Wait...\n");      p[j] += xi[j]; 
   fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");    } 
   for (i=1;i<=npar;i++){    free_vector(xicom,1,n); 
     printf("%d",i);fflush(stdout);    free_vector(pcom,1,n); 
     fprintf(ficlog,"%d",i);fflush(ficlog);  } 
     hess[i][i]=hessii(p,ftolhess,i,delti);  
     /*printf(" %f ",p[i]);*/  char *asc_diff_time(long time_sec, char ascdiff[])
     /*printf(" %lf ",hess[i][i]);*/  {
   }    long sec_left, days, hours, minutes;
      days = (time_sec) / (60*60*24);
   for (i=1;i<=npar;i++) {    sec_left = (time_sec) % (60*60*24);
     for (j=1;j<=npar;j++)  {    hours = (sec_left) / (60*60) ;
       if (j>i) {    sec_left = (sec_left) %(60*60);
         printf(".%d%d",i,j);fflush(stdout);    minutes = (sec_left) /60;
         fprintf(ficlog,".%d%d",i,j);fflush(ficlog);    sec_left = (sec_left) % (60);
         hess[i][j]=hessij(p,delti,i,j);    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
         hess[j][i]=hess[i][j];        return ascdiff;
         /*printf(" %lf ",hess[i][j]);*/  }
       }  
     }  /*************** powell ************************/
   }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
   printf("\n");              double (*func)(double [])) 
   fprintf(ficlog,"\n");  { 
     void linmin(double p[], double xi[], int n, double *fret, 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");                double (*func)(double [])); 
   fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");    int i,ibig,j; 
      double del,t,*pt,*ptt,*xit;
   a=matrix(1,npar,1,npar);    double fp,fptt;
   y=matrix(1,npar,1,npar);    double *xits;
   x=vector(1,npar);    int niterf, itmp;
   indx=ivector(1,npar);  
   for (i=1;i<=npar;i++)    pt=vector(1,n); 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];    ptt=vector(1,n); 
   ludcmp(a,npar,indx,&pd);    xit=vector(1,n); 
     xits=vector(1,n); 
   for (j=1;j<=npar;j++) {    *fret=(*func)(p); 
     for (i=1;i<=npar;i++) x[i]=0;    for (j=1;j<=n;j++) pt[j]=p[j]; 
     x[j]=1;    for (*iter=1;;++(*iter)) { 
     lubksb(a,npar,indx,x);      fp=(*fret); 
     for (i=1;i<=npar;i++){      ibig=0; 
       matcov[i][j]=x[i];      del=0.0; 
     }      last_time=curr_time;
   }      (void) gettimeofday(&curr_time,&tzp);
       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);
   printf("\n#Hessian matrix#\n");      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
   fprintf(ficlog,"\n#Hessian matrix#\n");  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
   for (i=1;i<=npar;i++) {     for (i=1;i<=n;i++) {
     for (j=1;j<=npar;j++) {        printf(" %d %.12f",i, p[i]);
       printf("%.3e ",hess[i][j]);        fprintf(ficlog," %d %.12lf",i, p[i]);
       fprintf(ficlog,"%.3e ",hess[i][j]);        fprintf(ficrespow," %.12lf", p[i]);
     }      }
     printf("\n");      printf("\n");
     fprintf(ficlog,"\n");      fprintf(ficlog,"\n");
   }      fprintf(ficrespow,"\n");fflush(ficrespow);
       if(*iter <=3){
   /* Recompute Inverse */        tm = *localtime(&curr_time.tv_sec);
   for (i=1;i<=npar;i++)        strcpy(strcurr,asctime(&tm));
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  /*       asctime_r(&tm,strcurr); */
   ludcmp(a,npar,indx,&pd);        forecast_time=curr_time; 
         itmp = strlen(strcurr);
   /*  printf("\n#Hessian matrix recomputed#\n");        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
           strcurr[itmp-1]='\0';
   for (j=1;j<=npar;j++) {        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     for (i=1;i<=npar;i++) x[i]=0;        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     x[j]=1;        for(niterf=10;niterf<=30;niterf+=10){
     lubksb(a,npar,indx,x);          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
     for (i=1;i<=npar;i++){          tmf = *localtime(&forecast_time.tv_sec);
       y[i][j]=x[i];  /*      asctime_r(&tmf,strfor); */
       printf("%.3e ",y[i][j]);          strcpy(strfor,asctime(&tmf));
       fprintf(ficlog,"%.3e ",y[i][j]);          itmp = strlen(strfor);
     }          if(strfor[itmp-1]=='\n')
     printf("\n");          strfor[itmp-1]='\0';
     fprintf(ficlog,"\n");          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);
   */        }
       }
   free_matrix(a,1,npar,1,npar);      for (i=1;i<=n;i++) { 
   free_matrix(y,1,npar,1,npar);        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   free_vector(x,1,npar);        fptt=(*fret); 
   free_ivector(indx,1,npar);  #ifdef DEBUG
   free_matrix(hess,1,npar,1,npar);        printf("fret=%lf \n",*fret);
         fprintf(ficlog,"fret=%lf \n",*fret);
   #endif
 }        printf("%d",i);fflush(stdout);
         fprintf(ficlog,"%d",i);fflush(ficlog);
 /*************** hessian matrix ****************/        linmin(p,xit,n,fret,func); 
 double hessii( double x[], double delta, int theta, double delti[])        if (fabs(fptt-(*fret)) > del) { 
 {          del=fabs(fptt-(*fret)); 
   int i;          ibig=i; 
   int l=1, lmax=20;        } 
   double k1,k2;  #ifdef DEBUG
   double p2[NPARMAX+1];        printf("%d %.12e",i,(*fret));
   double res;        fprintf(ficlog,"%d %.12e",i,(*fret));
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;        for (j=1;j<=n;j++) {
   double fx;          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
   int k=0,kmax=10;          printf(" x(%d)=%.12e",j,xit[j]);
   double l1;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         }
   fx=func(x);        for(j=1;j<=n;j++) {
   for (i=1;i<=npar;i++) p2[i]=x[i];          printf(" p=%.12e",p[j]);
   for(l=0 ; l <=lmax; l++){          fprintf(ficlog," p=%.12e",p[j]);
     l1=pow(10,l);        }
     delts=delt;        printf("\n");
     for(k=1 ; k <kmax; k=k+1){        fprintf(ficlog,"\n");
       delt = delta*(l1*k);  #endif
       p2[theta]=x[theta] +delt;      } 
       k1=func(p2)-fx;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       p2[theta]=x[theta]-delt;  #ifdef DEBUG
       k2=func(p2)-fx;        int k[2],l;
       /*res= (k1-2.0*fx+k2)/delt/delt; */        k[0]=1;
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        k[1]=-1;
              printf("Max: %.12e",(*func)(p));
 #ifdef DEBUG        fprintf(ficlog,"Max: %.12e",(*func)(p));
       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);        for (j=1;j<=n;j++) {
       fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);          printf(" %.12e",p[j]);
 #endif          fprintf(ficlog," %.12e",p[j]);
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */        }
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){        printf("\n");
         k=kmax;        fprintf(ficlog,"\n");
       }        for(l=0;l<=1;l++) {
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */          for (j=1;j<=n;j++) {
         k=kmax; l=lmax*10.;            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
       }            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
         delts=delt;          }
       }          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     }          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
   }        }
   delti[theta]=delts;  #endif
   return res;  
    
 }        free_vector(xit,1,n); 
         free_vector(xits,1,n); 
 double hessij( double x[], double delti[], int thetai,int thetaj)        free_vector(ptt,1,n); 
 {        free_vector(pt,1,n); 
   int i;        return; 
   int l=1, l1, lmax=20;      } 
   double k1,k2,k3,k4,res,fx;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   double p2[NPARMAX+1];      for (j=1;j<=n;j++) { 
   int k;        ptt[j]=2.0*p[j]-pt[j]; 
         xit[j]=p[j]-pt[j]; 
   fx=func(x);        pt[j]=p[j]; 
   for (k=1; k<=2; k++) {      } 
     for (i=1;i<=npar;i++) p2[i]=x[i];      fptt=(*func)(ptt); 
     p2[thetai]=x[thetai]+delti[thetai]/k;      if (fptt < fp) { 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     k1=func(p2)-fx;        if (t < 0.0) { 
            linmin(p,xit,n,fret,func); 
     p2[thetai]=x[thetai]+delti[thetai]/k;          for (j=1;j<=n;j++) { 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            xi[j][ibig]=xi[j][n]; 
     k2=func(p2)-fx;            xi[j][n]=xit[j]; 
            }
     p2[thetai]=x[thetai]-delti[thetai]/k;  #ifdef DEBUG
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
     k3=func(p2)-fx;          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
            for(j=1;j<=n;j++){
     p2[thetai]=x[thetai]-delti[thetai]/k;            printf(" %.12e",xit[j]);
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;            fprintf(ficlog," %.12e",xit[j]);
     k4=func(p2)-fx;          }
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */          printf("\n");
 #ifdef DEBUG          fprintf(ficlog,"\n");
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);  #endif
     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      } 
   }    } 
   return res;  } 
 }  
   /**** Prevalence limit (stable or period prevalence)  ****************/
 /************** Inverse of matrix **************/  
 void ludcmp(double **a, int n, int *indx, double *d)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
 {  {
   int i,imax,j,k;    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
   double big,dum,sum,temp;       matrix by transitions matrix until convergence is reached */
   double *vv;  
      int i, ii,j,k;
   vv=vector(1,n);    double min, max, maxmin, maxmax,sumnew=0.;
   *d=1.0;    double **matprod2();
   for (i=1;i<=n;i++) {    double **out, cov[NCOVMAX], **pmij();
     big=0.0;    double **newm;
     for (j=1;j<=n;j++)    double agefin, delaymax=50 ; /* Max number of years to converge */
       if ((temp=fabs(a[i][j])) > big) big=temp;  
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    for (ii=1;ii<=nlstate+ndeath;ii++)
     vv[i]=1.0/big;      for (j=1;j<=nlstate+ndeath;j++){
   }        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (j=1;j<=n;j++) {      }
     for (i=1;i<j;i++) {  
       sum=a[i][j];     cov[1]=1.;
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];   
       a[i][j]=sum;   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     }    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
     big=0.0;      newm=savm;
     for (i=j;i<=n;i++) {      /* Covariates have to be included here again */
       sum=a[i][j];       cov[2]=agefin;
       for (k=1;k<j;k++)    
         sum -= a[i][k]*a[k][j];        for (k=1; k<=cptcovn;k++) {
       a[i][j]=sum;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
       if ( (dum=vv[i]*fabs(sum)) >= big) {          /*      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]]);*/
         big=dum;        }
         imax=i;        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]]];
     if (j != imax) {  
       for (k=1;k<=n;k++) {        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         dum=a[imax][k];        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         a[imax][k]=a[j][k];        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
         a[j][k]=dum;      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
       }  
       *d = -(*d);      savm=oldm;
       vv[imax]=vv[j];      oldm=newm;
     }      maxmax=0.;
     indx[j]=imax;      for(j=1;j<=nlstate;j++){
     if (a[j][j] == 0.0) a[j][j]=TINY;        min=1.;
     if (j != n) {        max=0.;
       dum=1.0/(a[j][j]);        for(i=1; i<=nlstate; i++) {
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          sumnew=0;
     }          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   }          prlim[i][j]= newm[i][j]/(1-sumnew);
   free_vector(vv,1,n);  /* Doesn't work */          max=FMAX(max,prlim[i][j]);
 ;          min=FMIN(min,prlim[i][j]);
 }        }
         maxmin=max-min;
 void lubksb(double **a, int n, int *indx, double b[])        maxmax=FMAX(maxmax,maxmin);
 {      }
   int i,ii=0,ip,j;      if(maxmax < ftolpl){
   double sum;        return prlim;
        }
   for (i=1;i<=n;i++) {    }
     ip=indx[i];  }
     sum=b[ip];  
     b[ip]=b[i];  /*************** transition probabilities ***************/ 
     if (ii)  
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
     else if (sum) ii=i;  {
     b[i]=sum;    double s1, s2;
   }    /*double t34;*/
   for (i=n;i>=1;i--) {    int i,j,j1, nc, ii, jj;
     sum=b[i];  
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];      for(i=1; i<= nlstate; i++){
     b[i]=sum/a[i][i];        for(j=1; j<i;j++){
   }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
 }            /*s2 += param[i][j][nc]*cov[nc];*/
             s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
 /************ Frequencies ********************/  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2,double jprev1, double mprev1,double anprev1,double jprev2, double mprev2,double anprev2)          }
 {  /* Some frequencies */          ps[i][j]=s2;
    /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;        }
   int first;        for(j=i+1; j<=nlstate+ndeath;j++){
   double ***freq; /* Frequencies */          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
   double *pp;            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
   double pos, k2, dateintsum=0,k2cpt=0;  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
   FILE *ficresp;          }
   char fileresp[FILENAMELENGTH];          ps[i][j]=s2;
          }
   pp=vector(1,nlstate);      }
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);      /*ps[3][2]=1;*/
   strcpy(fileresp,"p");      
   strcat(fileresp,fileres);      for(i=1; i<= nlstate; i++){
   if((ficresp=fopen(fileresp,"w"))==NULL) {        s1=0;
     printf("Problem with prevalence resultfile: %s\n", fileresp);        for(j=1; j<i; j++)
     fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);          s1+=exp(ps[i][j]);
     exit(0);        for(j=i+1; j<=nlstate+ndeath; j++)
   }          s1+=exp(ps[i][j]);
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        ps[i][i]=1./(s1+1.);
   j1=0;        for(j=1; j<i; j++)
            ps[i][j]= exp(ps[i][j])*ps[i][i];
   j=cptcoveff;        for(j=i+1; j<=nlstate+ndeath; j++)
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          ps[i][j]= exp(ps[i][j])*ps[i][i];
         /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
   first=1;      } /* end i */
       
   for(k1=1; k1<=j;k1++){      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     for(i1=1; i1<=ncodemax[k1];i1++){        for(jj=1; jj<= nlstate+ndeath; jj++){
       j1++;          ps[ii][jj]=0;
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);          ps[ii][ii]=1;
         scanf("%d", i);*/        }
       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;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
        /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
       dateintsum=0;  /*         printf("ddd %lf ",ps[ii][jj]); */
       k2cpt=0;  /*       } */
       for (i=1; i<=imx; i++) {  /*       printf("\n "); */
         bool=1;  /*        } */
         if  (cptcovn>0) {  /*        printf("\n ");printf("%lf ",cov[2]); */
           for (z1=1; z1<=cptcoveff; z1++)         /*
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        for(i=1; i<= npar; i++) printf("%f ",x[i]);
               bool=0;        goto end;*/
         }      return ps;
         if (bool==1) {  }
           for(m=firstpass; m<=lastpass; m++){  
             k2=anint[m][i]+(mint[m][i]/12.);  /**************** Product of 2 matrices ******************/
             if ((k2>=dateprev1) && (k2<=dateprev2)) {  
               if(agev[m][i]==0) agev[m][i]=agemax+1;  double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
               if(agev[m][i]==1) agev[m][i]=agemax+2;  {
               if (m<lastpass) {    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    /* in, b, out are matrice of pointers which should have been initialized 
               }       before: only the contents of out is modified. The function returns
                     a pointer to pointers identical to out */
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {    long i, j, k;
                 dateintsum=dateintsum+k2;    for(i=nrl; i<= nrh; i++)
                 k2cpt++;      for(k=ncolol; k<=ncoloh; k++)
               }        for(j=ncl,out[i][k]=0.; j<=nch; j++)
             }          out[i][k] +=in[i][j]*b[j][k];
           }  
         }    return out;
       }  }
          
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
   /************* Higher Matrix Product ***************/
       if  (cptcovn>0) {  
         fprintf(ficresp, "\n#********** Variable ");  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);  {
         fprintf(ficresp, "**********\n#");    /* Computes the transition matrix starting at age 'age' over 
       }       'nhstepm*hstepm*stepm' months (i.e. until
       for(i=1; i<=nlstate;i++)       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);       nhstepm*hstepm matrices. 
       fprintf(ficresp, "\n");       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
             (typically every 2 years instead of every month which is too big 
       for(i=(int)agemin; i <= (int)agemax+3; i++){       for the memory).
         if(i==(int)agemax+3){       Model is determined by parameters x and covariates have to be 
           fprintf(ficlog,"Total");       included manually here. 
         }else{  
           if(first==1){       */
             first=0;  
             printf("See log file for details...\n");    int i, j, d, h, k;
           }    double **out, cov[NCOVMAX];
           fprintf(ficlog,"Age %d", i);    double **newm;
         }  
         for(jk=1; jk <=nlstate ; jk++){    /* Hstepm could be zero and should return the unit matrix */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)    for (i=1;i<=nlstate+ndeath;i++)
             pp[jk] += freq[jk][m][i];      for (j=1;j<=nlstate+ndeath;j++){
         }        oldm[i][j]=(i==j ? 1.0 : 0.0);
         for(jk=1; jk <=nlstate ; jk++){        po[i][j][0]=(i==j ? 1.0 : 0.0);
           for(m=-1, pos=0; m <=0 ; m++)      }
             pos += freq[jk][m][i];    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
           if(pp[jk]>=1.e-10){    for(h=1; h <=nhstepm; h++){
             if(first==1){      for(d=1; d <=hstepm; d++){
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        newm=savm;
             }        /* Covariates have to be included here again */
             fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);        cov[1]=1.;
           }else{        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
             if(first==1)        for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
               printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        for (k=1; k<=cptcovage;k++)
             fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           }        for (k=1; k<=cptcovprod;k++)
         }          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
             pp[jk] += freq[jk][m][i];        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
         }        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
                      pmij(pmmij,cov,ncovmodel,x,nlstate));
         for(jk=1,pos=0; jk <=nlstate ; jk++)        savm=oldm;
           pos += pp[jk];        oldm=newm;
         for(jk=1; jk <=nlstate ; jk++){      }
           if(pos>=1.e-5){      for(i=1; i<=nlstate+ndeath; i++)
             if(first==1)        for(j=1;j<=nlstate+ndeath;j++) {
               printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          po[i][j][h]=newm[i][j];
             fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
           }else{        }
             if(first==1)      /*printf("h=%d ",h);*/
               printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    } /* end h */
             fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);  /*     printf("\n H=%d \n",h); */
           }    return po;
           if( i <= (int) agemax){  }
             if(pos>=1.e-5){  
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  
               probs[i][jk][j1]= pp[jk]/pos;  /*************** log-likelihood *************/
               /*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 func( double *x)
             }  {
             else    int i, ii, j, k, mi, d, kk;
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    double l, ll[NLSTATEMAX], cov[NCOVMAX];
           }    double **out;
         }    double sw; /* Sum of weights */
            double lli; /* Individual log likelihood */
         for(jk=-1; jk <=nlstate+ndeath; jk++)    int s1, s2;
           for(m=-1; m <=nlstate+ndeath; m++)    double bbh, survp;
             if(freq[jk][m][i] !=0 ) {    long ipmx;
             if(first==1)    /*extern weight */
               printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    /* We are differentiating ll according to initial status */
               fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
             }    /*for(i=1;i<imx;i++) 
         if(i <= (int) agemax)      printf(" %d\n",s[4][i]);
           fprintf(ficresp,"\n");    */
         if(first==1)    cov[1]=1.;
           printf("Others in log...\n");  
         fprintf(ficlog,"\n");    for(k=1; k<=nlstate; k++) ll[k]=0.;
       }  
     }    if(mle==1){
   }      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   dateintmean=dateintsum/k2cpt;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          for(mi=1; mi<= wav[i]-1; mi++){
   fclose(ficresp);          for (ii=1;ii<=nlstate+ndeath;ii++)
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);            for (j=1;j<=nlstate+ndeath;j++){
   free_vector(pp,1,nlstate);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                savm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* End of Freq */            }
 }          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
 /************ Prevalence ********************/            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
 void prevalence(int agemin, float agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, double calagedate)            for (kk=1; kk<=cptcovage;kk++) {
 {  /* Some frequencies */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
              }
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double ***freq; /* Frequencies */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   double *pp;            savm=oldm;
   double pos, k2;            oldm=newm;
           } /* end mult */
   pp=vector(1,nlstate);        
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
            /* But now since version 0.9 we anticipate for bias at large stepm.
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);           * If stepm is larger than one month (smallest stepm) and if the exact delay 
   j1=0;           * (in months) between two waves is not a multiple of stepm, we rounded to 
             * the nearest (and in case of equal distance, to the lowest) interval but now
   j=cptcoveff;           * we keep into memory the bias bh[mi][i] and also the previous matrix product
   if (cptcovn<1) {j=1;ncodemax[1]=1;}           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
             * probability in order to take into account the bias as a fraction of the way
   for(k1=1; k1<=j;k1++){           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
     for(i1=1; i1<=ncodemax[k1];i1++){           * -stepm/2 to stepm/2 .
       j1++;           * 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+ndeath; i++)             */
         for (jk=-1; jk<=nlstate+ndeath; jk++)            s1=s[mw[mi][i]][i];
           for(m=agemin; m <= agemax+3; m++)          s2=s[mw[mi+1][i]][i];
             freq[i][jk][m]=0;          bbh=(double)bh[mi][i]/(double)stepm; 
                /* bias bh is positive if real duration
       for (i=1; i<=imx; i++) {           * is higher than the multiple of stepm and negative otherwise.
         bool=1;           */
         if  (cptcovn>0) {          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
           for (z1=1; z1<=cptcoveff; z1++)          if( s2 > nlstate){ 
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])            /* i.e. if s2 is a death state and if the date of death is known 
               bool=0;               then the contribution to the likelihood is the probability to 
         }               die between last step unit time and current  step unit time, 
         if (bool==1) {               which is also equal to probability to die before dh 
           for(m=firstpass; m<=lastpass; m++){               minus probability to die before dh-stepm . 
             k2=anint[m][i]+(mint[m][i]/12.);               In version up to 0.92 likelihood was computed
             if ((k2>=dateprev1) && (k2<=dateprev2)) {          as if date of death was unknown. Death was treated as any other
               if(agev[m][i]==0) agev[m][i]=agemax+1;          health state: the date of the interview describes the actual state
               if(agev[m][i]==1) agev[m][i]=agemax+2;          and not the date of a change in health state. The former idea was
               if (m<lastpass) {          to consider that at each interview the state was recorded
                 if (calagedate>0)          (healthy, disable or death) and IMaCh was corrected; but when we
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];          introduced the exact date of death then we should have modified
                 else          the contribution of an exact death to the likelihood. This new
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];          contribution is smaller and very dependent of the step unit
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];          stepm. It is no more the probability to die between last interview
               }          and month of death but the probability to survive from last
             }          interview up to one month before death multiplied by the
           }          probability to die within a month. Thanks to Chris
         }          Jackson for correcting this bug.  Former versions increased
       }          mortality artificially. The bad side is that we add another loop
       for(i=(int)agemin; i <= (int)agemax+3; i++){          which slows down the processing. The difference can be up to 10%
         for(jk=1; jk <=nlstate ; jk++){          lower mortality.
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)            */
             pp[jk] += freq[jk][m][i];            lli=log(out[s1][s2] - savm[s1][s2]);
         }  
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=-1, pos=0; m <=0 ; m++)          } else if  (s2==-2) {
             pos += freq[jk][m][i];            for (j=1,survp=0. ; j<=nlstate; j++) 
         }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
                    /*survp += out[s1][j]; */
         for(jk=1; jk <=nlstate ; jk++){            lli= log(survp);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)          }
             pp[jk] += freq[jk][m][i];          
         }          else if  (s2==-4) { 
                    for (j=3,survp=0. ; j<=nlstate; j++)  
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
                    lli= log(survp); 
         for(jk=1; jk <=nlstate ; jk++){              } 
           if( i <= (int) agemax){  
             if(pos>=1.e-5){          else if  (s2==-5) { 
               probs[i][jk][j1]= pp[jk]/pos;            for (j=1,survp=0. ; j<=2; j++)  
             }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           }            lli= log(survp); 
         }/* end jk */          } 
       }/* end i */          
     } /* end i1 */          else{
   } /* end k1 */            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 */
            } 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
   free_vector(pp,1,nlstate);          /*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); */
 }  /* End of Freq */          ipmx +=1;
           sw += weight[i];
 /************* Waves Concatenation ***************/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         } /* end of wave */
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)      } /* end of individual */
 {    }  else if(mle==2){
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
      Death is a valid wave (if date is known).        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        for(mi=1; mi<= wav[i]-1; mi++){
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]          for (ii=1;ii<=nlstate+ndeath;ii++)
      and mw[mi+1][i]. dh depends on stepm.            for (j=1;j<=nlstate+ndeath;j++){
      */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
   int i, mi, m;            }
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          for(d=0; d<=dh[mi][i]; d++){
      double sum=0., jmean=0.;*/            newm=savm;
   int first;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   int j, k=0,jk, ju, jl;            for (kk=1; kk<=cptcovage;kk++) {
   double sum=0.;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   first=0;            }
   jmin=1e+5;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   jmax=-1;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   jmean=0.;            savm=oldm;
   for(i=1; i<=imx; i++){            oldm=newm;
     mi=0;          } /* end mult */
     m=firstpass;        
     while(s[m][i] <= nlstate){          s1=s[mw[mi][i]][i];
       if(s[m][i]>=1)          s2=s[mw[mi+1][i]][i];
         mw[++mi][i]=m;          bbh=(double)bh[mi][i]/(double)stepm; 
       if(m >=lastpass)          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 */
         break;          ipmx +=1;
       else          sw += weight[i];
         m++;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }/* end while */        } /* end of wave */
     if (s[m][i] > nlstate){      } /* end of individual */
       mi++;     /* Death is another wave */    }  else if(mle==3){  /* exponential inter-extrapolation */
       /* if(mi==0)  never been interviewed correctly before death */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
          /* Only death is a correct wave */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       mw[mi][i]=m;        for(mi=1; mi<= wav[i]-1; mi++){
     }          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
     wav[i]=mi;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     if(mi==0){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       if(first==0){            }
         printf("Warning, no any valid information for:%d line=%d and may be others, see log file\n",num[i],i);          for(d=0; d<dh[mi][i]; d++){
         first=1;            newm=savm;
       }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       if(first==1){            for (kk=1; kk<=cptcovage;kk++) {
         fprintf(ficlog,"Warning, no any valid information for:%d line=%d\n",num[i],i);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       }            }
     } /* end mi==0 */            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
   for(i=1; i<=imx; i++){            oldm=newm;
     for(mi=1; mi<wav[i];mi++){          } /* end mult */
       if (stepm <=0)        
         dh[mi][i]=1;          s1=s[mw[mi][i]][i];
       else{          s2=s[mw[mi+1][i]][i];
         if (s[mw[mi+1][i]][i] > nlstate) {          bbh=(double)bh[mi][i]/(double)stepm; 
           if (agedc[i] < 2*AGESUP) {          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 */
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);          ipmx +=1;
           if(j==0) j=1;  /* Survives at least one month after exam */          sw += weight[i];
           k=k+1;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
           if (j >= jmax) jmax=j;        } /* end of wave */
           if (j <= jmin) jmin=j;      } /* end of individual */
           sum=sum+j;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
           /*if (j<0) printf("j=%d num=%d \n",j,i); */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         }        for(mi=1; mi<= wav[i]-1; mi++){
         else{          for (ii=1;ii<=nlstate+ndeath;ii++)
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));            for (j=1;j<=nlstate+ndeath;j++){
           k=k+1;              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           if (j >= jmax) jmax=j;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           else if (j <= jmin)jmin=j;            }
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */          for(d=0; d<dh[mi][i]; d++){
           sum=sum+j;            newm=savm;
         }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         jk= j/stepm;            for (kk=1; kk<=cptcovage;kk++) {
         jl= j -jk*stepm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         ju= j -(jk+1)*stepm;            }
         if(jl <= -ju)          
           dh[mi][i]=jk;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
         else                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           dh[mi][i]=jk+1;            savm=oldm;
         if(dh[mi][i]==0)            oldm=newm;
           dh[mi][i]=1; /* At least one step */          } /* end mult */
       }        
     }          s1=s[mw[mi][i]][i];
   }          s2=s[mw[mi+1][i]][i];
   jmean=sum/k;          if( s2 > nlstate){ 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);            lli=log(out[s1][s2] - savm[s1][s2]);
   fprintf(ficlog,"Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);          }else{
  }            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
           }
 /*********** Tricode ****************************/          ipmx +=1;
 void tricode(int *Tvar, int **nbcode, int imx)          sw += weight[i];
 {          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   int Ndum[20],ij=1, k, j, 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]); */
   int cptcode=0;        } /* end of wave */
   cptcoveff=0;      } /* end of individual */
      }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
   for (k=0; k<19; k++) Ndum[k]=0;      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   for (k=1; k<=7; k++) ncodemax[k]=0;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         for(mi=1; mi<= wav[i]-1; mi++){
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          for (ii=1;ii<=nlstate+ndeath;ii++)
     for (i=1; i<=imx; i++) {            for (j=1;j<=nlstate+ndeath;j++){
       ij=(int)(covar[Tvar[j]][i]);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       Ndum[ij]++;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/            }
       if (ij > cptcode) cptcode=ij;          for(d=0; d<dh[mi][i]; d++){
     }            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     for (i=0; i<=cptcode; i++) {            for (kk=1; kk<=cptcovage;kk++) {
       if(Ndum[i]!=0) ncodemax[j]++;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     }            }
     ij=1;          
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                          1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     for (i=1; i<=ncodemax[j]; i++) {            savm=oldm;
       for (k=0; k<=19; k++) {            oldm=newm;
         if (Ndum[k] != 0) {          } /* end mult */
           nbcode[Tvar[j]][ij]=k;        
                    s1=s[mw[mi][i]][i];
           ij++;          s2=s[mw[mi+1][i]][i];
         }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
         if (ij > ncodemax[j]) break;          ipmx +=1;
       }            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]);*/
         } /* end of wave */
  for (k=0; k<19; k++) Ndum[k]=0;      } /* end of individual */
     } /* End of if */
  for (i=1; i<=ncovmodel-2; i++) {    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
    ij=Tvar[i];    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
    Ndum[ij]++;    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
  }    return -l;
   }
  ij=1;  
  for (i=1; i<=10; i++) {  /*************** log-likelihood *************/
    if((Ndum[i]!=0) && (i<=ncovcol)){  double funcone( double *x)
      Tvaraff[ij]=i;  {
      ij++;    /* Same as likeli but slower because of a lot of printf and if */
    }    int i, ii, j, k, mi, d, kk;
  }    double l, ll[NLSTATEMAX], cov[NCOVMAX];
      double **out;
  cptcoveff=ij-1;    double lli; /* Individual log likelihood */
 }    double llt;
     int s1, s2;
 /*********** Health Expectancies ****************/    double bbh, survp;
     /*extern weight */
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov )    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
 {    /*for(i=1;i<imx;i++) 
   /* Health expectancies */      printf(" %d\n",s[4][i]);
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;    */
   double age, agelim, hf;    cov[1]=1.;
   double ***p3mat,***varhe;  
   double **dnewm,**doldm;    for(k=1; k<=nlstate; k++) ll[k]=0.;
   double *xp;  
   double **gp, **gm;    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   double ***gradg, ***trgradg;      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   int theta;      for(mi=1; mi<= wav[i]-1; mi++){
         for (ii=1;ii<=nlstate+ndeath;ii++)
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          for (j=1;j<=nlstate+ndeath;j++){
   xp=vector(1,npar);            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   dnewm=matrix(1,nlstate*2,1,npar);            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   doldm=matrix(1,nlstate*2,1,nlstate*2);          }
          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];
       fprintf(ficreseij," %1d-%1d (SE)",i,j);          }
   fprintf(ficreseij,"\n");          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   if(estepm < stepm){          savm=oldm;
     printf ("Problem %d lower than %d\n",estepm, stepm);          oldm=newm;
   }        } /* end mult */
   else  hstepm=estepm;          
   /* We compute the life expectancy from trapezoids spaced every estepm months        s1=s[mw[mi][i]][i];
    * This is mainly to measure the difference between two models: for example        s2=s[mw[mi+1][i]][i];
    * if stepm=24 months pijx are given only every 2 years and by summing them        bbh=(double)bh[mi][i]/(double)stepm; 
    * we are calculating an estimate of the Life Expectancy assuming a linear        /* bias is positive if real duration
    * progression inbetween and thus overestimating or underestimating according         * is higher than the multiple of stepm and negative otherwise.
    * 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        if( s2 > nlstate && (mle <5) ){  /* Jackson */
    * to compare the new estimate of Life expectancy with the same linear          lli=log(out[s1][s2] - savm[s1][s2]);
    * hypothesis. A more precise result, taking into account a more precise        } else if  (s2==-2) {
    * curvature will be obtained if estepm is as small as stepm. */          for (j=1,survp=0. ; j<=nlstate; j++) 
             survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   /* For example we decided to compute the life expectancy with the smallest unit */          lli= log(survp);
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.        }else if (mle==1){
      nhstepm is the number of hstepm from age to agelim          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
      nstepm is the number of stepm from age to agelin.        } else if(mle==2){
      Look at hpijx to understand the reason of that which relies in memory size          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 */
      and note for a fixed period like estepm months */        } else if(mle==3){  /* exponential inter-extrapolation */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          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 */
      survival function given by stepm (the optimization length). Unfortunately it        } else if (mle==4){  /* mle=4 no inter-extrapolation */
      means that if the survival funtion is printed only each two years of age and if          lli=log(out[s1][s2]); /* Original formula */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same        } else{  /* ml>=5 no inter-extrapolation no jackson =0.8a */
      results. So we changed our mind and took the option of the best precision.          lli=log(out[s1][s2]); /* Original formula */
   */        } /* End of if */
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        ipmx +=1;
         sw += weight[i];
   agelim=AGESUP;        ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  /*       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]); */
     /* nhstepm age range expressed in number of stepm */        if(globpr){
     nstepm=(int) rint((agelim-age)*YEARM/stepm);          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */   %11.6f %11.6f %11.6f ", \
     /* if (stepm >= YEARM) hstepm=1;*/                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);            llt +=ll[k]*gipmx/gsw;
     gp=matrix(0,nhstepm,1,nlstate*2);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
     gm=matrix(0,nhstepm,1,nlstate*2);          }
           fprintf(ficresilk," %10.6f\n", -llt);
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        }
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */      } /* end of wave */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);      } /* end of individual */
      for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    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 */
     /* Computing Variances of health expectancies */      gipmx=ipmx;
       gsw=sw;
      for(theta=1; theta <=npar; theta++){    }
       for(i=1; i<=npar; i++){    return -l;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  }
       }  
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
    /*************** function likelione ***********/
       cptj=0;  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       for(j=1; j<= nlstate; j++){  {
         for(i=1; i<=nlstate; i++){    /* This routine should help understanding what is done with 
           cptj=cptj+1;       the selection of individuals/waves and
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){       to check the exact contribution to the likelihood.
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;       Plotting could be done.
           }     */
         }    int k;
       }  
          if(*globpri !=0){ /* Just counts and sums, no printings */
            strcpy(fileresilk,"ilk"); 
       for(i=1; i<=npar; i++)      strcat(fileresilk,fileres);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          printf("Problem with resultfile: %s\n", fileresilk);
              fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       cptj=0;      }
       for(j=1; j<= nlstate; j++){      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
         for(i=1;i<=nlstate;i++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
           cptj=cptj+1;      /*  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(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){      for(k=1; k<=nlstate; k++) 
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
           }      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
         }    }
       }  
       for(j=1; j<= nlstate*2; j++)    *fretone=(*funcone)(p);
         for(h=0; h<=nhstepm-1; h++){    if(*globpri !=0){
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];      fclose(ficresilk);
         }      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
      }      fflush(fichtm); 
        } 
 /* End theta */    return;
   }
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);  
   
      for(h=0; h<=nhstepm-1; h++)  /*********** Maximum Likelihood Estimation ***************/
       for(j=1; j<=nlstate*2;j++)  
         for(theta=1; theta <=npar; theta++)  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
           trgradg[h][j][theta]=gradg[h][theta][j];  {
          int i,j, iter;
     double **xi;
      for(i=1;i<=nlstate*2;i++)    double fret;
       for(j=1;j<=nlstate*2;j++)    double fretone; /* Only one call to likelihood */
         varhe[i][j][(int)age] =0.;    /*  char filerespow[FILENAMELENGTH];*/
     xi=matrix(1,npar,1,npar);
      printf("%d|",(int)age);fflush(stdout);    for (i=1;i<=npar;i++)
      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);      for (j=1;j<=npar;j++)
      for(h=0;h<=nhstepm-1;h++){        xi[i][j]=(i==j ? 1.0 : 0.0);
       for(k=0;k<=nhstepm-1;k++){    printf("Powell\n");  fprintf(ficlog,"Powell\n");
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);    strcpy(filerespow,"pow"); 
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);    strcat(filerespow,fileres);
         for(i=1;i<=nlstate*2;i++)    if((ficrespow=fopen(filerespow,"w"))==NULL) {
           for(j=1;j<=nlstate*2;j++)      printf("Problem with resultfile: %s\n", filerespow);
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }    }
     }    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     /* Computing expectancies */    for (i=1;i<=nlstate;i++)
     for(i=1; i<=nlstate;i++)      for(j=1;j<=nlstate+ndeath;j++)
       for(j=1; j<=nlstate;j++)        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){    fprintf(ficrespow,"\n");
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;  
              powell(p,xi,npar,ftol,&iter,&fret,func);
 /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/  
     free_matrix(xi,1,npar,1,npar);
         }    fclose(ficrespow);
     printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
     fprintf(ficreseij,"%3.0f",age );    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     cptj=0;    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++){  }
         cptj++;  
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );  /**** Computes Hessian and covariance matrix ***/
       }  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
     fprintf(ficreseij,"\n");  {
        double  **a,**y,*x,pd;
     free_matrix(gm,0,nhstepm,1,nlstate*2);    double **hess;
     free_matrix(gp,0,nhstepm,1,nlstate*2);    int i, j,jk;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);    int *indx;
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);  
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   }    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
   printf("\n");    void lubksb(double **a, int npar, int *indx, double b[]) ;
   fprintf(ficlog,"\n");    void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
   free_vector(xp,1,npar);    hess=matrix(1,npar,1,npar);
   free_matrix(dnewm,1,nlstate*2,1,npar);  
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);    printf("\nCalculation of the hessian matrix. Wait...\n");
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
 }    for (i=1;i<=npar;i++){
       printf("%d",i);fflush(stdout);
 /************ Variance ******************/      fprintf(ficlog,"%d",i);fflush(ficlog);
 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)     
 {       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   /* Variance of health expectancies */      
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/      /*  printf(" %f ",p[i]);
   /* double **newm;*/          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   double **dnewm,**doldm;    }
   double **dnewmp,**doldmp;    
   int i, j, nhstepm, hstepm, h, nstepm ;    for (i=1;i<=npar;i++) {
   int k, cptcode;      for (j=1;j<=npar;j++)  {
   double *xp;        if (j>i) { 
   double **gp, **gm;  /* for var eij */          printf(".%d%d",i,j);fflush(stdout);
   double ***gradg, ***trgradg; /*for var eij */          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   double **gradgp, **trgradgp; /* for var p point j */          hess[i][j]=hessij(p,delti,i,j,func,npar);
   double *gpp, *gmp; /* for var p point j */          
   double **varppt; /* for var p point j nlstate to nlstate+ndeath */          hess[j][i]=hess[i][j];    
   double ***p3mat;          /*printf(" %lf ",hess[i][j]);*/
   double age,agelim, hf;        }
   int theta;      }
   char digit[4];    }
   char digitp[16];    printf("\n");
     fprintf(ficlog,"\n");
   char fileresprobmorprev[FILENAMELENGTH];  
     printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   if(popbased==1)    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
     strcpy(digitp,"-populbased-");    
   else    a=matrix(1,npar,1,npar);
     strcpy(digitp,"-stablbased-");    y=matrix(1,npar,1,npar);
     x=vector(1,npar);
   strcpy(fileresprobmorprev,"prmorprev");    indx=ivector(1,npar);
   sprintf(digit,"%-d",ij);    for (i=1;i<=npar;i++)
   /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
   strcat(fileresprobmorprev,digit); /* Tvar to be done */    ludcmp(a,npar,indx,&pd);
   strcat(fileresprobmorprev,digitp); /* Popbased or not */  
   strcat(fileresprobmorprev,fileres);    for (j=1;j<=npar;j++) {
   if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {      for (i=1;i<=npar;i++) x[i]=0;
     printf("Problem with resultfile: %s\n", fileresprobmorprev);      x[j]=1;
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);      lubksb(a,npar,indx,x);
   }      for (i=1;i<=npar;i++){ 
   printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);        matcov[i][j]=x[i];
   fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);      }
   fprintf(ficresprobmorprev,"# probabilities of dying during a year and weighted mean w1*p1j+w2*p2j+... stand dev in()\n");    }
   fprintf(ficresprobmorprev,"# Age cov=%-d",ij);  
   for(j=nlstate+1; j<=(nlstate+ndeath);j++){    printf("\n#Hessian matrix#\n");
     fprintf(ficresprobmorprev," p.%-d SE",j);    fprintf(ficlog,"\n#Hessian matrix#\n");
     for(i=1; i<=nlstate;i++)    for (i=1;i<=npar;i++) { 
       fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);      for (j=1;j<=npar;j++) { 
   }          printf("%.3e ",hess[i][j]);
   fprintf(ficresprobmorprev,"\n");        fprintf(ficlog,"%.3e ",hess[i][j]);
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      }
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);      printf("\n");
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);      fprintf(ficlog,"\n");
     exit(0);    }
   }  
   else{    /* Recompute Inverse */
     fprintf(ficgp,"\n# Routine varevsij");    for (i=1;i<=npar;i++)
   }      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    ludcmp(a,npar,indx,&pd);
     printf("Problem with html file: %s\n", optionfilehtm);  
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);    /*  printf("\n#Hessian matrix recomputed#\n");
     exit(0);  
   }    for (j=1;j<=npar;j++) {
   else{      for (i=1;i<=npar;i++) x[i]=0;
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");      x[j]=1;
   }      lubksb(a,npar,indx,x);
   varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);      for (i=1;i<=npar;i++){ 
         y[i][j]=x[i];
   fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are the stable prevalence in health states i\n");        printf("%.3e ",y[i][j]);
   fprintf(ficresvij,"# Age");        fprintf(ficlog,"%.3e ",y[i][j]);
   for(i=1; i<=nlstate;i++)      }
     for(j=1; j<=nlstate;j++)      printf("\n");
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);      fprintf(ficlog,"\n");
   fprintf(ficresvij,"\n");    }
     */
   xp=vector(1,npar);  
   dnewm=matrix(1,nlstate,1,npar);    free_matrix(a,1,npar,1,npar);
   doldm=matrix(1,nlstate,1,nlstate);    free_matrix(y,1,npar,1,npar);
   dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);    free_vector(x,1,npar);
   doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    free_ivector(indx,1,npar);
     free_matrix(hess,1,npar,1,npar);
   gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);  
   gpp=vector(nlstate+1,nlstate+ndeath);  
   gmp=vector(nlstate+1,nlstate+ndeath);  }
   trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/  
    /*************** hessian matrix ****************/
   if(estepm < stepm){  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
     printf ("Problem %d lower than %d\n",estepm, stepm);  {
   }    int i;
   else  hstepm=estepm;      int l=1, lmax=20;
   /* For example we decided to compute the life expectancy with the smallest unit */    double k1,k2;
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.    double p2[NPARMAX+1];
      nhstepm is the number of hstepm from age to agelim    double res;
      nstepm is the number of stepm from age to agelin.    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
      Look at hpijx to understand the reason of that which relies in memory size    double fx;
      and note for a fixed period like k years */    int k=0,kmax=10;
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    double l1;
      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    fx=func(x);
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    for (i=1;i<=npar;i++) p2[i]=x[i];
      results. So we changed our mind and took the option of the best precision.    for(l=0 ; l <=lmax; l++){
   */      l1=pow(10,l);
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */      delts=delt;
   agelim = AGESUP;      for(k=1 ; k <kmax; k=k+1){
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        delt = delta*(l1*k);
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        p2[theta]=x[theta] +delt;
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */        k1=func(p2)-fx;
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        p2[theta]=x[theta]-delt;
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);        k2=func(p2)-fx;
     gp=matrix(0,nhstepm,1,nlstate);        /*res= (k1-2.0*fx+k2)/delt/delt; */
     gm=matrix(0,nhstepm,1,nlstate);        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         
   #ifdef DEBUG
     for(theta=1; theta <=npar; theta++){        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);
       for(i=1; i<=npar; i++){ /* Computes gradient */        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);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  #endif
       }        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          k=kmax;
         }
       if (popbased==1) {        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
         for(i=1; i<=nlstate;i++)          k=kmax; l=lmax*10.;
           prlim[i][i]=probs[(int)age][i][ij];        }
       }        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
            delts=delt;
       for(j=1; j<= nlstate; j++){        }
         for(h=0; h<=nhstepm; h++){      }
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)    }
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];    delti[theta]=delts;
         }    return res; 
       }    
       /* This for computing forces of mortality (h=1)as a weighted average */  }
       for(j=nlstate+1,gpp[j]=0.;j<=nlstate+ndeath;j++){  
         for(i=1; i<= nlstate; i++)  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
           gpp[j] += prlim[i][i]*p3mat[i][j][1];  {
       }        int i;
       /* end force of mortality */    int l=1, l1, lmax=20;
     double k1,k2,k3,k4,res,fx;
       for(i=1; i<=npar; i++) /* Computes gradient */    double p2[NPARMAX+1];
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    int k;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);    
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fx=func(x);
      for (k=1; k<=2; k++) {
       if (popbased==1) {      for (i=1;i<=npar;i++) p2[i]=x[i];
         for(i=1; i<=nlstate;i++)      p2[thetai]=x[thetai]+delti[thetai]/k;
           prlim[i][i]=probs[(int)age][i][ij];      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       }      k1=func(p2)-fx;
     
       for(j=1; j<= nlstate; j++){      p2[thetai]=x[thetai]+delti[thetai]/k;
         for(h=0; h<=nhstepm; h++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)      k2=func(p2)-fx;
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];    
         }      p2[thetai]=x[thetai]-delti[thetai]/k;
       }      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       /* This for computing force of mortality (h=1)as a weighted average */      k3=func(p2)-fx;
       for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){    
         for(i=1; i<= nlstate; i++)      p2[thetai]=x[thetai]-delti[thetai]/k;
           gmp[j] += prlim[i][i]*p3mat[i][j][1];      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       }          k4=func(p2)-fx;
       /* end force of mortality */      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   #ifdef DEBUG
       for(j=1; j<= nlstate; j++) /* vareij */      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);
         for(h=0; h<=nhstepm; h++){      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);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];  #endif
         }    }
       for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */    return res;
         gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];  }
       }  
   /************** Inverse of matrix **************/
     } /* End theta */  void ludcmp(double **a, int n, int *indx, double *d) 
   { 
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */    int i,imax,j,k; 
     double big,dum,sum,temp; 
     for(h=0; h<=nhstepm; h++) /* veij */    double *vv; 
       for(j=1; j<=nlstate;j++)   
         for(theta=1; theta <=npar; theta++)    vv=vector(1,n); 
           trgradg[h][j][theta]=gradg[h][theta][j];    *d=1.0; 
     for (i=1;i<=n;i++) { 
     for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */      big=0.0; 
       for(theta=1; theta <=npar; theta++)      for (j=1;j<=n;j++) 
         trgradgp[j][theta]=gradgp[theta][j];        if ((temp=fabs(a[i][j])) > big) big=temp; 
       if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */      vv[i]=1.0/big; 
     for(i=1;i<=nlstate;i++)    } 
       for(j=1;j<=nlstate;j++)    for (j=1;j<=n;j++) { 
         vareij[i][j][(int)age] =0.;      for (i=1;i<j;i++) { 
         sum=a[i][j]; 
     for(h=0;h<=nhstepm;h++){        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
       for(k=0;k<=nhstepm;k++){        a[i][j]=sum; 
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);      } 
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);      big=0.0; 
         for(i=1;i<=nlstate;i++)      for (i=j;i<=n;i++) { 
           for(j=1;j<=nlstate;j++)        sum=a[i][j]; 
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;        for (k=1;k<j;k++) 
       }          sum -= a[i][k]*a[k][j]; 
     }        a[i][j]=sum; 
         if ( (dum=vv[i]*fabs(sum)) >= big) { 
     /* pptj */          big=dum; 
     matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);          imax=i; 
     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++)      if (j != imax) { 
         varppt[j][i]=doldmp[j][i];        for (k=1;k<=n;k++) { 
     /* end ppptj */          dum=a[imax][k]; 
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);            a[imax][k]=a[j][k]; 
     prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);          a[j][k]=dum; 
          } 
     if (popbased==1) {        *d = -(*d); 
       for(i=1; i<=nlstate;i++)        vv[imax]=vv[j]; 
         prlim[i][i]=probs[(int)age][i][ij];      } 
     }      indx[j]=imax; 
          if (a[j][j] == 0.0) a[j][j]=TINY; 
     /* This for computing force of mortality (h=1)as a weighted average */      if (j != n) { 
     for(j=nlstate+1,gmp[j]=0.;j<=nlstate+ndeath;j++){        dum=1.0/(a[j][j]); 
       for(i=1; i<= nlstate; i++)        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
         gmp[j] += prlim[i][i]*p3mat[i][j][1];      } 
     }        } 
     /* end force of mortality */    free_vector(vv,1,n);  /* Doesn't work */
   ;
     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]));  void lubksb(double **a, int n, int *indx, double b[]) 
       for(i=1; i<=nlstate;i++){  { 
         fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);    int i,ii=0,ip,j; 
       }    double sum; 
     }   
     fprintf(ficresprobmorprev,"\n");    for (i=1;i<=n;i++) { 
       ip=indx[i]; 
     fprintf(ficresvij,"%.0f ",age );      sum=b[ip]; 
     for(i=1; i<=nlstate;i++)      b[ip]=b[i]; 
       for(j=1; j<=nlstate;j++){      if (ii) 
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       }      else if (sum) ii=i; 
     fprintf(ficresvij,"\n");      b[i]=sum; 
     free_matrix(gp,0,nhstepm,1,nlstate);    } 
     free_matrix(gm,0,nhstepm,1,nlstate);    for (i=n;i>=1;i--) { 
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);      sum=b[i]; 
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      b[i]=sum/a[i][i]; 
   } /* 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);  void pstamp(FILE *fichier)
   free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/  {
   fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */  }
   fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");  
   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm);  /************ Frequencies ********************/
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm);  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[])
   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm);  {  /* Some frequencies */
   fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",fileresprobmorprev,fileresprobmorprev);    
   fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,digitp,digit);    int i, m, jk, k1,i1, j1, bool, z1,j;
   /*  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);    int first;
 */    double ***freq; /* Frequencies */
   fprintf(ficgp,"\nset out \"varmuptjgr%s%s.png\";replot;",digitp,digit);    double *pp, **prop;
     double pos,posprop, k2, dateintsum=0,k2cpt=0;
   free_vector(xp,1,npar);    char fileresp[FILENAMELENGTH];
   free_matrix(doldm,1,nlstate,1,nlstate);    
   free_matrix(dnewm,1,nlstate,1,npar);    pp=vector(1,nlstate);
   free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    prop=matrix(1,nlstate,iagemin,iagemax+3);
   free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);    strcpy(fileresp,"p");
   free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);    strcat(fileresp,fileres);
   fclose(ficresprobmorprev);    if((ficresp=fopen(fileresp,"w"))==NULL) {
   fclose(ficgp);      printf("Problem with prevalence resultfile: %s\n", fileresp);
   fclose(fichtm);      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
       exit(0);
 }    }
     freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
 /************ Variance of prevlim ******************/    j1=0;
 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)    
 {    j=cptcoveff;
   /* Variance of prevalence limit */    if (cptcovn<1) {j=1;ncodemax[1]=1;}
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/  
   double **newm;    first=1;
   double **dnewm,**doldm;  
   int i, j, nhstepm, hstepm;    for(k1=1; k1<=j;k1++){
   int k, cptcode;      for(i1=1; i1<=ncodemax[k1];i1++){
   double *xp;        j1++;
   double *gp, *gm;        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
   double **gradg, **trgradg;          scanf("%d", i);*/
   double age,agelim;        for (i=-5; i<=nlstate+ndeath; i++)  
   int theta;          for (jk=-5; jk<=nlstate+ndeath; jk++)  
                for(m=iagemin; m <= iagemax+3; m++)
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");              freq[i][jk][m]=0;
   fprintf(ficresvpl,"# Age");  
   for(i=1; i<=nlstate;i++)      for (i=1; i<=nlstate; i++)  
       fprintf(ficresvpl," %1d-%1d",i,i);        for(m=iagemin; m <= iagemax+3; m++)
   fprintf(ficresvpl,"\n");          prop[i][m]=0;
         
   xp=vector(1,npar);        dateintsum=0;
   dnewm=matrix(1,nlstate,1,npar);        k2cpt=0;
   doldm=matrix(1,nlstate,1,nlstate);        for (i=1; i<=imx; i++) {
            bool=1;
   hstepm=1*YEARM; /* Every year of age */          if  (cptcovn>0) {
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */            for (z1=1; z1<=cptcoveff; z1++) 
   agelim = AGESUP;              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */                bool=0;
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          }
     if (stepm >= YEARM) hstepm=1;          if (bool==1){
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */            for(m=firstpass; m<=lastpass; m++){
     gradg=matrix(1,npar,1,nlstate);              k2=anint[m][i]+(mint[m][i]/12.);
     gp=vector(1,nlstate);              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
     gm=vector(1,nlstate);                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
     for(theta=1; theta <=npar; theta++){                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
       for(i=1; i<=npar; i++){ /* Computes gradient */                if (m<lastpass) {
         xp[i] = x[i] + (i==theta ?delti[theta]:0);                  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];
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);                }
       for(i=1;i<=nlstate;i++)                
         gp[i] = prlim[i][i];                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                      dateintsum=dateintsum+k2;
       for(i=1; i<=npar; i++) /* Computes gradient */                  k2cpt++;
         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];        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
     } /* End theta */        pstamp(ficresp);
         if  (cptcovn>0) {
     trgradg =matrix(1,nlstate,1,npar);          fprintf(ficresp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(j=1; j<=nlstate;j++)          fprintf(ficresp, "**********\n#");
       for(theta=1; theta <=npar; theta++)        }
         trgradg[j][theta]=gradg[theta][j];        for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
     for(i=1;i<=nlstate;i++)        fprintf(ficresp, "\n");
       varpl[i][(int)age] =0.;        
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);        for(i=iagemin; i <= iagemax+3; i++){
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);          if(i==iagemax+3){
     for(i=1;i<=nlstate;i++)            fprintf(ficlog,"Total");
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */          }else{
             if(first==1){
     fprintf(ficresvpl,"%.0f ",age );              first=0;
     for(i=1; i<=nlstate;i++)              printf("See log file for details...\n");
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));            }
     fprintf(ficresvpl,"\n");            fprintf(ficlog,"Age %d", i);
     free_vector(gp,1,nlstate);          }
     free_vector(gm,1,nlstate);          for(jk=1; jk <=nlstate ; jk++){
     free_matrix(gradg,1,npar,1,nlstate);            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
     free_matrix(trgradg,1,nlstate,1,npar);              pp[jk] += freq[jk][m][i]; 
   } /* End age */          }
           for(jk=1; jk <=nlstate ; jk++){
   free_vector(xp,1,npar);            for(m=-1, pos=0; m <=0 ; m++)
   free_matrix(doldm,1,nlstate,1,npar);              pos += freq[jk][m][i];
   free_matrix(dnewm,1,nlstate,1,nlstate);            if(pp[jk]>=1.e-10){
               if(first==1){
 }              printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               }
 /************ Variance of one-step probabilities  ******************/              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)            }else{
 {              if(first==1)
   int i, j=0,  i1, k1, l1, t, tj;                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   int k2, l2, j1,  z1;              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   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;          for(jk=1; jk <=nlstate ; jk++){
   double *xp;            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
   double *gp, *gm;              pp[jk] += freq[jk][m][i];
   double **gradg, **trgradg;          }       
   double **mu;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
   double age,agelim, cov[NCOVMAX];            pos += pp[jk];
   double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */            posprop += prop[jk][i];
   int theta;          }
   char fileresprob[FILENAMELENGTH];          for(jk=1; jk <=nlstate ; jk++){
   char fileresprobcov[FILENAMELENGTH];            if(pos>=1.e-5){
   char fileresprobcor[FILENAMELENGTH];              if(first==1)
                 printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
   double ***varpij;              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
   strcpy(fileresprob,"prob");              if(first==1)
   strcat(fileresprob,fileres);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
     printf("Problem with resultfile: %s\n", fileresprob);            }
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);            if( i <= iagemax){
   }              if(pos>=1.e-5){
   strcpy(fileresprobcov,"probcov");                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   strcat(fileresprobcov,fileres);                /*probs[i][jk][j1]= pp[jk]/pos;*/
   if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {                /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
     printf("Problem with resultfile: %s\n", fileresprobcov);              }
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);              else
   }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   strcpy(fileresprobcor,"probcor");            }
   strcat(fileresprobcor,fileres);          }
   if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {          
     printf("Problem with resultfile: %s\n", fileresprobcor);          for(jk=-1; jk <=nlstate+ndeath; jk++)
     fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);            for(m=-1; m <=nlstate+ndeath; m++)
   }              if(freq[jk][m][i] !=0 ) {
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);              if(first==1)
   fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
   printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
   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);          if(i <= iagemax)
   fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);            fprintf(ficresp,"\n");
            if(first==1)
   fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");            printf("Others in log...\n");
   fprintf(ficresprob,"# Age");          fprintf(ficlog,"\n");
   fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");        }
   fprintf(ficresprobcov,"# Age");      }
   fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");    }
   fprintf(ficresprobcov,"# Age");    dateintmean=dateintsum/k2cpt; 
    
     fclose(ficresp);
   for(i=1; i<=nlstate;i++)    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
     for(j=1; j<=(nlstate+ndeath);j++){    free_vector(pp,1,nlstate);
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
       fprintf(ficresprobcov," p%1d-%1d ",i,j);    /* End of Freq */
       fprintf(ficresprobcor," p%1d-%1d ",i,j);  }
     }    
   fprintf(ficresprob,"\n");  /************ Prevalence ********************/
   fprintf(ficresprobcov,"\n");  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   fprintf(ficresprobcor,"\n");  {  
   xp=vector(1,npar);    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
   dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);       in each health status at the date of interview (if between dateprev1 and dateprev2).
   doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));       We still use firstpass and lastpass as another selection.
   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;    int i, m, jk, k1, i1, j1, bool, z1,j;
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {    double ***freq; /* Frequencies */
     printf("Problem with gnuplot file: %s\n", optionfilegnuplot);    double *pp, **prop;
     fprintf(ficlog,"Problem with gnuplot file: %s\n", optionfilegnuplot);    double pos,posprop; 
     exit(0);    double  y2; /* in fractional years */
   }    int iagemin, iagemax;
   else{  
     fprintf(ficgp,"\n# Routine varprob");    iagemin= (int) agemin;
   }    iagemax= (int) agemax;
   if((fichtm=fopen(optionfilehtm,"a"))==NULL) {    /*pp=vector(1,nlstate);*/
     printf("Problem with html file: %s\n", optionfilehtm);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
     fprintf(ficlog,"Problem with html file: %s\n", optionfilehtm);    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     exit(0);    j1=0;
   }    
   else{    j=cptcoveff;
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");    if (cptcovn<1) {j=1;ncodemax[1]=1;}
     fprintf(fichtm,"\n");    
     for(k1=1; k1<=j;k1++){
     fprintf(fichtm,"\n<li><h4> Computing matrix of variance-covariance of step probabilities</h4></li>\n");      for(i1=1; i1<=ncodemax[k1];i1++){
     fprintf(fichtm,"\nWe have drawn ellipsoids of confidence around the p<inf>ij</inf>, p<inf>kl</inf> to understand the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");        j1++;
     fprintf(fichtm,"\n<br> We have drawn x'cov<sup>-1</sup>x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix 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> When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.<br> \n");        
         for (i=1; i<=nlstate; i++)  
   }          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
         
   cov[1]=1;        for (i=1; i<=imx; i++) { /* Each individual */
   tj=cptcoveff;          bool=1;
   if (cptcovn<1) {tj=1;ncodemax[1]=1;}          if  (cptcovn>0) {
   j1=0;            for (z1=1; z1<=cptcoveff; z1++) 
   for(t=1; t<=tj;t++){              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
     for(i1=1; i1<=ncodemax[t];i1++){                bool=0;
       j1++;          } 
                if (bool==1) { 
       if  (cptcovn>0) {            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
         fprintf(ficresprob, "\n#********** Variable ");              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
         fprintf(ficresprob, "**********\n#");                if(agev[m][i]==0) agev[m][i]=iagemax+1;
         fprintf(ficresprobcov, "\n#********** Variable ");                if(agev[m][i]==1) agev[m][i]=iagemax+2;
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);                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); 
         fprintf(ficresprobcov, "**********\n#");                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                          /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
         fprintf(ficgp, "\n#********** Variable ");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, "# V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);                  prop[s[m][i]][iagemax+3] += weight[i]; 
         fprintf(ficgp, "**********\n#");                } 
                      }
                    } /* end selection of waves */
         fprintf(fichtm, "\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(fichtm, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");        for(i=iagemin; i <= iagemax+3; i++){  
                  
         fprintf(ficresprobcor, "\n#********** Variable ");              for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);            posprop += prop[jk][i]; 
         fprintf(ficgp, "**********\n#");              } 
       }  
                for(jk=1; jk <=nlstate ; jk++){     
       for (age=bage; age<=fage; age ++){            if( i <=  iagemax){ 
         cov[2]=age;              if(posprop>=1.e-5){ 
         for (k=1; k<=cptcovn;k++) {                probs[i][jk][j1]= prop[jk][i]/posprop;
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];              } else
         }                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];            } 
         for (k=1; k<=cptcovprod;k++)          }/* end jk */ 
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];        }/* end i */ 
              } /* end i1 */
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));    } /* end k1 */
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);    
         gp=vector(1,(nlstate)*(nlstate+ndeath));    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
         gm=vector(1,(nlstate)*(nlstate+ndeath));    /*free_vector(pp,1,nlstate);*/
        free_matrix(prop,1,nlstate, iagemin,iagemax+3);
         for(theta=1; theta <=npar; theta++){  }  /* End of prevalence */
           for(i=1; i<=npar; i++)  
             xp[i] = x[i] + (i==theta ?delti[theta]:0);  /************* Waves Concatenation ***************/
            
           pmij(pmmij,cov,ncovmodel,xp,nlstate);  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)
            {
           k=0;    /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
           for(i=1; i<= (nlstate); i++){       Death is a valid wave (if date is known).
             for(j=1; j<=(nlstate+ndeath);j++){       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
               k=k+1;       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
               gp[k]=pmmij[i][j];       and mw[mi+1][i]. dh depends on stepm.
             }       */
           }  
              int i, mi, m;
           for(i=1; i<=npar; i++)    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
             xp[i] = x[i] - (i==theta ?delti[theta]:0);       double sum=0., jmean=0.;*/
        int first;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);    int j, k=0,jk, ju, jl;
           k=0;    double sum=0.;
           for(i=1; i<=(nlstate); i++){    first=0;
             for(j=1; j<=(nlstate+ndeath);j++){    jmin=1e+5;
               k=k+1;    jmax=-1;
               gm[k]=pmmij[i][j];    jmean=0.;
             }    for(i=1; i<=imx; i++){
           }      mi=0;
            m=firstpass;
           for(i=1; i<= (nlstate)*(nlstate+ndeath); i++)      while(s[m][i] <= nlstate){
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];          if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
         }          mw[++mi][i]=m;
         if(m >=lastpass)
         for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)          break;
           for(theta=1; theta <=npar; theta++)        else
             trgradg[j][theta]=gradg[theta][j];          m++;
              }/* end while */
         matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov);      if (s[m][i] > nlstate){
         matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);        mi++;     /* Death is another wave */
                /* if(mi==0)  never been interviewed correctly before death */
         pmij(pmmij,cov,ncovmodel,x,nlstate);           /* Only death is a correct wave */
                mw[mi][i]=m;
         k=0;      }
         for(i=1; i<=(nlstate); i++){  
           for(j=1; j<=(nlstate+ndeath);j++){      wav[i]=mi;
             k=k+1;      if(mi==0){
             mu[k][(int) age]=pmmij[i][j];        nbwarn++;
           }        if(first==0){
         }          printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
         for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)          first=1;
           for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)        }
             varpij[i][j][(int)age] = doldm[i][j];        if(first==1){
           fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
         /*printf("\n%d ",(int)age);        }
      for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){      } /* end mi==0 */
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));    } /* End individuals */
        fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));  
      }*/    for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
         fprintf(ficresprob,"\n%d ",(int)age);        if (stepm <=0)
         fprintf(ficresprobcov,"\n%d ",(int)age);          dh[mi][i]=1;
         fprintf(ficresprobcor,"\n%d ",(int)age);        else{
           if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)            if (agedc[i] < 2*AGESUP) {
           fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
         for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){              if(j==0) j=1;  /* Survives at least one month after exam */
           fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);              else if(j<0){
           fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);                nberr++;
         }                printf("Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
         i=0;                j=1; /* Temporary Dangerous patch */
         for (k=1; k<=(nlstate);k++){                printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
           for (l=1; l<=(nlstate+ndeath);l++){                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]);
             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);
             fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);              }
             fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);              k=k+1;
             for (j=1; j<=i;j++){              if (j >= jmax){
               fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);                jmax=j;
               fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));                ijmax=i;
             }              }
           }              if (j <= jmin){
         }/* end of loop for state */                jmin=j;
       } /* end of loop for age */                ijmin=i;
               }
       /* Confidence intervalle of pij  */              sum=sum+j;
       /*              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       fprintf(ficgp,"\nset noparametric;unset label");              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       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);          else{
       fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);  /*        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]); */
       fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);  
       */            k=k+1;
             if (j >= jmax) {
       /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/              jmax=j;
       first1=1;              ijmax=i;
       for (k2=1; k2<=(nlstate);k2++){            }
         for (l2=1; l2<=(nlstate+ndeath);l2++){            else if (j <= jmin){
           if(l2==k2) continue;              jmin=j;
           j=(k2-1)*(nlstate+ndeath)+l2;              ijmin=i;
           for (k1=1; k1<=(nlstate);k1++){            }
             for (l1=1; l1<=(nlstate+ndeath);l1++){            /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
               if(l1==k1) continue;            /*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]);*/
               i=(k1-1)*(nlstate+ndeath)+l1;            if(j<0){
               if(i<=j) continue;              nberr++;
               for (age=bage; age<=fage; age ++){              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]);
                 if ((int)age %5==0){              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]);
                   v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;            }
                   v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;            sum=sum+j;
                   cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;          }
                   mu1=mu[i][(int) age]/stepm*YEARM ;          jk= j/stepm;
                   mu2=mu[j][(int) age]/stepm*YEARM;          jl= j -jk*stepm;
                   c12=cv12/sqrt(v1*v2);          ju= j -(jk+1)*stepm;
                   /* Computing eigen value of matrix of covariance */          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
                   lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;            if(jl==0){
                   lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;              dh[mi][i]=jk;
                   /* Eigen vectors */              bh[mi][i]=0;
                   v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));            }else{ /* We want a negative bias in order to only have interpolation ie
                   /*v21=sqrt(1.-v11*v11); *//* error */                    * at the price of an extra matrix product in likelihood */
                   v21=(lc1-v1)/cv12*v11;              dh[mi][i]=jk+1;
                   v12=-v21;              bh[mi][i]=ju;
                   v22=v11;            }
                   tnalp=v21/v11;          }else{
                   if(first1==1){            if(jl <= -ju){
                     first1=0;              dh[mi][i]=jk;
                     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);              bh[mi][i]=jl;       /* bias is positive if real duration
                   }                                   * is higher than the multiple of stepm and negative otherwise.
                   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) */            else{
                   /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */              dh[mi][i]=jk+1;
                   if(first==1){              bh[mi][i]=ju;
                     first=0;            }
                     fprintf(ficgp,"\nset parametric;unset label");            if(dh[mi][i]==0){
                     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);              dh[mi][i]=1; /* At least one step */
                     fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");              bh[mi][i]=ju; /* At least one step */
                     fprintf(fichtm,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup> :<a href=\"varpijgr%s%d%1d%1d-%1d%1d.png\">varpijgr%s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2,optionfilefiname, j1,k1,l1,k2,l2);              /*  printf(" bh=%d ju=%d jl=%d dh=%d jk=%d stepm=%d %d\n",bh[mi][i],ju,jl,dh[mi][i],jk,stepm,i);*/
                     fprintf(fichtm,"\n<br><img src=\"varpijgr%s%d%1d%1d-%1d%1d.png\"> ",optionfilefiname, j1,k1,l1,k2,l2);            }
                     fprintf(fichtm,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);          } /* end if mle */
                     fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k1,l1,k2,l2);        }
                     fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);      } /* end wave */
                     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",\    jmean=sum/k;
                             mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\    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);
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));    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);
                   }else{   }
                     first=0;  
                     fprintf(fichtm," %d (%.3f),",(int) age, c12);  /*********** Tricode ****************************/
                     fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);  void tricode(int *Tvar, int **nbcode, int imx)
                     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),\    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
                             mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));  
                   }/* if first */    int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=19;
                 } /* age mod 5 */    int cptcode=0;
               } /* end loop age */    cptcoveff=0; 
               fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k1,l1,k2,l2);   
               first=1;    for (k=0; k<maxncov; k++) Ndum[k]=0;
             } /*l12 */    for (k=1; k<=7; k++) ncodemax[k]=0;
           } /* k12 */  
         } /*l1 */    for (j=1; j<=(cptcovn+2*cptcovprod); j++) {
       }/* k1 */      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum 
     } /* loop covariates */                                 modality*/ 
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);        ij=(int)(covar[Tvar[j]][i]); /* ij is the modality of this individual*/
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));        Ndum[ij]++; /*store the modality */
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);        if (ij > cptcode) cptcode=ij; /* getting the maximum of covariable 
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);                                         Tvar[j]. If V=sex and male is 0 and 
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);                                         female is 1, then  cptcode=1.*/
   }      }
   free_vector(xp,1,npar);  
   fclose(ficresprob);      for (i=0; i<=cptcode; i++) {
   fclose(ficresprobcov);        if(Ndum[i]!=0) ncodemax[j]++; /* Nomber of modalities of the j th covariates. In fact ncodemax[j]=2 (dichotom. variables) but it can be more */
   fclose(ficresprobcor);      }
   fclose(ficgp);  
   fclose(fichtm);      ij=1; 
 }      for (i=1; i<=ncodemax[j]; i++) {
         for (k=0; k<= maxncov; k++) {
           if (Ndum[k] != 0) {
 /******************* Printing html file ***********/            nbcode[Tvar[j]][ij]=k; 
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \            /* store the modality in an array. k is a modality. If we have model=V1+V1*sex then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
                   int lastpass, int stepm, int weightopt, char model[],\            
                   int imx,int jmin, int jmax, double jmeanint,char rfileres[],\            ij++;
                   int popforecast, int estepm ,\          }
                   double jprev1, double mprev1,double anprev1, \          if (ij > ncodemax[j]) break; 
                   double jprev2, double mprev2,double anprev2){        }  
   int jj1, k1, i1, cpt;      } 
   /*char optionfilehtm[FILENAMELENGTH];*/    }  
   if((fichtm=fopen(optionfilehtm,"a"))==NULL)    {  
     printf("Problem with %s \n",optionfilehtm), exit(0);   for (k=0; k< maxncov; k++) Ndum[k]=0;
     fprintf(ficlog,"Problem with %s \n",optionfilehtm), exit(0);  
   }   for (i=1; i<=ncovmodel-2; i++) { 
      /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
    fprintf(fichtm,"<ul><li><h4>Result files (first order: no variance)</h4>\n     ij=Tvar[i];
  - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"p%s\">p%s</a> <br>\n     Ndum[ij]++;
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n   }
  - Stable prevalence in each health state: <a href=\"pl%s\">pl%s</a> <br>\n  
  - Life expectancies by age and initial health status (estepm=%2d months):   ij=1;
    <a href=\"e%s\">e%s</a> <br>\n</li>", \   for (i=1; i<= maxncov; i++) {
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);     if((Ndum[i]!=0) && (i<=ncovcol)){
        Tvaraff[ij]=i; /*For printing */
 fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");       ij++;
      }
  m=cptcoveff;   }
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}   
    cptcoveff=ij-1; /*Number of simple covariates*/
  jj1=0;  }
  for(k1=1; k1<=m;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){  /*********** Health Expectancies ****************/
      jj1++;  
      if (cptcovn > 0) {  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
        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]]);    /* Health expectancies, no variances */
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
      }    int nhstepma, nstepma; /* Decreasing with age */
      /* Pij */    double age, agelim, hf;
      fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months before: pe%s%d1.png<br>    double ***p3mat;
 <img src=\"pe%s%d1.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);        double eip;
      /* 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: pe%s%d2.png<br>    pstamp(ficreseij);
 <img src=\"pe%s%d2.png\">",stepm,strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
        /* Stable prevalence in each health state */    fprintf(ficreseij,"# Age");
        for(cpt=1; cpt<nlstate;cpt++){    for(i=1; i<=nlstate;i++){
          fprintf(fichtm,"<br>- Stable prevalence in each health state : p%s%d%d.png<br>      for(j=1; j<=nlstate;j++){
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);        fprintf(ficreseij," e%1d%1d ",i,j);
        }      }
      for(cpt=1; cpt<=nlstate;cpt++) {      fprintf(ficreseij," e%1d. ",i);
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>    }
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    fprintf(ficreseij,"\n");
      }  
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    
 health expectancies in states (1) and (2): e%s%d.png<br>    if(estepm < stepm){
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);      printf ("Problem %d lower than %d\n",estepm, stepm);
    } /* end i1 */    }
  }/* End k1 */    else  hstepm=estepm;   
  fprintf(fichtm,"</ul>");    /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
      * if stepm=24 months pijx are given only every 2 years and by summing them
  fprintf(fichtm,"\n<br><li><h4> Result files (second order: variances)</h4>\n     * we are calculating an estimate of the Life Expectancy assuming a linear 
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n     * progression in between and thus overestimating or underestimating according
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n     * to the curvature of the survival function. If, for the same date, we 
  - Variance-covariance of one-step probabilities: <a href=\"probcov%s\">probcov%s</a> <br>\n     * estimate the model with stepm=1 month, we can keep estepm to 24 months
  - Correlation matrix of one-step probabilities: <a href=\"probcor%s\">probcor%s</a> <br>\n     * to compare the new estimate of Life expectancy with the same linear 
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n     * hypothesis. A more precise result, taking into account a more precise
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n     * curvature will be obtained if estepm is as small as stepm. */
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres,fileres,fileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);  
     /* For example we decided to compute the life expectancy with the smallest unit */
  if(popforecast==1) fprintf(fichtm,"\n    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n       nhstepm is the number of hstepm from age to agelim 
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n       nstepm is the number of stepm from age to agelin. 
         <br>",fileres,fileres,fileres,fileres);       Look at hpijx to understand the reason of that which relies in memory size
  else       and note for a fixed period like estepm months */
    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);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
 fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");       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
  m=cptcoveff;       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}       results. So we changed our mind and took the option of the best precision.
     */
  jj1=0;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
  for(k1=1; k1<=m;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){    agelim=AGESUP;
      jj1++;    /* If stepm=6 months */
      if (cptcovn > 0) {      /* Computed by stepm unit matrices, product of hstepm matrices, stored
        fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
        for (cpt=1; cpt<=cptcoveff;cpt++)      
          fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);  /* nhstepm age range expressed in number of stepm */
        fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
      }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      for(cpt=1; cpt<=nlstate;cpt++) {    /* if (stepm >= YEARM) hstepm=1;*/
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
 interval) in state (%d): v%s%d%d.png <br>    p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);    
      }    for (age=bage; age<=fage; age ++){ 
    } /* end i1 */      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
  }/* End k1 */      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
  fprintf(fichtm,"</ul>");      /* if (stepm >= YEARM) hstepm=1;*/
 fclose(fichtm);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
 }  
       /* If stepm=6 months */
 /******************* Gnuplot file **************/      /* Computed by stepm unit matrices, product of hstepma matrices, stored
 void printinggnuplot(char fileres[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   int ng;      
   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) {      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     printf("Problem with file %s",optionfilegnuplot);      
     fprintf(ficlog,"Problem with file %s",optionfilegnuplot);      printf("%d|",(int)age);fflush(stdout);
   }      fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       
 #ifdef windows      /* Computing expectancies */
     fprintf(ficgp,"cd \"%s\" \n",pathc);      for(i=1; i<=nlstate;i++)
 #endif        for(j=1; j<=nlstate;j++)
 m=pow(2,cptcoveff);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
              eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
  /* 1eme*/            
   for (cpt=1; cpt<= nlstate ; cpt ++) {            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
    for (k1=1; k1<= m ; k1 ++) {  
           }
 #ifdef windows  
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);      fprintf(ficreseij,"%3.0f",age );
      fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,fileres,k1-1,k1-1);      for(i=1; i<=nlstate;i++){
 #endif        eip=0;
 #ifdef unix        for(j=1; j<=nlstate;j++){
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);          eip +=eij[i][j][(int)age];
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);          fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
 #endif        }
         fprintf(ficreseij,"%9.4f", eip );
 for (i=1; i<= nlstate ; i ++) {      }
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");      fprintf(ficreseij,"\n");
   else fprintf(ficgp," \%%*lf (\%%*lf)");      
 }    }
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     for (i=1; i<= nlstate ; i ++) {    printf("\n");
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    fprintf(ficlog,"\n");
   else fprintf(ficgp," \%%*lf (\%%*lf)");    
 }  }
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);  
      for (i=1; i<= nlstate ; i ++) {  void cvevsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,double delti[],double **matcov,char strstart[] )
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");  {
 }      /* Covariances of health expectancies eij and of total life expectancies according
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));     to initial status i, ei. .
 #ifdef unix    */
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
 #endif    int nhstepma, nstepma; /* Decreasing with age */
    }    double age, agelim, hf;
   }    double ***p3matp, ***p3matm, ***varhe;
   /*2 eme*/    double **dnewm,**doldm;
     double *xp, *xm;
   for (k1=1; k1<= m ; k1 ++) {    double **gp, **gm;
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);    double ***gradg, ***trgradg;
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);    int theta;
      
     for (i=1; i<= nlstate+1 ; i ++) {    double eip, vip;
       k=2*i;  
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
       for (j=1; j<= nlstate+1 ; j ++) {    xp=vector(1,npar);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    xm=vector(1,npar);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    dnewm=matrix(1,nlstate*nlstate,1,npar);
 }      doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);    pstamp(ficresstdeij);
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
       for (j=1; j<= nlstate+1 ; j ++) {    fprintf(ficresstdeij,"# Age");
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    for(i=1; i<=nlstate;i++){
         else fprintf(ficgp," \%%*lf (\%%*lf)");      for(j=1; j<=nlstate;j++)
 }          fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
       fprintf(ficgp,"\" t\"\" w l 0,");      fprintf(ficresstdeij," e%1d. ",i);
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);    }
       for (j=1; j<= nlstate+1 ; j ++) {    fprintf(ficresstdeij,"\n");
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    pstamp(ficrescveij);
 }      fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    fprintf(ficrescveij,"# Age");
       else fprintf(ficgp,"\" t\"\" w l 0,");    for(i=1; i<=nlstate;i++)
     }      for(j=1; j<=nlstate;j++){
   }        cptj= (j-1)*nlstate+i;
          for(i2=1; i2<=nlstate;i2++)
   /*3eme*/          for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
   for (k1=1; k1<= m ; k1 ++) {            if(cptj2 <= cptj)
     for (cpt=1; cpt<= nlstate ; cpt ++) {              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
       k=2+nlstate*(2*cpt-2);          }
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);      }
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);    fprintf(ficrescveij,"\n");
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    if(estepm < stepm){
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);      printf ("Problem %d lower than %d\n",estepm, stepm);
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);    }
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");    else  hstepm=estepm;   
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);    /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
 */     * if stepm=24 months pijx are given only every 2 years and by summing them
       for (i=1; i< nlstate ; i ++) {     * we are calculating an estimate of the Life Expectancy assuming a linear 
         fprintf(ficgp," ,\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+2*i,cpt,i+1);     * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
       }     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     }     * to compare the new estimate of Life expectancy with the same linear 
   }     * hypothesis. A more precise result, taking into account a more precise
       * curvature will be obtained if estepm is as small as stepm. */
   /* CV preval stat */  
     for (k1=1; k1<= m ; k1 ++) {    /* For example we decided to compute the life expectancy with the smallest unit */
     for (cpt=1; cpt<nlstate ; cpt ++) {    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
       k=3;       nhstepm is the number of hstepm from age to agelim 
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);       nstepm is the number of stepm from age to agelin. 
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);       Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like estepm months */
       for (i=1; i< nlstate ; i ++)    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
         fprintf(ficgp,"+$%d",k+i+1);       survival function given by stepm (the optimization length). Unfortunately it
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);       means that if the survival funtion is printed only each two years of age and if
             you sum them up and add 1 year (area under the trapezoids) you won't get the same 
       l=3+(nlstate+ndeath)*cpt;       results. So we changed our mind and took the option of the best precision.
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    */
       for (i=1; i< nlstate ; i ++) {    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
         l=3+(nlstate+ndeath)*cpt;  
         fprintf(ficgp,"+$%d",l+i+1);    /* If stepm=6 months */
       }    /* nhstepm age range expressed in number of stepm */
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);      agelim=AGESUP;
     }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
   }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      /* if (stepm >= YEARM) hstepm=1;*/
   /* proba elementaires */    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
    for(i=1,jk=1; i <=nlstate; i++){    
     for(k=1; k <=(nlstate+ndeath); k++){    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       if (k != i) {    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         for(j=1; j <=ncovmodel; j++){    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
           jk++;    gp=matrix(0,nhstepm,1,nlstate*nlstate);
           fprintf(ficgp,"\n");    gm=matrix(0,nhstepm,1,nlstate*nlstate);
         }  
       }    for (age=bage; age<=fage; age ++){ 
     }      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
    }      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
      for(jk=1; jk <=m; jk++) {  
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);      /* If stepm=6 months */
        if (ng==2)      /* Computed by stepm unit matrices, product of hstepma matrices, stored
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
        else      
          fprintf(ficgp,"\nset title \"Probability\"\n");      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);  
        i=1;      /* Computing  Variances of health expectancies */
        for(k2=1; k2<=nlstate; k2++) {      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          k3=i;         decrease memory allocation */
          for(k=1; k<=(nlstate+ndeath); k++) {      for(theta=1; theta <=npar; theta++){
            if (k != k2){        for(i=1; i<=npar; i++){ 
              if(ng==2)          xp[i] = x[i] + (i==theta ?delti[theta]:0);
                fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
              else        }
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
              ij=1;        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
              for(j=3; j <=ncovmodel; j++) {    
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {        for(j=1; j<= nlstate; j++){
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);          for(i=1; i<=nlstate; i++){
                  ij++;            for(h=0; h<=nhstepm-1; h++){
                }              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
                else              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
                  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++){          for(ij=1; ij<= nlstate*nlstate; ij++)
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);          for(h=0; h<=nhstepm-1; h++){
                ij=1;            gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
                for(j=3; j <=ncovmodel; j++){          }
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {      }/* End theta */
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);      
                    ij++;      
                  }      for(h=0; h<=nhstepm-1; h++)
                  else        for(j=1; j<=nlstate*nlstate;j++)
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          for(theta=1; theta <=npar; theta++)
                }            trgradg[h][j][theta]=gradg[h][theta][j];
                fprintf(ficgp,")");      
              }  
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);       for(ij=1;ij<=nlstate*nlstate;ij++)
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");        for(ji=1;ji<=nlstate*nlstate;ji++)
              i=i+ncovmodel;          varhe[ij][ji][(int)age] =0.;
            }  
          } /* end k */       printf("%d|",(int)age);fflush(stdout);
        } /* end k2 */       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
      } /* end jk */       for(h=0;h<=nhstepm-1;h++){
    } /* end ng */        for(k=0;k<=nhstepm-1;k++){
    fclose(ficgp);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
 }  /* end gnuplot */          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(ij=1;ij<=nlstate*nlstate;ij++)
             for(ji=1;ji<=nlstate*nlstate;ji++)
 /*************** Moving average **************/              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){        }
       }
   int i, cpt, cptcod;  
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)      /* Computing expectancies */
       for (i=1; i<=nlstate;i++)      hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)      for(i=1; i<=nlstate;i++)
           mobaverage[(int)agedeb][i][cptcod]=0.;        for(j=1; j<=nlstate;j++)
              for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
       for (i=1; i<=nlstate;i++){            
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
           for (cpt=0;cpt<=4;cpt++){  
             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;      fprintf(ficresstdeij,"%3.0f",age );
         }      for(i=1; i<=nlstate;i++){
       }        eip=0.;
     }        vip=0.;
            for(j=1; j<=nlstate;j++){
 }          eip += eij[i][j][(int)age];
           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];
 /************** Forecasting ******************/          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
 prevforecast(char fileres[], double anproj1,double mproj1,double jproj1,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anproj2,double p[], int i2){        }
          fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      }
   int *popage;      fprintf(ficresstdeij,"\n");
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;  
   double *popeffectif,*popcount;      fprintf(ficrescveij,"%3.0f",age );
   double ***p3mat;      for(i=1; i<=nlstate;i++)
   char fileresf[FILENAMELENGTH];        for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
  agelim=AGESUP;          for(i2=1; i2<=nlstate;i2++)
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;            for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);              if(cptj2 <= cptj)
                  fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
              }
   strcpy(fileresf,"f");        }
   strcat(fileresf,fileres);      fprintf(ficrescveij,"\n");
   if((ficresf=fopen(fileresf,"w"))==NULL) {     
     printf("Problem with forecast resultfile: %s\n", fileresf);    }
     fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
   }    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
   printf("Computing forecasting: result on file '%s' \n", fileresf);    free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
   fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
   if (mobilav==1) {    fprintf(ficlog,"\n");
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
     movingaverage(agedeb, fage, ageminpar, mobaverage);    free_vector(xm,1,npar);
   }    free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
   stepsize=(int) (stepm+YEARM-1)/YEARM;    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
   if (stepm<=12) stepsize=1;    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
    }
   agelim=AGESUP;  
    /************ Variance ******************/
   hstepm=1;  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[])
   hstepm=hstepm/stepm;  {
   yp1=modf(dateintmean,&yp);    /* Variance of health expectancies */
   anprojmean=yp;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
   yp2=modf((yp1*12),&yp);    /* double **newm;*/
   mprojmean=yp;    double **dnewm,**doldm;
   yp1=modf((yp2*30.5),&yp);    double **dnewmp,**doldmp;
   jprojmean=yp;    int i, j, nhstepm, hstepm, h, nstepm ;
   if(jprojmean==0) jprojmean=1;    int k, cptcode;
   if(mprojmean==0) jprojmean=1;    double *xp;
      double **gp, **gm;  /* for var eij */
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);    double ***gradg, ***trgradg; /*for var eij */
      double **gradgp, **trgradgp; /* for var p point j */
   for(cptcov=1;cptcov<=i2;cptcov++){    double *gpp, *gmp; /* for var p point j */
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
       k=k+1;    double ***p3mat;
       fprintf(ficresf,"\n#******");    double age,agelim, hf;
       for(j=1;j<=cptcoveff;j++) {    double ***mobaverage;
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    int theta;
       }    char digit[4];
       fprintf(ficresf,"******\n");    char digitp[25];
       fprintf(ficresf,"# StartingAge FinalAge");  
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);    char fileresprobmorprev[FILENAMELENGTH];
        
          if(popbased==1){
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {      if(mobilav!=0)
         fprintf(ficresf,"\n");        strcpy(digitp,"-populbased-mobilav-");
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);        else strcpy(digitp,"-populbased-nomobil-");
     }
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){    else 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);      strcpy(digitp,"-stablbased-");
           nhstepm = nhstepm/hstepm;  
              if (mobilav!=0) {
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           oldm=oldms;savm=savms;      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);          fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
                printf(" Error in movingaverage mobilav=%d\n",mobilav);
           for (h=0; h<=nhstepm; h++){      }
             if (h==(int) (calagedate+YEARM*cpt)) {    }
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);  
             }    strcpy(fileresprobmorprev,"prmorprev"); 
             for(j=1; j<=nlstate+ndeath;j++) {    sprintf(digit,"%-d",ij);
               kk1=0.;kk2=0;    /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
               for(i=1; i<=nlstate;i++) {                  strcat(fileresprobmorprev,digit); /* Tvar to be done */
                 if (mobilav==1)    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    strcat(fileresprobmorprev,fileres);
                 else {    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];      printf("Problem with resultfile: %s\n", fileresprobmorprev);
                 }      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
                    }
               }    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
               if (h==(int)(calagedate+12*cpt)){   
                 fprintf(ficresf," %.3f", kk1);    fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
                            pstamp(ficresprobmorprev);
               }    fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
             }    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
           }    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficresprobmorprev," p.%-d SE",j);
         }      for(i=1; i<=nlstate;i++)
       }        fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }    }  
   }    fprintf(ficresprobmorprev,"\n");
            fprintf(ficgp,"\n# Routine varevsij");
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    /* 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");
   fclose(ficresf);    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
 }  /*   } */
 /************** Forecasting ******************/    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
 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){    pstamp(ficresvij);
      fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;    if(popbased==1)
   int *popage;      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);
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    else
   double *popeffectif,*popcount;      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
   double ***p3mat,***tabpop,***tabpopprev;    fprintf(ficresvij,"# Age");
   char filerespop[FILENAMELENGTH];    for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    fprintf(ficresvij,"\n");
   agelim=AGESUP;  
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;    xp=vector(1,npar);
      dnewm=matrix(1,nlstate,1,npar);
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    doldm=matrix(1,nlstate,1,nlstate);
      dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
      doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   strcpy(filerespop,"pop");  
   strcat(filerespop,fileres);    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
   if((ficrespop=fopen(filerespop,"w"))==NULL) {    gpp=vector(nlstate+1,nlstate+ndeath);
     printf("Problem with forecast resultfile: %s\n", filerespop);    gmp=vector(nlstate+1,nlstate+ndeath);
     fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
   }    
   printf("Computing forecasting: result on file '%s' \n", filerespop);    if(estepm < stepm){
   fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);      printf ("Problem %d lower than %d\n",estepm, stepm);
     }
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    else  hstepm=estepm;   
     /* For example we decided to compute the life expectancy with the smallest unit */
   if (mobilav==1) {    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);       nhstepm is the number of hstepm from age to agelim 
     movingaverage(agedeb, fage, ageminpar, mobaverage);       nstepm is the number of stepm from age to agelin. 
   }       Look at function hpijx to understand why (it is linked to memory size questions) */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   stepsize=(int) (stepm+YEARM-1)/YEARM;       survival function given by stepm (the optimization length). Unfortunately it
   if (stepm<=12) stepsize=1;       means that if the survival funtion is printed every two years of age and if
         you sum them up and add 1 year (area under the trapezoids) you won't get the same 
   agelim=AGESUP;       results. So we changed our mind and took the option of the best precision.
      */
   hstepm=1;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   hstepm=hstepm/stepm;    agelim = AGESUP;
      for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
   if (popforecast==1) {      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     if((ficpop=fopen(popfile,"r"))==NULL) {      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       printf("Problem with population file : %s\n",popfile);exit(0);      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
     }      gp=matrix(0,nhstepm,1,nlstate);
     popage=ivector(0,AGESUP);      gm=matrix(0,nhstepm,1,nlstate);
     popeffectif=vector(0,AGESUP);  
     popcount=vector(0,AGESUP);  
          for(theta=1; theta <=npar; theta++){
     i=1;          for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;          xp[i] = x[i] + (i==theta ?delti[theta]:0);
            }
     imx=i;        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   }  
         if (popbased==1) {
   for(cptcov=1;cptcov<=i2;cptcov++){          if(mobilav ==0){
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){            for(i=1; i<=nlstate;i++)
       k=k+1;              prlim[i][i]=probs[(int)age][i][ij];
       fprintf(ficrespop,"\n#******");          }else{ /* mobilav */ 
       for(j=1;j<=cptcoveff;j++) {            for(i=1; i<=nlstate;i++)
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);              prlim[i][i]=mobaverage[(int)age][i][ij];
       }          }
       fprintf(ficrespop,"******\n");        }
       fprintf(ficrespop,"# Age");    
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);        for(j=1; j<= nlstate; j++){
       if (popforecast==1)  fprintf(ficrespop," [Population]");          for(h=0; h<=nhstepm; h++){
                  for(i=1, gp[h][j]=0.;i<=nlstate;i++)
       for (cpt=0; cpt<=0;cpt++) {              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);            }
                }
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        /* This for computing probability of death (h=1 means
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);           computed over hstepm matrices product = hstepm*stepm months) 
           nhstepm = nhstepm/hstepm;           as a weighted average of prlim.
                  */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        for(j=nlstate+1;j<=nlstate+ndeath;j++){
           oldm=oldms;savm=savms;          for(i=1,gpp[j]=0.; i<= nlstate; i++)
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);              gpp[j] += prlim[i][i]*p3mat[i][j][1];
                }    
           for (h=0; h<=nhstepm; h++){        /* end probability of death */
             if (h==(int) (calagedate+YEARM*cpt)) {  
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
             }          xp[i] = x[i] - (i==theta ?delti[theta]:0);
             for(j=1; j<=nlstate+ndeath;j++) {        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
               kk1=0.;kk2=0;        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
               for(i=1; i<=nlstate;i++) {                 
                 if (mobilav==1)        if (popbased==1) {
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];          if(mobilav ==0){
                 else {            for(i=1; i<=nlstate;i++)
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];              prlim[i][i]=probs[(int)age][i][ij];
                 }          }else{ /* mobilav */ 
               }            for(i=1; i<=nlstate;i++)
               if (h==(int)(calagedate+12*cpt)){              prlim[i][i]=mobaverage[(int)age][i][ij];
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;          }
                   /*fprintf(ficrespop," %.3f", kk1);        }
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/  
               }        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
             }          for(h=0; h<=nhstepm; h++){
             for(i=1; i<=nlstate;i++){            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               kk1=0.;              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
                 for(j=1; j<=nlstate;j++){          }
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];        }
                 }        /* This for computing probability of death (h=1 means
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];           computed over hstepm matrices product = hstepm*stepm months) 
             }           as a weighted average of prlim.
         */
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)        for(j=nlstate+1;j<=nlstate+ndeath;j++){
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);          for(i=1,gmp[j]=0.; i<= nlstate; i++)
           }           gmp[j] += prlim[i][i]*p3mat[i][j][1];
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        }    
         }        /* end probability of death */
       }  
          for(j=1; j<= nlstate; j++) /* vareij */
   /******/          for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {          }
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);    
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
           nhstepm = nhstepm/hstepm;        }
            
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      } /* End theta */
           oldm=oldms;savm=savms;  
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
           for (h=0; h<=nhstepm; h++){  
             if (h==(int) (calagedate+YEARM*cpt)) {      for(h=0; h<=nhstepm; h++) /* veij */
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);        for(j=1; j<=nlstate;j++)
             }          for(theta=1; theta <=npar; theta++)
             for(j=1; j<=nlstate+ndeath;j++) {            trgradg[h][j][theta]=gradg[h][theta][j];
               kk1=0.;kk2=0;  
               for(i=1; i<=nlstate;i++) {                    for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];            for(theta=1; theta <=npar; theta++)
               }          trgradgp[j][theta]=gradgp[theta][j];
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    
             }  
           }      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      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++){
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
   if (popforecast==1) {          for(i=1;i<=nlstate;i++)
     free_ivector(popage,0,AGESUP);            for(j=1;j<=nlstate;j++)
     free_vector(popeffectif,0,AGESUP);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
     free_vector(popcount,0,AGESUP);        }
   }      }
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      /* pptj */
   fclose(ficrespop);      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++)
 /**************** Main Program *****************/          varppt[j][i]=doldmp[j][i];
 /***********************************************/      /* end ppptj */
       /*  x centered again */
 int main(int argc, char *argv[])      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
 {      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      if (popbased==1) {
   double agedeb, agefin,hf;        if(mobilav ==0){
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;          for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
   double fret;        }else{ /* mobilav */ 
   double **xi,tmp,delta;          for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
   double dum; /* Dummy variable */        }
   double ***p3mat;      }
   int *indx;               
   char line[MAXLINE], linepar[MAXLINE];      /* This for computing probability of death (h=1 means
   char path[80],pathc[80],pathcd[80],pathtot[80],model[80];         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
   int firstobs=1, lastobs=10;         as a weighted average of prlim.
   int sdeb, sfin; /* Status at beginning and end */      */
   int c,  h , cpt,l;      for(j=nlstate+1;j<=nlstate+ndeath;j++){
   int ju,jl, mi;        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;          gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;      }    
   int mobilav=0,popforecast=0;      /* end probability of death */
   int hstepm, nhstepm;  
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   double bage, fage, age, agelim, agebase;        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
   double ftolpl=FTOL;        for(i=1; i<=nlstate;i++){
   double **prlim;          fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
   double *severity;        }
   double ***param; /* Matrix of parameters */      } 
   double  *p;      fprintf(ficresprobmorprev,"\n");
   double **matcov; /* Matrix of covariance */  
   double ***delti3; /* Scale */      fprintf(ficresvij,"%.0f ",age );
   double *delti; /* Scale */      for(i=1; i<=nlstate;i++)
   double ***eij, ***vareij;        for(j=1; j<=nlstate;j++){
   double **varpl; /* Variances of prevalence limits by age */          fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
   double *epj, vepp;        }
   double kk1, kk2;      fprintf(ficresvij,"\n");
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;      free_matrix(gp,0,nhstepm,1,nlstate);
        free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
   char *alph[]={"a","a","b","c","d","e"}, str[4];      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
   char z[1]="c", occ;    free_vector(gpp,nlstate+1,nlstate+ndeath);
 #include <sys/time.h>    free_vector(gmp,nlstate+1,nlstate+ndeath);
 #include <time.h>    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
      fprintf(ficgp,"\nset noparametric;set nolabel; set ter png small;set size 0.65, 0.65");
   /* long total_usecs;    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
   struct timeval start_time, end_time;    fprintf(ficgp,"\n set log y; set nolog x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
    /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   getcwd(pathcd, size);  /*   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));
   printf("\n%s",version);    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
   if(argc <=1){    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
     printf("\nEnter the parameter file name: ");    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     scanf("%s",pathtot);    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);
   else{  */
     strcpy(pathtot,argv[1]);  /*   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);
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/  
   /*cygwin_split_path(pathtot,path,optionfile);    free_vector(xp,1,npar);
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/    free_matrix(doldm,1,nlstate,1,nlstate);
   /* cutv(path,optionfile,pathtot,'\\');*/    free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   chdir(path);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   replace(pathc,path);    fclose(ficresprobmorprev);
     fflush(ficgp);
 /*-------- arguments in the command line --------*/    fflush(fichtm); 
   }  /* end varevsij */
   /* Log file */  
   strcat(filelog, optionfilefiname);  /************ Variance of prevlim ******************/
   strcat(filelog,".log");    /* */  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[])
   if((ficlog=fopen(filelog,"w"))==NULL)    {  {
     printf("Problem with logfile %s\n",filelog);    /* Variance of prevalence limit */
     goto end;    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   }    double **newm;
   fprintf(ficlog,"Log filename:%s\n",filelog);    double **dnewm,**doldm;
   fprintf(ficlog,"\n%s",version);    int i, j, nhstepm, hstepm;
   fprintf(ficlog,"\nEnter the parameter file name: ");    int k, cptcode;
   fprintf(ficlog,"pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    double *xp;
   fflush(ficlog);    double *gp, *gm;
     double **gradg, **trgradg;
   /* */    double age,agelim;
   strcpy(fileres,"r");    int theta;
   strcat(fileres, optionfilefiname);    
   strcat(fileres,".txt");    /* Other files have txt extension */    pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
   /*---------arguments file --------*/    fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        fprintf(ficresvpl," %1d-%1d",i,i);
     printf("Problem with optionfile %s\n",optionfile);    fprintf(ficresvpl,"\n");
     fprintf(ficlog,"Problem with optionfile %s\n",optionfile);  
     goto end;    xp=vector(1,npar);
   }    dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
   strcpy(filereso,"o");    
   strcat(filereso,fileres);    hstepm=1*YEARM; /* Every year of age */
   if((ficparo=fopen(filereso,"w"))==NULL) {    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     printf("Problem with Output resultfile: %s\n", filereso);    agelim = AGESUP;
     fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     goto end;      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 */
   /* Reads comments: lines beginning with '#' */      gradg=matrix(1,npar,1,nlstate);
   while((c=getc(ficpar))=='#' && c!= EOF){      gp=vector(1,nlstate);
     ungetc(c,ficpar);      gm=vector(1,nlstate);
     fgets(line, MAXLINE, ficpar);  
     puts(line);      for(theta=1; theta <=npar; theta++){
     fputs(line,ficparo);        for(i=1; i<=npar; i++){ /* Computes gradient */
   }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
   ungetc(c,ficpar);        }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   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);        for(i=1;i<=nlstate;i++)
   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);          gp[i] = prlim[i][i];
   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);      
 while((c=getc(ficpar))=='#' && c!= EOF){        for(i=1; i<=npar; i++) /* Computes gradient */
     ungetc(c,ficpar);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     fgets(line, MAXLINE, ficpar);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     puts(line);        for(i=1;i<=nlstate;i++)
     fputs(line,ficparo);          gm[i] = prlim[i][i];
   }  
   ungetc(c,ficpar);        for(i=1;i<=nlstate;i++)
            gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
          } /* End theta */
   covar=matrix(0,NCOVMAX,1,n);  
   cptcovn=0;      trgradg =matrix(1,nlstate,1,npar);
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;  
       for(j=1; j<=nlstate;j++)
   ncovmodel=2+cptcovn;        for(theta=1; theta <=npar; theta++)
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */          trgradg[j][theta]=gradg[theta][j];
    
   /* Read guess parameters */      for(i=1;i<=nlstate;i++)
   /* Reads comments: lines beginning with '#' */        varpl[i][(int)age] =0.;
   while((c=getc(ficpar))=='#' && c!= EOF){      matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
     ungetc(c,ficpar);      matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
     fgets(line, MAXLINE, ficpar);      for(i=1;i<=nlstate;i++)
     puts(line);        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
     fputs(line,ficparo);  
   }      fprintf(ficresvpl,"%.0f ",age );
   ungetc(c,ficpar);      for(i=1; i<=nlstate;i++)
          fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      fprintf(ficresvpl,"\n");
     for(i=1; i <=nlstate; i++)      free_vector(gp,1,nlstate);
     for(j=1; j <=nlstate+ndeath-1; j++){      free_vector(gm,1,nlstate);
       fscanf(ficpar,"%1d%1d",&i1,&j1);      free_matrix(gradg,1,npar,1,nlstate);
       fprintf(ficparo,"%1d%1d",i1,j1);      free_matrix(trgradg,1,nlstate,1,npar);
       if(mle==1)    } /* End age */
         printf("%1d%1d",i,j);  
       fprintf(ficlog,"%1d%1d",i,j);    free_vector(xp,1,npar);
       for(k=1; k<=ncovmodel;k++){    free_matrix(doldm,1,nlstate,1,npar);
         fscanf(ficpar," %lf",&param[i][j][k]);    free_matrix(dnewm,1,nlstate,1,nlstate);
         if(mle==1){  
           printf(" %lf",param[i][j][k]);  }
           fprintf(ficlog," %lf",param[i][j][k]);  
         }  /************ Variance of one-step probabilities  ******************/
         else  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[])
           fprintf(ficlog," %lf",param[i][j][k]);  {
         fprintf(ficparo," %lf",param[i][j][k]);    int i, j=0,  i1, k1, l1, t, tj;
       }    int k2, l2, j1,  z1;
       fscanf(ficpar,"\n");    int k=0,l, cptcode;
       if(mle==1)    int first=1, first1;
         printf("\n");    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
       fprintf(ficlog,"\n");    double **dnewm,**doldm;
       fprintf(ficparo,"\n");    double *xp;
     }    double *gp, *gm;
      double **gradg, **trgradg;
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;    double **mu;
     double age,agelim, cov[NCOVMAX];
   p=param[1][1];    double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
      int theta;
   /* Reads comments: lines beginning with '#' */    char fileresprob[FILENAMELENGTH];
   while((c=getc(ficpar))=='#' && c!= EOF){    char fileresprobcov[FILENAMELENGTH];
     ungetc(c,ficpar);    char fileresprobcor[FILENAMELENGTH];
     fgets(line, MAXLINE, ficpar);  
     puts(line);    double ***varpij;
     fputs(line,ficparo);  
   }    strcpy(fileresprob,"prob"); 
   ungetc(c,ficpar);    strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      printf("Problem with resultfile: %s\n", fileresprob);
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
   for(i=1; i <=nlstate; i++){    }
     for(j=1; j <=nlstate+ndeath-1; j++){    strcpy(fileresprobcov,"probcov"); 
       fscanf(ficpar,"%1d%1d",&i1,&j1);    strcat(fileresprobcov,fileres);
       printf("%1d%1d",i,j);    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       fprintf(ficparo,"%1d%1d",i1,j1);      printf("Problem with resultfile: %s\n", fileresprobcov);
       for(k=1; k<=ncovmodel;k++){      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
         fscanf(ficpar,"%le",&delti3[i][j][k]);    }
         printf(" %le",delti3[i][j][k]);    strcpy(fileresprobcor,"probcor"); 
         fprintf(ficparo," %le",delti3[i][j][k]);    strcat(fileresprobcor,fileres);
       }    if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       fscanf(ficpar,"\n");      printf("Problem with resultfile: %s\n", fileresprobcor);
       printf("\n");      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficparo,"\n");    }
     }    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);
   delti=delti3[1][1];    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);
   /* Reads comments: lines beginning with '#' */    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   while((c=getc(ficpar))=='#' && c!= EOF){    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     ungetc(c,ficpar);    pstamp(ficresprob);
     fgets(line, MAXLINE, ficpar);    fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     puts(line);    fprintf(ficresprob,"# Age");
     fputs(line,ficparo);    pstamp(ficresprobcov);
   }    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   ungetc(c,ficpar);    fprintf(ficresprobcov,"# Age");
      pstamp(ficresprobcor);
   matcov=matrix(1,npar,1,npar);    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   for(i=1; i <=npar; i++){    fprintf(ficresprobcor,"# Age");
     fscanf(ficpar,"%s",&str);  
     if(mle==1)  
       printf("%s",str);    for(i=1; i<=nlstate;i++)
     fprintf(ficlog,"%s",str);      for(j=1; j<=(nlstate+ndeath);j++){
     fprintf(ficparo,"%s",str);        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
     for(j=1; j <=i; j++){        fprintf(ficresprobcov," p%1d-%1d ",i,j);
       fscanf(ficpar," %le",&matcov[i][j]);        fprintf(ficresprobcor," p%1d-%1d ",i,j);
       if(mle==1){      }  
         printf(" %.5le",matcov[i][j]);   /* fprintf(ficresprob,"\n");
         fprintf(ficlog," %.5le",matcov[i][j]);    fprintf(ficresprobcov,"\n");
       }    fprintf(ficresprobcor,"\n");
       else   */
         fprintf(ficlog," %.5le",matcov[i][j]);   xp=vector(1,npar);
       fprintf(ficparo," %.5le",matcov[i][j]);    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     }    doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     fscanf(ficpar,"\n");    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     if(mle==1)    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
       printf("\n");    first=1;
     fprintf(ficlog,"\n");    fprintf(ficgp,"\n# Routine varprob");
     fprintf(ficparo,"\n");    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
   }    fprintf(fichtm,"\n");
   for(i=1; i <=npar; i++)  
     for(j=i+1;j<=npar;j++)    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
       matcov[i][j]=matcov[j][i];    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
        file %s<br>\n",optionfilehtmcov);
   if(mle==1)    fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
     printf("\n");  and drawn. It helps understanding how is the covariance between two incidences.\
   fprintf(ficlog,"\n");   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 \
     /*-------- Rewriting paramater file ----------*/  would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
      strcpy(rfileres,"r");    /* "Rparameterfile */  standard deviations wide on each axis. <br>\
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
      strcat(rfileres,".");    /* */   and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
      strcat(rfileres,optionfilext);    /* Other files have txt extension */  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
     if((ficres =fopen(rfileres,"w"))==NULL) {  
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    cov[1]=1;
       fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;    tj=cptcoveff;
     }    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     fprintf(ficres,"#%s\n",version);    j1=0;
        for(t=1; t<=tj;t++){
     /*-------- data file ----------*/      for(i1=1; i1<=ncodemax[t];i1++){ 
     if((fic=fopen(datafile,"r"))==NULL)    {        j1++;
       printf("Problem with datafile: %s\n", datafile);goto end;        if  (cptcovn>0) {
       fprintf(ficlog,"Problem with datafile: %s\n", datafile);goto end;          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");
     n= lastobs;          fprintf(ficresprobcov, "\n#********** Variable "); 
     severity = vector(1,maxwav);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     outcome=imatrix(1,maxwav+1,1,n);          fprintf(ficresprobcov, "**********\n#\n");
     num=ivector(1,n);          
     moisnais=vector(1,n);          fprintf(ficgp, "\n#********** Variable "); 
     annais=vector(1,n);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     moisdc=vector(1,n);          fprintf(ficgp, "**********\n#\n");
     andc=vector(1,n);          
     agedc=vector(1,n);          
     cod=ivector(1,n);          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
     weight=vector(1,n);          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
     mint=matrix(1,maxwav,1,n);          
     anint=matrix(1,maxwav,1,n);          fprintf(ficresprobcor, "\n#********** Variable ");    
     s=imatrix(1,maxwav+1,1,n);          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
     adl=imatrix(1,maxwav+1,1,n);              fprintf(ficresprobcor, "**********\n#");    
     tab=ivector(1,NCOVMAX);        }
     ncodemax=ivector(1,8);        
         for (age=bage; age<=fage; age ++){ 
     i=1;          cov[2]=age;
     while (fgets(line, MAXLINE, fic) != NULL)    {          for (k=1; k<=cptcovn;k++) {
       if ((i >= firstobs) && (i <=lastobs)) {            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
                  }
         for (j=maxwav;j>=1;j--){          for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          for (k=1; k<=cptcovprod;k++)
           strcpy(line,stra);            cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
         }          trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
                  gp=vector(1,(nlstate)*(nlstate+ndeath));
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);          gm=vector(1,(nlstate)*(nlstate+ndeath));
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);      
           for(theta=1; theta <=npar; theta++){
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);            for(i=1; i<=npar; i++)
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);            pmij(pmmij,cov,ncovmodel,xp,nlstate);
         for (j=ncovcol;j>=1;j--){            
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);            k=0;
         }            for(i=1; i<= (nlstate); i++){
         num[i]=atol(stra);              for(j=1; j<=(nlstate+ndeath);j++){
                        k=k+1;
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){                gp[k]=pmmij[i][j];
           printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/              }
             }
         i=i+1;            
       }            for(i=1; i<=npar; i++)
     }              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
     /* printf("ii=%d", ij);      
        scanf("%d",i);*/            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   imx=i-1; /* Number of individuals */            k=0;
             for(i=1; i<=(nlstate); i++){
   /* for (i=1; i<=imx; i++){              for(j=1; j<=(nlstate+ndeath);j++){
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;                k=k+1;
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;                gm[k]=pmmij[i][j];
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;              }
     }*/            }
    /*  for (i=1; i<=imx; i++){       
      if (s[4][i]==9)  s[4][i]=-1;            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
      printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/              gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
            }
    
   /* Calculation of the number of parameter from char model*/          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
   Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */            for(theta=1; theta <=npar; theta++)
   Tprod=ivector(1,15);              trgradg[j][theta]=gradg[theta][j];
   Tvaraff=ivector(1,15);          
   Tvard=imatrix(1,15,1,2);          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
   Tage=ivector(1,15);                matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
              free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
   if (strlen(model) >1){          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
     j=0, j1=0, k1=1, k2=1;          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
     j=nbocc(model,'+');          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
     j1=nbocc(model,'*');  
     cptcovn=j+1;          pmij(pmmij,cov,ncovmodel,x,nlstate);
     cptcovprod=j1;          
              k=0;
     strcpy(modelsav,model);          for(i=1; i<=(nlstate); i++){
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){            for(j=1; j<=(nlstate+ndeath);j++){
       printf("Error. Non available option model=%s ",model);              k=k+1;
       fprintf(ficlog,"Error. Non available option model=%s ",model);              mu[k][(int) age]=pmmij[i][j];
       goto end;            }
     }          }
              for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
     for(i=(j+1); i>=1;i--){            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
       cutv(stra,strb,modelsav,'+'); /* keeps in strb after the last + */              varpij[i][j][(int)age] = doldm[i][j];
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyze it */  
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/          /*printf("\n%d ",(int)age);
       /*scanf("%d",i);*/            for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
       if (strchr(strb,'*')) {  /* Model includes a product */            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
         cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn (if not *age)*/            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
         if (strcmp(strc,"age")==0) { /* Vn*age */            }*/
           cptcovprod--;  
           cutv(strb,stre,strd,'V');          fprintf(ficresprob,"\n%d ",(int)age);
           Tvar[i]=atoi(stre); /* computes n in Vn and stores in Tvar*/          fprintf(ficresprobcov,"\n%d ",(int)age);
           cptcovage++;          fprintf(ficresprobcor,"\n%d ",(int)age);
             Tage[cptcovage]=i;  
             /*printf("stre=%s ", stre);*/          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
         }            fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
         else if (strcmp(strd,"age")==0) { /* or age*Vn */          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
           cptcovprod--;            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
           cutv(strb,stre,strc,'V');            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           Tvar[i]=atoi(stre);          }
           cptcovage++;          i=0;
           Tage[cptcovage]=i;          for (k=1; k<=(nlstate);k++){
         }            for (l=1; l<=(nlstate+ndeath);l++){ 
         else {  /* Age is not in the model */              i=i++;
           cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n*/              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
           Tvar[i]=ncovcol+k1;              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
           cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */              for (j=1; j<=i;j++){
           Tprod[k1]=i;                fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
           Tvard[k1][1]=atoi(strc); /* m*/                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
           Tvard[k1][2]=atoi(stre); /* n */              }
           Tvar[cptcovn+k2]=Tvard[k1][1];            }
           Tvar[cptcovn+k2+1]=Tvard[k1][2];          }/* end of loop for state */
           for (k=1; k<=lastobs;k++)        } /* end of loop for age */
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];  
           k1++;        /* Confidence intervalle of pij  */
           k2=k2+2;        /*
         }          fprintf(ficgp,"\nset noparametric;unset label");
       }          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
       else { /* no more sum */          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/          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);
        /*  scanf("%d",i);*/          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
       cutv(strd,strc,strb,'V');          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
       Tvar[i]=atoi(strc);          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
       }        */
       strcpy(modelsav,stra);    
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         scanf("%d",i);*/        first1=1;
     } /* end of loop + */        for (k2=1; k2<=(nlstate);k2++){
   } /* end model */          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
              if(l2==k2) continue;
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);            j=(k2-1)*(nlstate+ndeath)+l2;
   printf("cptcovprod=%d ", cptcovprod);            for (k1=1; k1<=(nlstate);k1++){
   fprintf(ficlog,"cptcovprod=%d ", cptcovprod);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   scanf("%d ",i);*/                if(l1==k1) continue;
     fclose(fic);                i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
     /*  if(mle==1){*/                for (age=bage; age<=fage; age ++){ 
     if (weightopt != 1) { /* Maximisation without weights*/                  if ((int)age %5==0){
       for(i=1;i<=n;i++) weight[i]=1.0;                    v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
     }                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
     /*-calculation of age at interview from date of interview and age at death -*/                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
     agev=matrix(1,maxwav,1,imx);                    mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
     for (i=1; i<=imx; i++) {                    c12=cv12/sqrt(v1*v2);
       for(m=2; (m<= maxwav); m++) {                    /* Computing eigen value of matrix of covariance */
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
          anint[m][i]=9999;                    lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
          s[m][i]=-1;                    /* Eigen vectors */
        }                    v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;                    /*v21=sqrt(1.-v11*v11); *//* error */
       }                    v21=(lc1-v1)/cv12*v11;
     }                    v12=-v21;
                     v22=v11;
     for (i=1; i<=imx; i++)  {                    tnalp=v21/v11;
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);                    if(first1==1){
       for(m=1; (m<= maxwav); m++){                      first1=0;
         if(s[m][i] >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);
           if (s[m][i] >= nlstate+1) {                    }
             if(agedc[i]>0)                    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);
               if(moisdc[i]!=99 && andc[i]!=9999)                    /*printf(fignu*/
                 agev[m][i]=agedc[i];                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
            else {                    if(first==1){
               if (andc[i]!=9999){                      first=0;
               printf("Warning negative age at death: %d line:%d\n",num[i],i);                      fprintf(ficgp,"\nset parametric;unset label");
               fprintf(ficlog,"Warning negative age at death: %d line:%d\n",num[i],i);                      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);
               agev[m][i]=-1;                      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,\
           else if(s[m][i] !=9){ /* Should no more exist */                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
             if(mint[m][i]==99 || anint[m][i]==9999)                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
               agev[m][i]=1;                      fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
             else if(agev[m][i] <agemin){                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
               agemin=agev[m][i];                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/                      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",\
             else if(agev[m][i] >agemax){                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
               agemax=agev[m][i];                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/                    }else{
             }                      first=0;
             /*agev[m][i]=anint[m][i]-annais[i];*/                      fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
             /*   agev[m][i] = age[i]+2*m;*/                      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);
           else { /* =9 */                      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",\
             agev[m][i]=1;                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
             s[m][i]=-1;                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
           }                    }/* if first */
         }                  } /* age mod 5 */
         else /*= 0 Unknown */                } /* end loop age */
           agev[m][i]=1;                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
       }                first=1;
                  } /*l12 */
     }            } /* k12 */
     for (i=1; i<=imx; i++)  {          } /*l1 */
       for(m=1; (m<= maxwav); m++){        }/* k1 */
         if (s[m][i] > (nlstate+ndeath)) {      } /* loop covariates */
           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);      free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
           goto end;    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);
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    fclose(ficresprobcov);
  fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);    fclose(ficresprobcor);
     fflush(ficgp);
     free_vector(severity,1,maxwav);    fflush(fichtmcov);
     free_imatrix(outcome,1,maxwav+1,1,n);  }
     free_vector(moisnais,1,n);  
     free_vector(annais,1,n);  
     /* free_matrix(mint,1,maxwav,1,n);  /******************* Printing html file ***********/
        free_matrix(anint,1,maxwav,1,n);*/  void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
     free_vector(moisdc,1,n);                    int lastpass, int stepm, int weightopt, char model[],\
     free_vector(andc,1,n);                    int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                        double jprev1, double mprev1,double anprev1, \
     wav=ivector(1,imx);                    double jprev2, double mprev2,double anprev2){
     dh=imatrix(1,lastpass-firstpass+1,1,imx);    int jj1, k1, i1, cpt;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);  
         fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
     /* Concatenates waves */     <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);  </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 ",
       Tcode=ivector(1,100);             jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);     fprintf(fichtm,"\
       ncodemax[1]=1;   - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);             stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
           fprintf(fichtm,"\
    codtab=imatrix(1,100,1,10);   - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
    h=0;             subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
    m=pow(2,cptcoveff);     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): \
    for(k=1;k<=cptcoveff; k++){     <a href=\"%s\">%s</a> <br>\n",
      for(i=1; i <=(m/pow(2,k));i++){             estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
        for(j=1; j <= ncodemax[k]; j++){     fprintf(fichtm,"\
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){   - Population projections by age and states: \
            h++;     <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;  
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/  fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
          }  
        }   m=cptcoveff;
      }   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
    }  
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);   jj1=0;
       codtab[1][2]=1;codtab[2][2]=2; */   for(k1=1; k1<=m;k1++){
    /* for(i=1; i <=m ;i++){     for(i1=1; i1<=ncodemax[k1];i1++){
       for(k=1; k <=cptcovn; k++){       jj1++;
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);       if (cptcovn > 0) {
       }         fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
       printf("\n");         for (cpt=1; cpt<=cptcoveff;cpt++) 
       }           fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
       scanf("%d",i);*/         fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
           }
    /* Calculates basic frequencies. Computes observed prevalence at single age       /* Pij */
        and prints on file fileres'p'. */       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\
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */   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> \
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         /* Period (stable) prevalence in each health state */
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         for(cpt=1; cpt<nlstate;cpt++){
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */           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 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] */       for(cpt=1; cpt<=nlstate;cpt++) {
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */          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);
     if(mle==1){       }
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);     } /* end i1 */
     }   }/* End k1 */
       fprintf(fichtm,"</ul>");
     /*--------- 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(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    jk=1;   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");  
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");   fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
    fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");           subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    for(i=1,jk=1; i <=nlstate; i++){   fprintf(fichtm,"\
      for(k=1; k <=(nlstate+ndeath); k++){   - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
        if (k != i)           subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
          {  
            printf("%d%d ",i,k);   fprintf(fichtm,"\
            fprintf(ficlog,"%d%d ",i,k);   - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            fprintf(ficres,"%1d%1d ",i,k);           subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
            for(j=1; j <=ncovmodel; j++){   fprintf(fichtm,"\
              printf("%f ",p[jk]);   - 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): \
              fprintf(ficlog,"%f ",p[jk]);     <a href=\"%s\">%s</a> <br>\n</li>",
              fprintf(ficres,"%f ",p[jk]);             estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
              jk++;   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): \
            printf("\n");     <a href=\"%s\">%s</a> <br>\n</li>",
            fprintf(ficlog,"\n");             estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
            fprintf(ficres,"\n");   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,"\
    if(mle==1){   - 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",
      /* Computing hessian and covariance matrix */           estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
      ftolhess=ftol; /* Usually correct */   fprintf(fichtm,"\
      hesscov(matcov, p, npar, delti, ftolhess, func);   - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
    }           subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
    fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");  
    printf("# Scales (for hessian or gradient estimation)\n");  /*  if(popforecast==1) fprintf(fichtm,"\n */
    fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");  /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
    for(i=1,jk=1; i <=nlstate; i++){  /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
      for(j=1; j <=nlstate+ndeath; j++){  /*      <br>",fileres,fileres,fileres,fileres); */
        if (j!=i) {  /*  else  */
          fprintf(ficres,"%1d%1d",i,j);  /*    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); */
          printf("%1d%1d",i,j);   fflush(fichtm);
          fprintf(ficlog,"%1d%1d",i,j);   fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
          for(k=1; k<=ncovmodel;k++){  
            printf(" %.5e",delti[jk]);   m=cptcoveff;
            fprintf(ficlog," %.5e",delti[jk]);   if (cptcovn < 1) {m=1;ncodemax[1]=1;}
            fprintf(ficres," %.5e",delti[jk]);  
            jk++;   jj1=0;
          }   for(k1=1; k1<=m;k1++){
          printf("\n");     for(i1=1; i1<=ncodemax[k1];i1++){
          fprintf(ficlog,"\n");       jj1++;
          fprintf(ficres,"\n");       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\">");
    k=1;       }
    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");       for(cpt=1; cpt<=nlstate;cpt++) {
    if(mle==1)         fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
      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");  prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
    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");  <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
    for(i=1;i<=npar;i++){       }
      /*  if (k>nlstate) k=1;       fprintf(fichtm,"\n<br>- Total life expectancy by age and \
          i1=(i-1)/(ncovmodel*nlstate)+1;  health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
          fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);  true period expectancies (those weighted with period prevalences are also\
          printf("%s%d%d",alph[k],i1,tab[i]);*/   drawn in addition to the population based expectancies computed using\
      fprintf(ficres,"%3d",i);   observed and cahotic prevalences: %s%d.png<br>\
      if(mle==1)  <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
        printf("%3d",i);     } /* end i1 */
      fprintf(ficlog,"%3d",i);   }/* End k1 */
      for(j=1; j<=i;j++){   fprintf(fichtm,"</ul>");
        fprintf(ficres," %.5e",matcov[i][j]);   fflush(fichtm);
        if(mle==1)  }
          printf(" %.5e",matcov[i][j]);  
        fprintf(ficlog," %.5e",matcov[i][j]);  /******************* Gnuplot file **************/
      }  void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
      fprintf(ficres,"\n");  
      if(mle==1)    char dirfileres[132],optfileres[132];
        printf("\n");    int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
      fprintf(ficlog,"\n");    int ng=0;
      k++;  /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
    }  /*     printf("Problem with file %s",optionfilegnuplot); */
      /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
    while((c=getc(ficpar))=='#' && c!= EOF){  /*   } */
      ungetc(c,ficpar);  
      fgets(line, MAXLINE, ficpar);    /*#ifdef windows */
      puts(line);    fprintf(ficgp,"cd \"%s\" \n",pathc);
      fputs(line,ficparo);      /*#endif */
    }    m=pow(2,cptcoveff);
    ungetc(c,ficpar);  
    estepm=0;    strcpy(dirfileres,optionfilefiname);
    fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);    strcpy(optfileres,"vpl");
    if (estepm==0 || estepm < stepm) estepm=stepm;   /* 1eme*/
    if (fage <= 2) {    for (cpt=1; cpt<= nlstate ; cpt ++) {
      bage = ageminpar;     for (k1=1; k1<= m ; k1 ++) {
      fage = agemaxpar;       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\
    fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");  set ylabel \"Probability\" \n\
    fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);  set ter png small\n\
    fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);  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);
    while((c=getc(ficpar))=='#' && c!= EOF){  
      ungetc(c,ficpar);       for (i=1; i<= nlstate ; i ++) {
      fgets(line, MAXLINE, ficpar);         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
      puts(line);         else fprintf(ficgp," \%%*lf (\%%*lf)");
      fputs(line,ficparo);       }
    }       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);
    ungetc(c,ficpar);       for (i=1; i<= nlstate ; i ++) {
           if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
    fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);         else fprintf(ficgp," \%%*lf (\%%*lf)");
    fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);       } 
    fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);       fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
           for (i=1; i<= nlstate ; i ++) {
    while((c=getc(ficpar))=='#' && c!= EOF){         if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
      ungetc(c,ficpar);         else fprintf(ficgp," \%%*lf (\%%*lf)");
      fgets(line, MAXLINE, ficpar);       }  
      puts(line);       fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      fputs(line,ficparo);     }
    }    }
    ungetc(c,ficpar);    /*2 eme*/
      
     for (k1=1; k1<= m ; k1 ++) { 
    dateprev1=anprev1+mprev1/12.+jprev1/365.;      fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
    dateprev2=anprev2+mprev2/12.+jprev2/365.;      fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
   fscanf(ficpar,"pop_based=%d\n",&popbased);      for (i=1; i<= nlstate+1 ; i ++) {
   fprintf(ficparo,"pop_based=%d\n",popbased);          k=2*i;
   fprintf(ficres,"pop_based=%d\n",popbased);          fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
          for (j=1; j<= nlstate+1 ; j ++) {
   while((c=getc(ficpar))=='#' && c!= EOF){          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
     ungetc(c,ficpar);          else fprintf(ficgp," \%%*lf (\%%*lf)");
     fgets(line, MAXLINE, ficpar);        }   
     puts(line);        if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
     fputs(line,ficparo);        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);
   ungetc(c,ficpar);        for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
   fscanf(ficpar,"starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mov_average=%d\n",&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilav);          else fprintf(ficgp," \%%*lf (\%%*lf)");
 fprintf(ficparo,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);        }   
 fprintf(ficres,"starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mov_average=%d\n",jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilav);        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 ++) {
 while((c=getc(ficpar))=='#' && c!= EOF){          if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
     ungetc(c,ficpar);          else fprintf(ficgp," \%%*lf (\%%*lf)");
     fgets(line, MAXLINE, ficpar);        }   
     puts(line);        if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
     fputs(line,ficparo);        else fprintf(ficgp,"\" t\"\" w l 0,");
   }      }
   ungetc(c,ficpar);    }
     
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    /*3eme*/
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);        /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
 /*------------ gnuplot -------------*/        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
   strcpy(optionfilegnuplot,optionfilefiname);        fprintf(ficgp,"set ter png small\n\
   strcat(optionfilegnuplot,".gp");  set size 0.65,0.65\n\
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {  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);
     printf("Problem with file %s",optionfilegnuplot);        /*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) ");
   fclose(ficgp);          fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
  printinggnuplot(fileres, ageminpar,agemaxpar,fage, pathc,p);          fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
 /*--------- index.htm --------*/          for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
   strcpy(optionfilehtm,optionfile);          
   strcat(optionfilehtm,".htm");        */
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {        for (i=1; i< nlstate ; i ++) {
     printf("Problem with %s \n",optionfilehtm), exit(0);          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(fichtm,"<body> <font size=\"2\">%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        fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
 \n      }
 Total number of observations=%d <br>\n    }
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n    
 <hr  size=\"2\" color=\"#EC5E5E\">    /* CV preval stable (period) */
  <ul><li><h4>Parameter files</h4>\n    for (k1=1; k1<= m ; k1 ++) { 
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n      for (cpt=1; cpt<=nlstate ; cpt ++) {
  - Log file of the run: <a href=\"%s\">%s</a><br>\n        k=3;
  - Gnuplot file name: <a href=\"%s\">%s</a></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,filelog,filelog,optionfilegnuplot,optionfilegnuplot);        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
   fclose(fichtm);        fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
  printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);  unset log y\n\
    plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
 /*------------ free_vector  -------------*/        
  chdir(path);        for (i=1; i< nlstate ; i ++)
            fprintf(ficgp,"+$%d",k+i+1);
  free_ivector(wav,1,imx);        fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);        
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);          l=3+(nlstate+ndeath)*cpt;
  free_ivector(num,1,n);        fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
  free_vector(agedc,1,n);        for (i=1; i< nlstate ; i ++) {
  /*free_matrix(covar,1,NCOVMAX,1,n);*/          l=3+(nlstate+ndeath)*cpt;
  fclose(ficparo);          fprintf(ficgp,"+$%d",l+i+1);
  fclose(ficres);        }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
   /*--------------- Prevalence limit --------------*/    }  
      
   strcpy(filerespl,"pl");    /* proba elementaires */
   strcat(filerespl,fileres);    for(i=1,jk=1; i <=nlstate; i++){
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      for(k=1; k <=(nlstate+ndeath); k++){
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;        if (k != i) {
     fprintf(ficlog,"Problem with Prev limit resultfile: %s\n", filerespl);goto end;          for(j=1; j <=ncovmodel; j++){
   }            fprintf(ficgp,"p%d=%f ",jk,p[jk]);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);            jk++; 
   fprintf(ficlog,"Computing prevalence limit: result on file '%s' \n", filerespl);            fprintf(ficgp,"\n");
   fprintf(ficrespl,"#Prevalence limit\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);     for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */       for(jk=1; jk <=m; jk++) {
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */         if (ng==2)
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */           fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */         else
   k=0;           fprintf(ficgp,"\nset title \"Probability\"\n");
   agebase=ageminpar;         fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
   agelim=agemaxpar;         i=1;
   ftolpl=1.e-10;         for(k2=1; k2<=nlstate; k2++) {
   i1=cptcoveff;           k3=i;
   if (cptcovn < 1){i1=1;}           for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
   for(cptcov=1;cptcov<=i1;cptcov++){               if(ng==2)
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                 fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
         k=k+1;               else
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/                 fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
         fprintf(ficrespl,"\n#******");               ij=1;
         printf("\n#******");               for(j=3; j <=ncovmodel; j++) {
         fprintf(ficlog,"\n#******");                 if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
         for(j=1;j<=cptcoveff;j++) {                   fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);                   ij++;
           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]]);                 else
         }                   fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
         fprintf(ficrespl,"******\n");               }
         printf("******\n");               fprintf(ficgp,")/(1");
         fprintf(ficlog,"******\n");               
                       for(k1=1; k1 <=nlstate; k1++){   
         for (age=agebase; age<=agelim; age++){                 fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);                 ij=1;
           fprintf(ficrespl,"%.0f",age );                 for(j=3; j <=ncovmodel; j++){
           for(i=1; i<=nlstate;i++)                   if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
           fprintf(ficrespl," %.5f", prlim[i][i]);                     fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
           fprintf(ficrespl,"\n");                     ij++;
         }                   }
       }                   else
     }                     fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
   fclose(ficrespl);                 }
                  fprintf(ficgp,")");
   /*------------- h Pij x at various ages ------------*/               }
                 fprintf(ficgp,") t \"p%d%d\" ", k2,k);
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);               if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
   if((ficrespij=fopen(filerespij,"w"))==NULL) {               i=i+ncovmodel;
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;             }
     fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;           } /* end k */
   }         } /* end k2 */
   printf("Computing pij: result on file '%s' \n", filerespij);       } /* end jk */
   fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);     } /* end ng */
       fflush(ficgp); 
   stepsize=(int) (stepm+YEARM-1)/YEARM;  }  /* end gnuplot */
   /*if (stepm<=24) stepsize=2;*/  
   
   agelim=AGESUP;  /*************** Moving average **************/
   hstepm=stepsize*YEARM; /* Every year of age */  int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  
     int i, cpt, cptcod;
   /* hstepm=1;   aff par mois*/    int modcovmax =1;
     int mobilavrange, mob;
   k=0;    double age;
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
       k=k+1;                             a covariate has 2 modalities */
         fprintf(ficrespij,"\n#****** ");    if (cptcovn<1) modcovmax=1; /* At least 1 pass */
         for(j=1;j<=cptcoveff;j++)  
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
         fprintf(ficrespij,"******\n");      if(mobilav==1) mobilavrange=5; /* default */
              else mobilavrange=mobilav;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */      for (age=bage; age<=fage; age++)
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        for (i=1; i<=nlstate;i++)
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
           /*      nhstepm=nhstepm*YEARM; aff par mois*/      /* 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
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         we use a 5 terms etc. until the borders are no more concerned. 
           oldm=oldms;savm=savms;      */ 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        for (mob=3;mob <=mobilavrange;mob=mob+2){
           fprintf(ficrespij,"# Age");        for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for(i=1; i<=nlstate;i++)          for (i=1; i<=nlstate;i++){
             for(j=1; j<=nlstate+ndeath;j++)            for (cptcod=1;cptcod<=modcovmax;cptcod++){
               fprintf(ficrespij," %1d-%1d",i,j);              mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
           fprintf(ficrespij,"\n");                for (cpt=1;cpt<=(mob-1)/2;cpt++){
            for (h=0; h<=nhstepm; h++){                  mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
             fprintf(ficrespij,"%d %f %f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );                  mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
             for(i=1; i<=nlstate;i++)                }
               for(j=1; j<=nlstate+ndeath;j++)              mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);            }
             fprintf(ficrespij,"\n");          }
              }        }/* end age */
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      }/* end mob */
           fprintf(ficrespij,"\n");    }else return -1;
         }    return 0;
     }  }/* End movingaverage */
   }  
   
   varprob(optionfilefiname, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);  /************** 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){
   fclose(ficrespij);    /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
   /*---------- Forecasting ------------------*/       anproj2 year of en of projection (same day and month as proj1).
   if((stepm == 1) && (strcmp(model,".")==0)){    */
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);    int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);    int *popage;
   }    double agec; /* generic age */
   else{    double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     erreur=108;    double *popeffectif,*popcount;
     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);    double ***p3mat;
     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);    double ***mobaverage;
   }    char fileresf[FILENAMELENGTH];
    
     agelim=AGESUP;
   /*---------- Health expectancies and variances ------------*/    prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
   strcpy(filerest,"t");    strcpy(fileresf,"f"); 
   strcat(filerest,fileres);    strcat(fileresf,fileres);
   if((ficrest=fopen(filerest,"w"))==NULL) {    if((ficresf=fopen(fileresf,"w"))==NULL) {
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      printf("Problem with forecast resultfile: %s\n", fileresf);
     fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;      fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
   }    }
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    printf("Computing forecasting: result on file '%s' \n", fileresf);
   fprintf(ficlog,"Computing Total LEs with variances: file '%s' \n", filerest);    fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   strcpy(filerese,"e");  
   strcat(filerese,fileres);    if (mobilav!=0) {
   if((ficreseij=fopen(filerese,"w"))==NULL) {      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);      if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
     fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   }        printf(" Error in movingaverage mobilav=%d\n",mobilav);
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);      }
   fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);    }
   
   strcpy(fileresv,"v");    stepsize=(int) (stepm+YEARM-1)/YEARM;
   strcat(fileresv,fileres);    if (stepm<=12) stepsize=1;
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    if(estepm < stepm){
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      printf ("Problem %d lower than %d\n",estepm, stepm);
     fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);    }
   }    else  hstepm=estepm;   
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);  
   fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);    hstepm=hstepm/stepm; 
   calagedate=-1;    yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);                                 fractional in yp1 */
     anprojmean=yp;
   k=0;    yp2=modf((yp1*12),&yp);
   for(cptcov=1;cptcov<=i1;cptcov++){    mprojmean=yp;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    yp1=modf((yp2*30.5),&yp);
       k=k+1;    jprojmean=yp;
       fprintf(ficrest,"\n#****** ");    if(jprojmean==0) jprojmean=1;
       for(j=1;j<=cptcoveff;j++)    if(mprojmean==0) jprojmean=1;
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficrest,"******\n");    i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
       fprintf(ficreseij,"\n#****** ");    
       for(j=1;j<=cptcoveff;j++)    fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    
       fprintf(ficreseij,"******\n");    fprintf(ficresf,"#****** Routine prevforecast **\n");
   
       fprintf(ficresvij,"\n#****** ");  /*            if (h==(int)(YEARM*yearp)){ */
       for(j=1;j<=cptcoveff;j++)    for(cptcov=1, k=0;cptcov<=i1;cptcov++){
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
       fprintf(ficresvij,"******\n");        k=k+1;
         fprintf(ficresf,"\n#******");
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        for(j=1;j<=cptcoveff;j++) {
       oldm=oldms;savm=savms;          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]]);
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);          }
          fprintf(ficresf,"******\n");
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);        fprintf(ficresf,"# Covariate valuofcovar yearproj age");
       oldm=oldms;savm=savms;        for(j=1; j<=nlstate+ndeath;j++){ 
       varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,0);          for(i=1; i<=nlstate;i++)              
       if(popbased==1){            fprintf(ficresf," p%d%d",i,j);
         varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,popbased);          fprintf(ficresf," p.%d",j);
        }        }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
            fprintf(ficresf,"\n");
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);  
       fprintf(ficrest,"\n");          for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
       epj=vector(1,nlstate+1);            nhstepm = nhstepm/hstepm; 
       for(age=bage; age <=fage ;age++){            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            oldm=oldms;savm=savms;
         if (popbased==1) {            hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           for(i=1; i<=nlstate;i++)          
             prlim[i][i]=probs[(int)age][i][k];            for (h=0; h<=nhstepm; h++){
         }              if (h*hstepm/YEARM*stepm ==yearp) {
                        fprintf(ficresf,"\n");
         fprintf(ficrest," %4.0f",age);                for(j=1;j<=cptcoveff;j++) 
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){                  fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
             epj[j] += prlim[i][i]*eij[i][j][(int)age];              } 
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/              for(j=1; j<=nlstate+ndeath;j++) {
           }                ppij=0.;
           epj[nlstate+1] +=epj[j];                for(i=1; i<=nlstate;i++) {
         }                  if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
         for(i=1, vepp=0.;i <=nlstate;i++)                  else {
           for(j=1;j <=nlstate;j++)                    ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
             vepp += vareij[i][j][(int)age];                  }
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));                  if (h*hstepm/YEARM*stepm== yearp) {
         for(j=1;j <=nlstate;j++){                    fprintf(ficresf," %.3f", p3mat[i][j][h]);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));                  }
         }                } /* end i */
         fprintf(ficrest,"\n");                if (h*hstepm/YEARM*stepm==yearp) {
       }                  fprintf(ficresf," %.3f", ppij);
     }                }
   }              }/* end j */
 free_matrix(mint,1,maxwav,1,n);            } /* end h */
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);            free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_vector(weight,1,n);          } /* end agec */
   fclose(ficreseij);        } /* end yearp */
   fclose(ficresvij);      } /* end cptcod */
   fclose(ficrest);    } /* end  cptcov */
   fclose(ficpar);         
   free_vector(epj,1,nlstate+1);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
    
   /*------- Variance limit prevalence------*/      fclose(ficresf);
   }
   strcpy(fileresvpl,"vpl");  
   strcat(fileresvpl,fileres);  /************** Forecasting *****not tested NB*************/
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {  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){
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    
     exit(0);    int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
   }    int *popage;
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
   k=0;    double ***p3mat,***tabpop,***tabpopprev;
   for(cptcov=1;cptcov<=i1;cptcov++){    double ***mobaverage;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    char filerespop[FILENAMELENGTH];
       k=k+1;  
       fprintf(ficresvpl,"\n#****** ");    tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(j=1;j<=cptcoveff;j++)    tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    agelim=AGESUP;
       fprintf(ficresvpl,"******\n");    calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
          
       varpl=matrix(1,nlstate,(int) bage, (int) fage);    prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       oldm=oldms;savm=savms;    
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    
     }    strcpy(filerespop,"pop"); 
  }    strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
   fclose(ficresvpl);      printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
   /*---------- End : free ----------------*/    }
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    printf("Computing forecasting: result on file '%s' \n", filerespop);
      fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);  
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    if (cptcoveff==0) ncodemax[cptcoveff]=1;
    
      if (mobilav!=0) {
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);      if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);        fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);        printf(" Error in movingaverage mobilav=%d\n",mobilav);
        }
   free_matrix(matcov,1,npar,1,npar);    }
   free_vector(delti,1,npar);  
   free_matrix(agev,1,maxwav,1,imx);    stepsize=(int) (stepm+YEARM-1)/YEARM;
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);    if (stepm<=12) stepsize=1;
     
   fprintf(fichtm,"\n</body>");    agelim=AGESUP;
   fclose(fichtm);    
   fclose(ficgp);    hstepm=1;
      hstepm=hstepm/stepm; 
     
   if(erreur >0){    if (popforecast==1) {
     printf("End of Imach with error or warning %d\n",erreur);      if((ficpop=fopen(popfile,"r"))==NULL) {
     fprintf(ficlog,"End of Imach with error or warning %d\n",erreur);        printf("Problem with population file : %s\n",popfile);exit(0);
   }else{        fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
    printf("End of Imach\n");      } 
    fprintf(ficlog,"End of Imach\n");      popage=ivector(0,AGESUP);
   }      popeffectif=vector(0,AGESUP);
   printf("See log file on %s\n",filelog);      popcount=vector(0,AGESUP);
   fclose(ficlog);      
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */      i=1;   
        while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
   /* printf("Total time was %d Sec. %d uSec.\n", end_time.tv_sec -start_time.tv_sec, end_time.tv_usec -start_time.tv_usec);*/     
   /*printf("Total time was %d uSec.\n", total_usecs);*/      imx=i;
   /*------ End -----------*/      for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
  end:    for(cptcov=1,k=0;cptcov<=i2;cptcov++){
 #ifdef windows     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
   /* chdir(pathcd);*/        k=k+1;
 #endif        fprintf(ficrespop,"\n#******");
  /*system("wgnuplot graph.plt");*/        for(j=1;j<=cptcoveff;j++) {
  /*system("../gp37mgw/wgnuplot graph.plt");*/          fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
  /*system("cd ../gp37mgw");*/        }
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/        fprintf(ficrespop,"******\n");
  strcpy(plotcmd,GNUPLOTPROGRAM);        fprintf(ficrespop,"# Age");
  strcat(plotcmd," ");        for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
  strcat(plotcmd,optionfilegnuplot);        if (popforecast==1)  fprintf(ficrespop," [Population]");
  system(plotcmd);        
         for (cpt=0; cpt<=0;cpt++) { 
 #ifdef windows          fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
   while (z[0] != 'q') {          
     /* chdir(path); */          for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");            nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
     scanf("%s",z);            nhstepm = nhstepm/hstepm; 
     if (z[0] == 'c') system("./imach");            
     else if (z[0] == 'e') system(optionfilehtm);            p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     else if (z[0] == 'g') system(plotcmd);            oldm=oldms;savm=savms;
     else if (z[0] == 'q') exit(0);            hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
   }          
 #endif            for (h=0; h<=nhstepm; h++){
 }              if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   
   
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     char dummy[]="                         ";
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double *severity;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];
     char  *strt, strtend[80];
     char *stratrunc;
     int lstra;
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement*/
     if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;
   
     ncovmodel=2+cptcovn; /*Number of variables = cptcovn + intercept + age */
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/
   
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
     /*-------- data file ----------*/
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);goto end;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);goto end;
     }
   
     n= lastobs;
     severity = vector(1,maxwav);
     outcome=imatrix(1,maxwav+1,1,n);
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n);
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %d %s for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
           exit(1);
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           exit(1);
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         exit(1);
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld %s for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line,j);
         exit(1);
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         exit(1);
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         errno=0;
         lval=strtol(strb,&endptr,10); 
         if( strb[0]=='\0' || (*endptr != '\0')){
           printf("Error reading data around '%d' at line number %ld %s for individual %d, '%s'\nShould be a covar (meaning 0 for the reference or 1).  Exiting.\n",lval, linei,i, line);
           exit(1);
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           goto end;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
     fclose(fic);
     /* printf("ii=%d", ij);
        scanf("%d",i);*/
     imx=i-1; /* Number of individuals */
   
     /* for (i=1; i<=imx; i++){
       if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;
       if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;
       if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;
       }*/
      /*  for (i=1; i<=imx; i++){
        if (s[4][i]==9)  s[4][i]=-1; 
        printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));}*/
     
     /* for (i=1; i<=imx; i++) */
    
      /*if ((s[3][i]==3) ||  (s[4][i]==3)) weight[i]=0.08;
        else weight[i]=1;*/
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,15); /* stores the number n of the covariates in Vm+Vn at 1 and m at 2 */
     Tprod=ivector(1,15); 
     Tvaraff=ivector(1,15); 
     Tvard=imatrix(1,15,1,2);
     Tage=ivector(1,15);      
      
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; /* Number of covariates V1+V2+V3 =>2+1=3 */
       cptcovprod=j1; /*Number of products  V1*V2 =1 */
       
       strcpy(modelsav,model); 
       if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){
         printf("Error. Non available option model=%s ",model);
         fprintf(ficlog,"Error. Non available option model=%s ",model);
         goto end;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       for(i=(j+1); i>=1;i--){
         cutv(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav=V2+V3*age+V1+V4 strb=V3*age+V1+V4 
                                        stra=V2
                                       */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V1+V3*age+V2 strb=V3*age*/
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V');
             Tvar[i]=atoi(stre);  /* V1+V3*age+V2 Tvar[2]=3 */
             cptcovage++; /* Sum the number of covariates including ages as a product */
             Tage[cptcovage]=i;  /* Tage[1] =2 */
             /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[i]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=i;
           }
           else {  /* Age is not in the model V1+V3*V2+V2  strb=V3*V2*/
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[i]=ncovcol+k1;  /* find 'n' in Vn and stores in Tvar. 
                                     If already ncovcol=2 and model=V2*V1 Tvar[1]=2+1 and Tvar[2]=2+2 etc */
             cutv(strb,strc,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=i;  /* Tprod[1]  */
             Tvard[k1][1]=atoi(strc); /* m*/
             Tvard[k1][2]=atoi(stre); /* n */
             Tvar[cptcovn+k2]=Tvard[k1][1];
             Tvar[cptcovn+k2+1]=Tvard[k1][2]; 
             for (k=1; k<=lastobs;k++) 
               covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];
             k1++;
             k2=k2+2;
           }
         }
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
         cutv(strd,strc,strb,'V');
         Tvar[i]=atoi(strc);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V3*age+V1+V4 strb=V3*age+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights*/
       for(i=1;i<=n;i++) weight[i]=1.0;
     }
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] <agemin){ 
               agemin=agev[m][i];
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
             }
             else if(agev[m][i] >agemax){
               agemax=agev[m][i];
               /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           goto end;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     agegomp=(int)agemin;
     free_vector(severity,1,maxwav);
     free_imatrix(outcome,1,maxwav+1,1,n);
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     Tcode=ivector(1,100);
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){
       for(i=1; i <=(m/pow(2,k));i++){
         for(j=1; j <= ncodemax[k]; j++){
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){
             h++;
             if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
        printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm), exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM);
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
       
       powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
     
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
       free_ivector(Tcode,1,100);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   
Removed from v.1.52  
changed lines
  Added in v.1.130

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