Diff for /imach/src/imach.c between versions 1.43 and 1.136

version 1.43, 2002/05/24 13:00:54 version 1.136, 2010/04/26 20:30:53
Line 1 Line 1
 /* $Id$  /* $Id$
    Interpolated Markov Chain    $State$
     $Log$
   Short summary of the programme:    Revision 1.136  2010/04/26 20:30:53  brouard
      (Module): merging some libgsl code. Fixing computation
   This program computes Healthy Life Expectancies from    of likelione (using inter/intrapolation if mle = 0) in order to
   cross-longitudinal data. Cross-longitudinal data consist in: -1- a    get same likelihood as if mle=1.
   first survey ("cross") where individuals from different ages are    Some cleaning of code and comments added.
   interviewed on their health status or degree of disability (in the  
   case of a health survey which is our main interest) -2- at least a    Revision 1.135  2009/10/29 15:33:14  brouard
   second wave of interviews ("longitudinal") which measure each change    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   (if any) in individual health status.  Health expectancies are  
   computed from the time spent in each health state according to a    Revision 1.134  2009/10/29 13:18:53  brouard
   model. More health states you consider, more time is necessary to reach the    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   Maximum Likelihood of the parameters involved in the model.  The  
   simplest model is the multinomial logistic model where pij is the    Revision 1.133  2009/07/06 10:21:25  brouard
   probability to be observed in state j at the second wave    just nforces
   conditional to be observed in state i at the first wave. Therefore  
   the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where    Revision 1.132  2009/07/06 08:22:05  brouard
   'age' is age and 'sex' is a covariate. If you want to have a more    Many tings
   complex model than "constant and age", you should modify the program  
   where the markup *Covariates have to be included here again* invites    Revision 1.131  2009/06/20 16:22:47  brouard
   you to do it.  More covariates you add, slower the    Some dimensions resccaled
   convergence.  
     Revision 1.130  2009/05/26 06:44:34  brouard
   The advantage of this computer programme, compared to a simple    (Module): Max Covariate is now set to 20 instead of 8. A
   multinomial logistic model, is clear when the delay between waves is not    lot of cleaning with variables initialized to 0. Trying to make
   identical for each individual. Also, if a individual missed an    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
   intermediate interview, the information is lost, but taken into  
   account using an interpolation or extrapolation.      Revision 1.129  2007/08/31 13:49:27  lievre
     Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   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 1.128  2006/06/30 13:02:05  brouard
   split into an exact number (nh*stepm) of unobserved intermediate    (Module): Clarifications on computing e.j
   states. This elementary transition (by month or quarter trimester,  
   semester or year) is model as a multinomial logistic.  The hPx    Revision 1.127  2006/04/28 18:11:50  brouard
   matrix is simply the matrix product of nh*stepm elementary matrices    (Module): Yes the sum of survivors was wrong since
   and the contribution of each individual to the likelihood is simply    imach-114 because nhstepm was no more computed in the age
   hPijx.    loop. Now we define nhstepma in the age loop.
     (Module): In order to speed up (in case of numerous covariates) we
   Also this programme outputs the covariance matrix of the parameters but also    compute health expectancies (without variances) in a first step
   of the life expectancies. It also computes the prevalence limits.    and then all the health expectancies with variances or standard
      deviation (needs data from the Hessian matrices) which slows the
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    computation.
            Institut national d'études démographiques, Paris.    In the future we should be able to stop the program is only health
   This software have been partly granted by Euro-REVES, a concerted action    expectancies and graph are needed without standard deviations.
   from the European Union.  
   It is copyrighted identically to a GNU software product, ie programme and    Revision 1.126  2006/04/28 17:23:28  brouard
   software can be distributed freely for non commercial use. Latest version    (Module): Yes the sum of survivors was wrong since
   can be accessed at http://euroreves.ined.fr/imach .    imach-114 because nhstepm was no more computed in the age
   **********************************************************************/    loop. Now we define nhstepma in the age loop.
      Version 0.98h
 #include <math.h>  
 #include <stdio.h>    Revision 1.125  2006/04/04 15:20:31  lievre
 #include <stdlib.h>    Errors in calculation of health expectancies. Age was not initialized.
 #include <unistd.h>    Forecasting file added.
   
 #define MAXLINE 256    Revision 1.124  2006/03/22 17:13:53  lievre
 #define GNUPLOTPROGRAM "gnuplot"    Parameters are printed with %lf instead of %f (more numbers after the comma).
 /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/    The log-likelihood is printed in the log file
 #define FILENAMELENGTH 80  
 /*#define DEBUG*/    Revision 1.123  2006/03/20 10:52:43  brouard
 #define windows    * imach.c (Module): <title> changed, corresponds to .htm file
 #define GLOCK_ERROR_NOPATH              -1      /* empty path */    name. <head> headers where missing.
 #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */  
     * imach.c (Module): Weights can have a decimal point as for
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    English (a comma might work with a correct LC_NUMERIC environment,
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
 #define NINTERVMAX 8    1.
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Version 0.98g
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */  
 #define NCOVMAX 8 /* Maximum number of covariates */    Revision 1.122  2006/03/20 09:45:41  brouard
 #define MAXN 20000    (Module): Weights can have a decimal point as for
 #define YEARM 12. /* Number of months per year */    English (a comma might work with a correct LC_NUMERIC environment,
 #define AGESUP 130    otherwise the weight is truncated).
 #define AGEBASE 40    Modification of warning when the covariates values are not 0 or
     1.
     Version 0.98g
 int erreur; /* Error number */  
 int nvar;    Revision 1.121  2006/03/16 17:45:01  lievre
 int cptcovn, cptcovage=0, cptcoveff=0,cptcov;    * imach.c (Module): Comments concerning covariates added
 int npar=NPARMAX;  
 int nlstate=2; /* Number of live states */    * imach.c (Module): refinements in the computation of lli if
 int ndeath=1; /* Number of dead states */    status=-2 in order to have more reliable computation if stepm is
 int ncovmodel, ncovcol;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    not 1 month. Version 0.98f
 int popbased=0;  
     Revision 1.120  2006/03/16 15:10:38  lievre
 int *wav; /* Number of waves for this individuual 0 is possible */    (Module): refinements in the computation of lli if
 int maxwav; /* Maxim number of waves */    status=-2 in order to have more reliable computation if stepm is
 int jmin, jmax; /* min, max spacing between 2 waves */    not 1 month. Version 0.98f
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.119  2006/03/15 17:42:26  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    (Module): Bug if status = -2, the loglikelihood was
 double jmean; /* Mean space between 2 waves */    computed as likelihood omitting the logarithm. Version O.98e
 double **oldm, **newm, **savm; /* Working pointers to matrices */  
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    Revision 1.118  2006/03/14 18:20:07  brouard
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;    (Module): varevsij Comments added explaining the second
 FILE *ficgp,*ficresprob,*ficpop;    table of variances if popbased=1 .
 FILE *ficreseij;    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   char filerese[FILENAMELENGTH];    (Module): Function pstamp added
  FILE  *ficresvij;    (Module): Version 0.98d
   char fileresv[FILENAMELENGTH];  
  FILE  *ficresvpl;    Revision 1.117  2006/03/14 17:16:22  brouard
   char fileresvpl[FILENAMELENGTH];    (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 #define NR_END 1    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
 #define FREE_ARG char*    (Module): Function pstamp added
 #define FTOL 1.0e-10    (Module): Version 0.98d
   
 #define NRANSI    Revision 1.116  2006/03/06 10:29:27  brouard
 #define ITMAX 200    (Module): Variance-covariance wrong links and
     varian-covariance of ej. is needed (Saito).
 #define TOL 2.0e-4  
     Revision 1.115  2006/02/27 12:17:45  brouard
 #define CGOLD 0.3819660    (Module): One freematrix added in mlikeli! 0.98c
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.114  2006/02/26 12:57:58  brouard
     (Module): Some improvements in processing parameter
 #define GOLD 1.618034    filename with strsep.
 #define GLIMIT 100.0  
 #define TINY 1.0e-20    Revision 1.113  2006/02/24 14:20:24  brouard
     (Module): Memory leaks checks with valgrind and:
 static double maxarg1,maxarg2;    datafile was not closed, some imatrix were not freed and on matrix
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    allocation too.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.112  2006/01/30 09:55:26  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    (Module): Back to gnuplot.exe instead of wgnuplot.exe
 #define rint(a) floor(a+0.5)  
     Revision 1.111  2006/01/25 20:38:18  brouard
 static double sqrarg;    (Module): Lots of cleaning and bugs added (Gompertz)
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    (Module): Comments can be added in data file. Missing date values
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    can be a simple dot '.'.
   
 int imx;    Revision 1.110  2006/01/25 00:51:50  brouard
 int stepm;    (Module): Lots of cleaning and bugs added (Gompertz)
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.109  2006/01/24 19:37:15  brouard
 int estepm;    (Module): Comments (lines starting with a #) are allowed in data.
 /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/  
     Revision 1.108  2006/01/19 18:05:42  lievre
 int m,nb;    Gnuplot problem appeared...
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage;    To be fixed
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;  
 double **pmmij, ***probs, ***mobaverage;    Revision 1.107  2006/01/19 16:20:37  brouard
 double dateintmean=0;    Test existence of gnuplot in imach path
   
 double *weight;    Revision 1.106  2006/01/19 13:24:36  brouard
 int **s; /* Status */    Some cleaning and links added in html output
 double *agedc, **covar, idx;  
 int **nbcode, *Tcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;    Revision 1.105  2006/01/05 20:23:19  lievre
     *** empty log message ***
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */  
 double ftolhess; /* Tolerance for computing hessian */    Revision 1.104  2005/09/30 16:11:43  lievre
     (Module): sump fixed, loop imx fixed, and simplifications.
 /**************** split *************************/    (Module): If the status is missing at the last wave but we know
 static  int split( char *path, char *dirc, char *name, char *ext, char *finame )    that the person is alive, then we can code his/her status as -2
 {    (instead of missing=-1 in earlier versions) and his/her
    char *s;                             /* pointer */    contributions to the likelihood is 1 - Prob of dying from last
    int  l1, l2;                         /* length counters */    health status (= 1-p13= p11+p12 in the easiest case of somebody in
     the healthy state at last known wave). Version is 0.98
    l1 = strlen( path );                 /* length of path */  
    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );    Revision 1.103  2005/09/30 15:54:49  lievre
 #ifdef windows    (Module): sump fixed, loop imx fixed, and simplifications.
    s = strrchr( path, '\\' );           /* find last / */  
 #else    Revision 1.102  2004/09/15 17:31:30  brouard
    s = strrchr( path, '/' );            /* find last / */    Add the possibility to read data file including tab characters.
 #endif  
    if ( s == NULL ) {                   /* no directory, so use current */    Revision 1.101  2004/09/15 10:38:38  brouard
 #if     defined(__bsd__)                /* get current working directory */    Fix on curr_time
       extern char       *getwd( );  
     Revision 1.100  2004/07/12 18:29:06  brouard
       if ( getwd( dirc ) == NULL ) {    Add version for Mac OS X. Just define UNIX in Makefile
 #else  
       extern char       *getcwd( );    Revision 1.99  2004/06/05 08:57:40  brouard
     *** empty log message ***
       if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {  
 #endif    Revision 1.98  2004/05/16 15:05:56  brouard
          return( GLOCK_ERROR_GETCWD );    New version 0.97 . First attempt to estimate force of mortality
       }    directly from the data i.e. without the need of knowing the health
       strcpy( name, path );             /* we've got it */    state at each age, but using a Gompertz model: log u =a + b*age .
    } else {                             /* strip direcotry from path */    This is the basic analysis of mortality and should be done before any
       s++;                              /* after this, the filename */    other analysis, in order to test if the mortality estimated from the
       l2 = strlen( s );                 /* length of filename */    cross-longitudinal survey is different from the mortality estimated
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );    from other sources like vital statistic data.
       strcpy( name, s );                /* save file name */  
       strncpy( dirc, path, l1 - l2 );   /* now the directory */    The same imach parameter file can be used but the option for mle should be -3.
       dirc[l1-l2] = 0;                  /* add zero */  
    }    Agnès, who wrote this part of the code, tried to keep most of the
    l1 = strlen( dirc );                 /* length of directory */    former routines in order to include the new code within the former code.
 #ifdef windows  
    if ( dirc[l1-1] != '\\' ) { dirc[l1] = '\\'; dirc[l1+1] = 0; }    The output is very simple: only an estimate of the intercept and of
 #else    the slope with 95% confident intervals.
    if ( dirc[l1-1] != '/' ) { dirc[l1] = '/'; dirc[l1+1] = 0; }  
 #endif    Current limitations:
    s = strrchr( name, '.' );            /* find last / */    A) Even if you enter covariates, i.e. with the
    s++;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
    strcpy(ext,s);                       /* save extension */    B) There is no computation of Life Expectancy nor Life Table.
    l1= strlen( name);  
    l2= strlen( s)+1;    Revision 1.97  2004/02/20 13:25:42  lievre
    strncpy( finame, name, l1-l2);    Version 0.96d. Population forecasting command line is (temporarily)
    finame[l1-l2]= 0;    suppressed.
    return( 0 );                         /* we're done */  
 }    Revision 1.96  2003/07/15 15:38:55  brouard
     * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
     rewritten within the same printf. Workaround: many printfs.
 /******************************************/  
     Revision 1.95  2003/07/08 07:54:34  brouard
 void replace(char *s, char*t)    * imach.c (Repository):
 {    (Repository): Using imachwizard code to output a more meaningful covariance
   int i;    matrix (cov(a12,c31) instead of numbers.
   int lg=20;  
   i=0;    Revision 1.94  2003/06/27 13:00:02  brouard
   lg=strlen(t);    Just cleaning
   for(i=0; i<= lg; i++) {  
     (s[i] = t[i]);    Revision 1.93  2003/06/25 16:33:55  brouard
     if (t[i]== '\\') s[i]='/';    (Module): On windows (cygwin) function asctime_r doesn't
   }    exist so I changed back to asctime which exists.
 }    (Module): Version 0.96b
   
 int nbocc(char *s, char occ)    Revision 1.92  2003/06/25 16:30:45  brouard
 {    (Module): On windows (cygwin) function asctime_r doesn't
   int i,j=0;    exist so I changed back to asctime which exists.
   int lg=20;  
   i=0;    Revision 1.91  2003/06/25 15:30:29  brouard
   lg=strlen(s);    * imach.c (Repository): Duplicated warning errors corrected.
   for(i=0; i<= lg; i++) {    (Repository): Elapsed time after each iteration is now output. It
   if  (s[i] == occ ) j++;    helps to forecast when convergence will be reached. Elapsed time
   }    is stamped in powell.  We created a new html file for the graphs
   return j;    concerning matrix of covariance. It has extension -cov.htm.
 }  
     Revision 1.90  2003/06/24 12:34:15  brouard
 void cutv(char *u,char *v, char*t, char occ)    (Module): Some bugs corrected for windows. Also, when
 {    mle=-1 a template is output in file "or"mypar.txt with the design
   int i,lg,j,p=0;    of the covariance matrix to be input.
   i=0;  
   for(j=0; j<=strlen(t)-1; j++) {    Revision 1.89  2003/06/24 12:30:52  brouard
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    (Module): Some bugs corrected for windows. Also, when
   }    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
   lg=strlen(t);  
   for(j=0; j<p; j++) {    Revision 1.88  2003/06/23 17:54:56  brouard
     (u[j] = t[j]);    * 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.
   }  
      u[p]='\0';    Revision 1.87  2003/06/18 12:26:01  brouard
     Version 0.96
    for(j=0; j<= lg; j++) {  
     if (j>=(p+1))(v[j-p-1] = t[j]);    Revision 1.86  2003/06/17 20:04:08  brouard
   }    (Module): Change position of html and gnuplot routines and added
 }    routine fileappend.
   
 /********************** nrerror ********************/    Revision 1.85  2003/06/17 13:12:43  brouard
     * imach.c (Repository): Check when date of death was earlier that
 void nrerror(char error_text[])    current date of interview. It may happen when the death was just
 {    prior to the death. In this case, dh was negative and likelihood
   fprintf(stderr,"ERREUR ...\n");    was wrong (infinity). We still send an "Error" but patch by
   fprintf(stderr,"%s\n",error_text);    assuming that the date of death was just one stepm after the
   exit(1);    interview.
 }    (Repository): Because some people have very long ID (first column)
 /*********************** vector *******************/    we changed int to long in num[] and we added a new lvector for
 double *vector(int nl, int nh)    memory allocation. But we also truncated to 8 characters (left
 {    truncation)
   double *v;    (Repository): No more line truncation errors.
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));  
   if (!v) nrerror("allocation failure in vector");    Revision 1.84  2003/06/13 21:44:43  brouard
   return v-nl+NR_END;    * imach.c (Repository): Replace "freqsummary" at a correct
 }    place. It differs from routine "prevalence" which may be called
     many times. Probs is memory consuming and must be used with
 /************************ free vector ******************/    parcimony.
 void free_vector(double*v, int nl, int nh)    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.83  2003/06/10 13:39:11  lievre
 }    *** empty log message ***
   
 /************************ivector *******************************/    Revision 1.82  2003/06/05 15:57:20  brouard
 int *ivector(long nl,long nh)    Add log in  imach.c and  fullversion number is now printed.
 {  
   int *v;  */
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  /*
   if (!v) nrerror("allocation failure in ivector");     Interpolated Markov Chain
   return v-nl+NR_END;  
 }    Short summary of the programme:
     
 /******************free ivector **************************/    This program computes Healthy Life Expectancies from
 void free_ivector(int *v, long nl, long nh)    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 {    first survey ("cross") where individuals from different ages are
   free((FREE_ARG)(v+nl-NR_END));    interviewed on their health status or degree of disability (in the
 }    case of a health survey which is our main interest) -2- at least a
     second wave of interviews ("longitudinal") which measure each change
 /******************* imatrix *******************************/    (if any) in individual health status.  Health expectancies are
 int **imatrix(long nrl, long nrh, long ncl, long nch)    computed from the time spent in each health state according to a
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */    model. More health states you consider, more time is necessary to reach the
 {    Maximum Likelihood of the parameters involved in the model.  The
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    simplest model is the multinomial logistic model where pij is the
   int **m;    probability to be observed in state j at the second wave
      conditional to be observed in state i at the first wave. Therefore
   /* allocate pointers to rows */    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    'age' is age and 'sex' is a covariate. If you want to have a more
   if (!m) nrerror("allocation failure 1 in matrix()");    complex model than "constant and age", you should modify the program
   m += NR_END;    where the markup *Covariates have to be included here again* invites
   m -= nrl;    you to do it.  More covariates you add, slower the
      convergence.
    
   /* allocate rows and set pointers to them */    The advantage of this computer programme, compared to a simple
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    multinomial logistic model, is clear when the delay between waves is not
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    identical for each individual. Also, if a individual missed an
   m[nrl] += NR_END;    intermediate interview, the information is lost, but taken into
   m[nrl] -= ncl;    account using an interpolation or extrapolation.  
    
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    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
   /* return pointer to array of pointers to rows */    split into an exact number (nh*stepm) of unobserved intermediate
   return m;    states. This elementary transition (by month, quarter,
 }    semester or year) is modelled as a multinomial logistic.  The hPx
     matrix is simply the matrix product of nh*stepm elementary matrices
 /****************** free_imatrix *************************/    and the contribution of each individual to the likelihood is simply
 void free_imatrix(m,nrl,nrh,ncl,nch)    hPijx.
       int **m;  
       long nch,ncl,nrh,nrl;    Also this programme outputs the covariance matrix of the parameters but also
      /* free an int matrix allocated by imatrix() */    of the life expectancies. It also computes the period (stable) prevalence. 
 {    
   free((FREE_ARG) (m[nrl]+ncl-NR_END));    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
   free((FREE_ARG) (m+nrl-NR_END));             Institut national d'études démographiques, Paris.
 }    This software have been partly granted by Euro-REVES, a concerted action
     from the European Union.
 /******************* matrix *******************************/    It is copyrighted identically to a GNU software product, ie programme and
 double **matrix(long nrl, long nrh, long ncl, long nch)    software can be distributed freely for non commercial use. Latest version
 {    can be accessed at http://euroreves.ined.fr/imach .
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;  
   double **m;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
     or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    
   if (!m) nrerror("allocation failure 1 in matrix()");    **********************************************************************/
   m += NR_END;  /*
   m -= nrl;    main
     read parameterfile
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    read datafile
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    concatwav
   m[nrl] += NR_END;    freqsummary
   m[nrl] -= ncl;    if (mle >= 1)
       mlikeli
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    print results files
   return m;    if mle==1 
 }       computes hessian
     read end of parameter file: agemin, agemax, bage, fage, estepm
 /*************************free matrix ************************/        begin-prev-date,...
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    open gnuplot file
 {    open html file
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    period (stable) prevalence
   free((FREE_ARG)(m+nrl-NR_END));     for age prevalim()
 }    h Pij x
     variance of p varprob
 /******************* ma3x *******************************/    forecasting if prevfcast==1 prevforecast call prevalence()
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    health expectancies
 {    Variance-covariance of DFLE
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    prevalence()
   double ***m;     movingaverage()
     varevsij() 
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    if popbased==1 varevsij(,popbased)
   if (!m) nrerror("allocation failure 1 in matrix()");    total life expectancies
   m += NR_END;    Variance of period (stable) prevalence
   m -= nrl;   end
   */
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));  
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;  
   m[nrl] -= ncl;   
   #include <math.h>
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  #include <stdio.h>
   #include <stdlib.h>
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));  #include <string.h>
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");  #include <unistd.h>
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;  #include <limits.h>
   for (j=ncl+1; j<=nch; j++)  #include <sys/types.h>
     m[nrl][j]=m[nrl][j-1]+nlay;  #include <sys/stat.h>
    #include <errno.h>
   for (i=nrl+1; i<=nrh; i++) {  extern int errno;
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)  /* #include <sys/time.h> */
       m[i][j]=m[i][j-1]+nlay;  #include <time.h>
   }  #include "timeval.h"
   return m;  
 }  #ifdef GSL
   #include <gsl/gsl_errno.h>
 /*************************free ma3x ************************/  #include <gsl/gsl_multimin.h>
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)  #endif
 {  
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  /* #include <libintl.h> */
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  /* #define _(String) gettext (String) */
   free((FREE_ARG)(m+nrl-NR_END));  
 }  #define MAXLINE 256
   
 /***************** f1dim *************************/  #define GNUPLOTPROGRAM "gnuplot"
 extern int ncom;  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
 extern double *pcom,*xicom;  #define FILENAMELENGTH 132
 extern double (*nrfunc)(double []);  
    #define GLOCK_ERROR_NOPATH              -1      /* empty path */
 double f1dim(double x)  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
 {  
   int j;  #define MAXPARM 128 /* Maximum number of parameters for the optimization */
   double f;  #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */
   double *xt;  
    #define NINTERVMAX 8
   xt=vector(1,ncom);  #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];  #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
   f=(*nrfunc)(xt);  #define NCOVMAX 20 /* Maximum number of covariates */
   free_vector(xt,1,ncom);  #define MAXN 20000
   return f;  #define YEARM 12. /* Number of months per year */
 }  #define AGESUP 130
   #define AGEBASE 40
 /*****************brent *************************/  #define AGEGOMP 10. /* Minimal age for Gompertz adjustment */
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)  #ifdef UNIX
 {  #define DIRSEPARATOR '/'
   int iter;  #define CHARSEPARATOR "/"
   double a,b,d,etemp;  #define ODIRSEPARATOR '\\'
   double fu,fv,fw,fx;  #else
   double ftemp;  #define DIRSEPARATOR '\\'
   double p,q,r,tol1,tol2,u,v,w,x,xm;  #define CHARSEPARATOR "\\"
   double e=0.0;  #define ODIRSEPARATOR '/'
    #endif
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  /* $Id$ */
   x=w=v=bx;  /* $State$ */
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {  char version[]="Imach version 0.98m, April 2010, INED-EUROREVES-Institut de longevite ";
     xm=0.5*(a+b);  char fullversion[]="$Revision$ $Date$"; 
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);  char strstart[80];
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
     printf(".");fflush(stdout);  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 #ifdef DEBUG  int nvar=0, nforce=0; /* Number of variables, number of forces */
     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);  int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov=0; /* Number of covariates, of covariates with '*age' */
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */  int npar=NPARMAX;
 #endif  int nlstate=2; /* Number of live states */
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){  int ndeath=1; /* Number of dead states */
       *xmin=x;  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       return fx;  int popbased=0;
     }  
     ftemp=fu;  int *wav; /* Number of waves for this individuual 0 is possible */
     if (fabs(e) > tol1) {  int maxwav=0; /* Maxim number of waves */
       r=(x-w)*(fx-fv);  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       q=(x-v)*(fx-fw);  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
       p=(x-v)*q-(x-w)*r;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
       q=2.0*(q-r);                     to the likelihood and the sum of weights (done by funcone)*/
       if (q > 0.0) p = -p;  int mle=1, weightopt=0;
       q=fabs(q);  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       etemp=e;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       e=d;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))             * wave mi and wave mi+1 is not an exact multiple of stepm. */
         d=CGOLD*(e=(x >= xm ? a-x : b-x));  double jmean=1; /* Mean space between 2 waves */
       else {  double **oldm, **newm, **savm; /* Working pointers to matrices */
         d=p/q;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
         u=x+d;  /*FILE *fic ; */ /* Used in readdata only */
         if (u-a < tol2 || b-u < tol2)  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
           d=SIGN(tol1,xm-x);  FILE *ficlog, *ficrespow;
       }  int globpr=0; /* Global variable for printing or not */
     } else {  double fretone; /* Only one call to likelihood */
       d=CGOLD*(e=(x >= xm ? a-x : b-x));  long ipmx=0; /* Number of contributions */
     }  double sw; /* Sum of weights */
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));  char filerespow[FILENAMELENGTH];
     fu=(*f)(u);  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
     if (fu <= fx) {  FILE *ficresilk;
       if (u >= x) a=x; else b=x;  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       SHFT(v,w,x,u)  FILE *ficresprobmorprev;
         SHFT(fv,fw,fx,fu)  FILE *fichtm, *fichtmcov; /* Html File */
         } else {  FILE *ficreseij;
           if (u < x) a=u; else b=u;  char filerese[FILENAMELENGTH];
           if (fu <= fw || w == x) {  FILE *ficresstdeij;
             v=w;  char fileresstde[FILENAMELENGTH];
             w=u;  FILE *ficrescveij;
             fv=fw;  char filerescve[FILENAMELENGTH];
             fw=fu;  FILE  *ficresvij;
           } else if (fu <= fv || v == x || v == w) {  char fileresv[FILENAMELENGTH];
             v=u;  FILE  *ficresvpl;
             fv=fu;  char fileresvpl[FILENAMELENGTH];
           }  char title[MAXLINE];
         }  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
   }  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
   nrerror("Too many iterations in brent");  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
   *xmin=x;  char command[FILENAMELENGTH];
   return fx;  int  outcmd=0;
 }  
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 /****************** mnbrak ***********************/  
   char filelog[FILENAMELENGTH]; /* Log file */
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  char filerest[FILENAMELENGTH];
             double (*func)(double))  char fileregp[FILENAMELENGTH];
 {  char popfile[FILENAMELENGTH];
   double ulim,u,r,q, dum;  
   double fu;  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
    
   *fa=(*func)(*ax);  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
   *fb=(*func)(*bx);  struct timezone tzp;
   if (*fb > *fa) {  extern int gettimeofday();
     SHFT(dum,*ax,*bx,dum)  struct tm tmg, tm, tmf, *gmtime(), *localtime();
       SHFT(dum,*fb,*fa,dum)  long time_value;
       }  extern long time();
   *cx=(*bx)+GOLD*(*bx-*ax);  char strcurr[80], strfor[80];
   *fc=(*func)(*cx);  
   while (*fb > *fc) {  char *endptr;
     r=(*bx-*ax)*(*fb-*fc);  long lval;
     q=(*bx-*cx)*(*fb-*fa);  double dval;
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));  #define NR_END 1
     ulim=(*bx)+GLIMIT*(*cx-*bx);  #define FREE_ARG char*
     if ((*bx-u)*(u-*cx) > 0.0) {  #define FTOL 1.0e-10
       fu=(*func)(u);  
     } else if ((*cx-u)*(u-ulim) > 0.0) {  #define NRANSI 
       fu=(*func)(u);  #define ITMAX 200 
       if (fu < *fc) {  
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))  #define TOL 2.0e-4 
           SHFT(*fb,*fc,fu,(*func)(u))  
           }  #define CGOLD 0.3819660 
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  #define ZEPS 1.0e-10 
       u=ulim;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
       fu=(*func)(u);  
     } else {  #define GOLD 1.618034 
       u=(*cx)+GOLD*(*cx-*bx);  #define GLIMIT 100.0 
       fu=(*func)(u);  #define TINY 1.0e-20 
     }  
     SHFT(*ax,*bx,*cx,u)  static double maxarg1,maxarg2;
       SHFT(*fa,*fb,*fc,fu)  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
       }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
 }    
   #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
 /*************** linmin ************************/  #define rint(a) floor(a+0.5)
   
 int ncom;  static double sqrarg;
 double *pcom,*xicom;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
 double (*nrfunc)(double []);  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
    int agegomp= AGEGOMP;
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  
 {  int imx; 
   double brent(double ax, double bx, double cx,  int stepm=1;
                double (*f)(double), double tol, double *xmin);  /* Stepm, step in month: minimum step interpolation*/
   double f1dim(double x);  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  int estepm;
               double *fc, double (*func)(double));  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
   int j;  
   double xx,xmin,bx,ax;  int m,nb;
   double fx,fb,fa;  long *num;
    int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   ncom=n;  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
   pcom=vector(1,n);  double **pmmij, ***probs;
   xicom=vector(1,n);  double *ageexmed,*agecens;
   nrfunc=func;  double dateintmean=0;
   for (j=1;j<=n;j++) {  
     pcom[j]=p[j];  double *weight;
     xicom[j]=xi[j];  int **s; /* Status */
   }  double *agedc, **covar, idx;
   ax=0.0;  int **nbcode, *Tvar, **codtab, **Tvard, *Tprod, cptcovprod, *Tvaraff;
   xx=1.0;  double *lsurv, *lpop, *tpop;
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  double ftol=FTOL; /* Tolerance for computing Max Likelihood */
 #ifdef DEBUG  double ftolhess; /* Tolerance for computing hessian */
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  
 #endif  /**************** split *************************/
   for (j=1;j<=n;j++) {  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
     xi[j] *= xmin;  {
     p[j] += xi[j];    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
   }       the name of the file (name), its extension only (ext) and its first part of the name (finame)
   free_vector(xicom,1,n);    */ 
   free_vector(pcom,1,n);    char  *ss;                            /* pointer */
 }    int   l1, l2;                         /* length counters */
   
 /*************** powell ************************/    l1 = strlen(path );                   /* length of path */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
             double (*func)(double []))    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
 {    if ( ss == NULL ) {                   /* no directory, so determine current directory */
   void linmin(double p[], double xi[], int n, double *fret,      strcpy( name, path );               /* we got the fullname name because no directory */
               double (*func)(double []));      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
   int i,ibig,j;        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
   double del,t,*pt,*ptt,*xit;      /* get current working directory */
   double fp,fptt;      /*    extern  char* getcwd ( char *buf , int len);*/
   double *xits;      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
   pt=vector(1,n);        return( GLOCK_ERROR_GETCWD );
   ptt=vector(1,n);      }
   xit=vector(1,n);      /* got dirc from getcwd*/
   xits=vector(1,n);      printf(" DIRC = %s \n",dirc);
   *fret=(*func)(p);    } else {                              /* strip direcotry from path */
   for (j=1;j<=n;j++) pt[j]=p[j];      ss++;                               /* after this, the filename */
   for (*iter=1;;++(*iter)) {      l2 = strlen( ss );                  /* length of filename */
     fp=(*fret);      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
     ibig=0;      strcpy( name, ss );         /* save file name */
     del=0.0;      strncpy( dirc, path, l1 - l2 );     /* now the directory */
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);      dirc[l1-l2] = 0;                    /* add zero */
     for (i=1;i<=n;i++)      printf(" DIRC2 = %s \n",dirc);
       printf(" %d %.12f",i, p[i]);    }
     printf("\n");    /* We add a separator at the end of dirc if not exists */
     for (i=1;i<=n;i++) {    l1 = strlen( dirc );                  /* length of directory */
       for (j=1;j<=n;j++) xit[j]=xi[j][i];    if( dirc[l1-1] != DIRSEPARATOR ){
       fptt=(*fret);      dirc[l1] =  DIRSEPARATOR;
 #ifdef DEBUG      dirc[l1+1] = 0; 
       printf("fret=%lf \n",*fret);      printf(" DIRC3 = %s \n",dirc);
 #endif    }
       printf("%d",i);fflush(stdout);    ss = strrchr( name, '.' );            /* find last / */
       linmin(p,xit,n,fret,func);    if (ss >0){
       if (fabs(fptt-(*fret)) > del) {      ss++;
         del=fabs(fptt-(*fret));      strcpy(ext,ss);                     /* save extension */
         ibig=i;      l1= strlen( name);
       }      l2= strlen(ss)+1;
 #ifdef DEBUG      strncpy( finame, name, l1-l2);
       printf("%d %.12e",i,(*fret));      finame[l1-l2]= 0;
       for (j=1;j<=n;j++) {    }
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  
         printf(" x(%d)=%.12e",j,xit[j]);    return( 0 );                          /* we're done */
       }  }
       for(j=1;j<=n;j++)  
         printf(" p=%.12e",p[j]);  
       printf("\n");  /******************************************/
 #endif  
     }  void replace_back_to_slash(char *s, char*t)
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  {
 #ifdef DEBUG    int i;
       int k[2],l;    int lg=0;
       k[0]=1;    i=0;
       k[1]=-1;    lg=strlen(t);
       printf("Max: %.12e",(*func)(p));    for(i=0; i<= lg; i++) {
       for (j=1;j<=n;j++)      (s[i] = t[i]);
         printf(" %.12e",p[j]);      if (t[i]== '\\') s[i]='/';
       printf("\n");    }
       for(l=0;l<=1;l++) {  }
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  char *trimbb(char *out, char *in)
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  { /* Trim multiple blanks in line */
         }    char *s;
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));    s=out;
       }    while (*in != '\0'){
 #endif      while( *in == ' ' && *(in+1) == ' ' && *(in+1) != '\0'){
         in++;
       }
       free_vector(xit,1,n);      *out++ = *in++;
       free_vector(xits,1,n);    }
       free_vector(ptt,1,n);    *out='\0';
       free_vector(pt,1,n);    return s;
       return;  }
     }  
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  int nbocc(char *s, char occ)
     for (j=1;j<=n;j++) {  {
       ptt[j]=2.0*p[j]-pt[j];    int i,j=0;
       xit[j]=p[j]-pt[j];    int lg=20;
       pt[j]=p[j];    i=0;
     }    lg=strlen(s);
     fptt=(*func)(ptt);    for(i=0; i<= lg; i++) {
     if (fptt < fp) {    if  (s[i] == occ ) j++;
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);    }
       if (t < 0.0) {    return j;
         linmin(p,xit,n,fret,func);  }
         for (j=1;j<=n;j++) {  
           xi[j][ibig]=xi[j][n];  void cutv(char *u,char *v, char*t, char occ)
           xi[j][n]=xit[j];  {
         }    /* cuts string t into u and v where u ends before first occurence of char 'occ' 
 #ifdef DEBUG       and v starts after first occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2')
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);       gives u="abcedf" and v="ghi2j" */
         for(j=1;j<=n;j++)    int i,lg,j,p=0;
           printf(" %.12e",xit[j]);    i=0;
         printf("\n");    for(j=0; j<=strlen(t)-1; j++) {
 #endif      if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;
       }    }
     }  
   }    lg=strlen(t);
 }    for(j=0; j<p; j++) {
       (u[j] = t[j]);
 /**** Prevalence limit ****************/    }
        u[p]='\0';
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  
 {     for(j=0; j<= lg; j++) {
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit      if (j>=(p+1))(v[j-p-1] = t[j]);
      matrix by transitions matrix until convergence is reached */    }
   }
   int i, ii,j,k;  
   double min, max, maxmin, maxmax,sumnew=0.;  /********************** nrerror ********************/
   double **matprod2();  
   double **out, cov[NCOVMAX], **pmij();  void nrerror(char error_text[])
   double **newm;  {
   double agefin, delaymax=50 ; /* Max number of years to converge */    fprintf(stderr,"ERREUR ...\n");
     fprintf(stderr,"%s\n",error_text);
   for (ii=1;ii<=nlstate+ndeath;ii++)    exit(EXIT_FAILURE);
     for (j=1;j<=nlstate+ndeath;j++){  }
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  /*********************** vector *******************/
     }  double *vector(int nl, int nh)
   {
    cov[1]=1.;    double *v;
      v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
  /* Even if hstepm = 1, at least one multiplication by the unit matrix */    if (!v) nrerror("allocation failure in vector");
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){    return v-nl+NR_END;
     newm=savm;  }
     /* Covariates have to be included here again */  
      cov[2]=agefin;  /************************ free vector ******************/
    void free_vector(double*v, int nl, int nh)
       for (k=1; k<=cptcovn;k++) {  {
         cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    free((FREE_ARG)(v+nl-NR_END));
         /*      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]]);*/  }
       }  
       for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];  /************************ivector *******************************/
       for (k=1; k<=cptcovprod;k++)  int *ivector(long nl,long nh)
         cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];  {
     int *v;
       /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
       /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/    if (!v) nrerror("allocation failure in ivector");
       /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/    return v-nl+NR_END;
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  }
   
     savm=oldm;  /******************free ivector **************************/
     oldm=newm;  void free_ivector(int *v, long nl, long nh)
     maxmax=0.;  {
     for(j=1;j<=nlstate;j++){    free((FREE_ARG)(v+nl-NR_END));
       min=1.;  }
       max=0.;  
       for(i=1; i<=nlstate; i++) {  /************************lvector *******************************/
         sumnew=0;  long *lvector(long nl,long nh)
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  {
         prlim[i][j]= newm[i][j]/(1-sumnew);    long *v;
         max=FMAX(max,prlim[i][j]);    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
         min=FMIN(min,prlim[i][j]);    if (!v) nrerror("allocation failure in ivector");
       }    return v-nl+NR_END;
       maxmin=max-min;  }
       maxmax=FMAX(maxmax,maxmin);  
     }  /******************free lvector **************************/
     if(maxmax < ftolpl){  void free_lvector(long *v, long nl, long nh)
       return prlim;  {
     }    free((FREE_ARG)(v+nl-NR_END));
   }  }
 }  
   /******************* imatrix *******************************/
 /*************** transition probabilities ***************/  int **imatrix(long nrl, long nrh, long ncl, long nch) 
        /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  { 
 {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
   double s1, s2;    int **m; 
   /*double t34;*/    
   int i,j,j1, nc, ii, jj;    /* allocate pointers to rows */ 
     m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     for(i=1; i<= nlstate; i++){    if (!m) nrerror("allocation failure 1 in matrix()"); 
     for(j=1; j<i;j++){    m += NR_END; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    m -= nrl; 
         /*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);*/    /* allocate rows and set pointers to them */ 
       }    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       ps[i][j]=s2;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/    m[nrl] += NR_END; 
     }    m[nrl] -= ncl; 
     for(j=i+1; j<=nlstate+ndeath;j++){    
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
         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);*/    /* return pointer to array of pointers to rows */ 
       }    return m; 
       ps[i][j]=s2;  } 
     }  
   }  /****************** free_imatrix *************************/
     /*ps[3][2]=1;*/  void free_imatrix(m,nrl,nrh,ncl,nch)
         int **m;
   for(i=1; i<= nlstate; i++){        long nch,ncl,nrh,nrl; 
      s1=0;       /* free an int matrix allocated by imatrix() */ 
     for(j=1; j<i; j++)  { 
       s1+=exp(ps[i][j]);    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
     for(j=i+1; j<=nlstate+ndeath; j++)    free((FREE_ARG) (m+nrl-NR_END)); 
       s1+=exp(ps[i][j]);  } 
     ps[i][i]=1./(s1+1.);  
     for(j=1; j<i; j++)  /******************* matrix *******************************/
       ps[i][j]= exp(ps[i][j])*ps[i][i];  double **matrix(long nrl, long nrh, long ncl, long nch)
     for(j=i+1; j<=nlstate+ndeath; j++)  {
       ps[i][j]= exp(ps[i][j])*ps[i][i];    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */    double **m;
   } /* end i */  
     m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){    if (!m) nrerror("allocation failure 1 in matrix()");
     for(jj=1; jj<= nlstate+ndeath; jj++){    m += NR_END;
       ps[ii][jj]=0;    m -= nrl;
       ps[ii][ii]=1;  
     }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   }    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
     m[nrl] -= ncl;
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
      printf("%lf ",ps[ii][jj]);    return m;
    }    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) 
     printf("\n ");     */
     }  }
     printf("\n ");printf("%lf ",cov[2]);*/  
 /*  /*************************free matrix ************************/
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   goto end;*/  {
     return ps;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
 }    free((FREE_ARG)(m+nrl-NR_END));
   }
 /**************** Product of 2 matrices ******************/  
   /******************* ma3x *******************************/
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
 {  {
   /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    double ***m;
   /* in, b, out are matrice of pointers which should have been initialized  
      before: only the contents of out is modified. The function returns    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
      a pointer to pointers identical to out */    if (!m) nrerror("allocation failure 1 in matrix()");
   long i, j, k;    m += NR_END;
   for(i=nrl; i<= nrh; i++)    m -= nrl;
     for(k=ncolol; k<=ncoloh; k++)  
       for(j=ncl,out[i][k]=0.; j<=nch; j++)    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
         out[i][k] +=in[i][j]*b[j][k];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
     m[nrl] += NR_END;
   return out;    m[nrl] -= ncl;
 }  
     for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   
 /************* Higher Matrix Product ***************/    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )    m[nrl][ncl] += NR_END;
 {    m[nrl][ncl] -= nll;
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month    for (j=ncl+1; j<=nch; j++) 
      duration (i.e. until      m[nrl][j]=m[nrl][j-1]+nlay;
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.    
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step    for (i=nrl+1; i<=nrh; i++) {
      (typically every 2 years instead of every month which is too big).      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
      Model is determined by parameters x and covariates have to be      for (j=ncl+1; j<=nch; j++) 
      included manually here.        m[i][j]=m[i][j-1]+nlay;
     }
      */    return m; 
     /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   int i, j, d, h, k;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   double **out, cov[NCOVMAX];    */
   double **newm;  }
   
   /* Hstepm could be zero and should return the unit matrix */  /*************************free ma3x ************************/
   for (i=1;i<=nlstate+ndeath;i++)  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     for (j=1;j<=nlstate+ndeath;j++){  {
       oldm[i][j]=(i==j ? 1.0 : 0.0);    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
       po[i][j][0]=(i==j ? 1.0 : 0.0);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     }    free((FREE_ARG)(m+nrl-NR_END));
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  }
   for(h=1; h <=nhstepm; h++){  
     for(d=1; d <=hstepm; d++){  /*************** function subdirf ***********/
       newm=savm;  char *subdirf(char fileres[])
       /* Covariates have to be included here again */  {
       cov[1]=1.;    /* Caution optionfilefiname is hidden */
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    strcpy(tmpout,optionfilefiname);
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];    strcat(tmpout,"/"); /* Add to the right */
       for (k=1; k<=cptcovage;k++)    strcat(tmpout,fileres);
         cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    return tmpout;
       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]]];  
   /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/  {
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    /* Caution optionfilefiname is hidden */
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    strcpy(tmpout,optionfilefiname);
       savm=oldm;    strcat(tmpout,"/");
       oldm=newm;    strcat(tmpout,preop);
     }    strcat(tmpout,fileres);
     for(i=1; i<=nlstate+ndeath; i++)    return tmpout;
       for(j=1;j<=nlstate+ndeath;j++) {  }
         po[i][j][h]=newm[i][j];  
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  /*************** function subdirf3 ***********/
          */  char *subdirf3(char fileres[], char *preop, char *preop2)
       }  {
   } /* end h */    
   return po;    /* Caution optionfilefiname is hidden */
 }    strcpy(tmpout,optionfilefiname);
     strcat(tmpout,"/");
     strcat(tmpout,preop);
 /*************** log-likelihood *************/    strcat(tmpout,preop2);
 double func( double *x)    strcat(tmpout,fileres);
 {    return tmpout;
   int i, ii, j, k, mi, d, kk;  }
   double l, ll[NLSTATEMAX], cov[NCOVMAX];  
   double **out;  /***************** f1dim *************************/
   double sw; /* Sum of weights */  extern int ncom; 
   double lli; /* Individual log likelihood */  extern double *pcom,*xicom;
   long ipmx;  extern double (*nrfunc)(double []); 
   /*extern weight */   
   /* We are differentiating ll according to initial status */  double f1dim(double x) 
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/  { 
   /*for(i=1;i<imx;i++)    int j; 
     printf(" %d\n",s[4][i]);    double f;
   */    double *xt; 
   cov[1]=1.;   
     xt=vector(1,ncom); 
   for(k=1; k<=nlstate; k++) ll[k]=0.;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    f=(*nrfunc)(xt); 
     for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];    free_vector(xt,1,ncom); 
     for(mi=1; mi<= wav[i]-1; mi++){    return f; 
       for (ii=1;ii<=nlstate+ndeath;ii++)  } 
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
       for(d=0; d<dh[mi][i]; d++){  /*****************brent *************************/
         newm=savm;  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
         cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  { 
         for (kk=1; kk<=cptcovage;kk++) {    int iter; 
           cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];    double a,b,d,etemp;
         }    double fu,fv,fw,fx;
            double ftemp;
         out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    double p,q,r,tol1,tol2,u,v,w,x,xm; 
                      1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    double e=0.0; 
         savm=oldm;   
         oldm=newm;    a=(ax < cx ? ax : cx); 
            b=(ax > cx ? ax : cx); 
            x=w=v=bx; 
       } /* end mult */    fw=fv=fx=(*f)(x); 
          for (iter=1;iter<=ITMAX;iter++) { 
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      xm=0.5*(a+b); 
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       ipmx +=1;      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       sw += weight[i];      printf(".");fflush(stdout);
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;      fprintf(ficlog,".");fflush(ficlog);
     } /* end of wave */  #ifdef DEBUG
   } /* end of individual */      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);
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  #endif
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   return -l;        *xmin=x; 
 }        return fx; 
       } 
       ftemp=fu;
 /*********** Maximum Likelihood Estimation ***************/      if (fabs(e) > tol1) { 
         r=(x-w)*(fx-fv); 
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))        q=(x-v)*(fx-fw); 
 {        p=(x-v)*q-(x-w)*r; 
   int i,j, iter;        q=2.0*(q-r); 
   double **xi,*delti;        if (q > 0.0) p = -p; 
   double fret;        q=fabs(q); 
   xi=matrix(1,npar,1,npar);        etemp=e; 
   for (i=1;i<=npar;i++)        e=d; 
     for (j=1;j<=npar;j++)        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
       xi[i][j]=(i==j ? 1.0 : 0.0);          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   printf("Powell\n");        else { 
   powell(p,xi,npar,ftol,&iter,&fret,func);          d=p/q; 
           u=x+d; 
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));          if (u-a < tol2 || b-u < tol2) 
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));            d=SIGN(tol1,xm-x); 
         } 
 }      } else { 
         d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
 /**** Computes Hessian and covariance matrix ***/      } 
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
 {      fu=(*f)(u); 
   double  **a,**y,*x,pd;      if (fu <= fx) { 
   double **hess;        if (u >= x) a=x; else b=x; 
   int i, j,jk;        SHFT(v,w,x,u) 
   int *indx;          SHFT(fv,fw,fx,fu) 
           } else { 
   double hessii(double p[], double delta, int theta, double delti[]);            if (u < x) a=u; else b=u; 
   double hessij(double p[], double delti[], int i, int j);            if (fu <= fw || w == x) { 
   void lubksb(double **a, int npar, int *indx, double b[]) ;              v=w; 
   void ludcmp(double **a, int npar, int *indx, double *d) ;              w=u; 
               fv=fw; 
   hess=matrix(1,npar,1,npar);              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
   printf("\nCalculation of the hessian matrix. Wait...\n");              v=u; 
   for (i=1;i<=npar;i++){              fv=fu; 
     printf("%d",i);fflush(stdout);            } 
     hess[i][i]=hessii(p,ftolhess,i,delti);          } 
     /*printf(" %f ",p[i]);*/    } 
     /*printf(" %lf ",hess[i][i]);*/    nrerror("Too many iterations in brent"); 
   }    *xmin=x; 
      return fx; 
   for (i=1;i<=npar;i++) {  } 
     for (j=1;j<=npar;j++)  {  
       if (j>i) {  /****************** mnbrak ***********************/
         printf(".%d%d",i,j);fflush(stdout);  
         hess[i][j]=hessij(p,delti,i,j);  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
         hess[j][i]=hess[i][j];                  double (*func)(double)) 
         /*printf(" %lf ",hess[i][j]);*/  { 
       }    double ulim,u,r,q, dum;
     }    double fu; 
   }   
   printf("\n");    *fa=(*func)(*ax); 
     *fb=(*func)(*bx); 
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");    if (*fb > *fa) { 
        SHFT(dum,*ax,*bx,dum) 
   a=matrix(1,npar,1,npar);        SHFT(dum,*fb,*fa,dum) 
   y=matrix(1,npar,1,npar);        } 
   x=vector(1,npar);    *cx=(*bx)+GOLD*(*bx-*ax); 
   indx=ivector(1,npar);    *fc=(*func)(*cx); 
   for (i=1;i<=npar;i++)    while (*fb > *fc) { 
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];      r=(*bx-*ax)*(*fb-*fc); 
   ludcmp(a,npar,indx,&pd);      q=(*bx-*cx)*(*fb-*fa); 
       u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
   for (j=1;j<=npar;j++) {        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
     for (i=1;i<=npar;i++) x[i]=0;      ulim=(*bx)+GLIMIT*(*cx-*bx); 
     x[j]=1;      if ((*bx-u)*(u-*cx) > 0.0) { 
     lubksb(a,npar,indx,x);        fu=(*func)(u); 
     for (i=1;i<=npar;i++){      } else if ((*cx-u)*(u-ulim) > 0.0) { 
       matcov[i][j]=x[i];        fu=(*func)(u); 
     }        if (fu < *fc) { 
   }          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
             SHFT(*fb,*fc,fu,(*func)(u)) 
   printf("\n#Hessian matrix#\n");            } 
   for (i=1;i<=npar;i++) {      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     for (j=1;j<=npar;j++) {        u=ulim; 
       printf("%.3e ",hess[i][j]);        fu=(*func)(u); 
     }      } else { 
     printf("\n");        u=(*cx)+GOLD*(*cx-*bx); 
   }        fu=(*func)(u); 
       } 
   /* Recompute Inverse */      SHFT(*ax,*bx,*cx,u) 
   for (i=1;i<=npar;i++)        SHFT(*fa,*fb,*fc,fu) 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];        } 
   ludcmp(a,npar,indx,&pd);  } 
   
   /*  printf("\n#Hessian matrix recomputed#\n");  /*************** linmin ************************/
   
   for (j=1;j<=npar;j++) {  int ncom; 
     for (i=1;i<=npar;i++) x[i]=0;  double *pcom,*xicom;
     x[j]=1;  double (*nrfunc)(double []); 
     lubksb(a,npar,indx,x);   
     for (i=1;i<=npar;i++){  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       y[i][j]=x[i];  { 
       printf("%.3e ",y[i][j]);    double brent(double ax, double bx, double cx, 
     }                 double (*f)(double), double tol, double *xmin); 
     printf("\n");    double f1dim(double x); 
   }    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   */                double *fc, double (*func)(double)); 
     int j; 
   free_matrix(a,1,npar,1,npar);    double xx,xmin,bx,ax; 
   free_matrix(y,1,npar,1,npar);    double fx,fb,fa;
   free_vector(x,1,npar);   
   free_ivector(indx,1,npar);    ncom=n; 
   free_matrix(hess,1,npar,1,npar);    pcom=vector(1,n); 
     xicom=vector(1,n); 
     nrfunc=func; 
 }    for (j=1;j<=n;j++) { 
       pcom[j]=p[j]; 
 /*************** hessian matrix ****************/      xicom[j]=xi[j]; 
 double hessii( double x[], double delta, int theta, double delti[])    } 
 {    ax=0.0; 
   int i;    xx=1.0; 
   int l=1, lmax=20;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   double k1,k2;    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   double p2[NPARMAX+1];  #ifdef DEBUG
   double res;    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
   double fx;  #endif
   int k=0,kmax=10;    for (j=1;j<=n;j++) { 
   double l1;      xi[j] *= xmin; 
       p[j] += xi[j]; 
   fx=func(x);    } 
   for (i=1;i<=npar;i++) p2[i]=x[i];    free_vector(xicom,1,n); 
   for(l=0 ; l <=lmax; l++){    free_vector(pcom,1,n); 
     l1=pow(10,l);  } 
     delts=delt;  
     for(k=1 ; k <kmax; k=k+1){  char *asc_diff_time(long time_sec, char ascdiff[])
       delt = delta*(l1*k);  {
       p2[theta]=x[theta] +delt;    long sec_left, days, hours, minutes;
       k1=func(p2)-fx;    days = (time_sec) / (60*60*24);
       p2[theta]=x[theta]-delt;    sec_left = (time_sec) % (60*60*24);
       k2=func(p2)-fx;    hours = (sec_left) / (60*60) ;
       /*res= (k1-2.0*fx+k2)/delt/delt; */    sec_left = (sec_left) %(60*60);
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    minutes = (sec_left) /60;
          sec_left = (sec_left) % (60);
 #ifdef DEBUG    sprintf(ascdiff,"%d day(s) %d hour(s) %d minute(s) %d second(s)",days, hours, minutes, sec_left);  
       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);    return ascdiff;
 #endif  }
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */  
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){  /*************** powell ************************/
         k=kmax;  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
       }              double (*func)(double [])) 
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  { 
         k=kmax; l=lmax*10.;    void linmin(double p[], double xi[], int n, double *fret, 
       }                double (*func)(double [])); 
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    int i,ibig,j; 
         delts=delt;    double del,t,*pt,*ptt,*xit;
       }    double fp,fptt;
     }    double *xits;
   }    int niterf, itmp;
   delti[theta]=delts;  
   return res;    pt=vector(1,n); 
      ptt=vector(1,n); 
 }    xit=vector(1,n); 
     xits=vector(1,n); 
 double hessij( double x[], double delti[], int thetai,int thetaj)    *fret=(*func)(p); 
 {    for (j=1;j<=n;j++) pt[j]=p[j]; 
   int i;    for (*iter=1;;++(*iter)) { 
   int l=1, l1, lmax=20;      fp=(*fret); 
   double k1,k2,k3,k4,res,fx;      ibig=0; 
   double p2[NPARMAX+1];      del=0.0; 
   int k;      last_time=curr_time;
       (void) gettimeofday(&curr_time,&tzp);
   fx=func(x);      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
   for (k=1; k<=2; k++) {      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);
     for (i=1;i<=npar;i++) p2[i]=x[i];  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
     p2[thetai]=x[thetai]+delti[thetai]/k;     for (i=1;i<=n;i++) {
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        printf(" %d %.12f",i, p[i]);
     k1=func(p2)-fx;        fprintf(ficlog," %d %.12lf",i, p[i]);
          fprintf(ficrespow," %.12lf", p[i]);
     p2[thetai]=x[thetai]+delti[thetai]/k;      }
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      printf("\n");
     k2=func(p2)-fx;      fprintf(ficlog,"\n");
        fprintf(ficrespow,"\n");fflush(ficrespow);
     p2[thetai]=x[thetai]-delti[thetai]/k;      if(*iter <=3){
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;        tm = *localtime(&curr_time.tv_sec);
     k3=func(p2)-fx;        strcpy(strcurr,asctime(&tm));
    /*       asctime_r(&tm,strcurr); */
     p2[thetai]=x[thetai]-delti[thetai]/k;        forecast_time=curr_time; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;        itmp = strlen(strcurr);
     k4=func(p2)-fx;        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */          strcurr[itmp-1]='\0';
 #ifdef DEBUG        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
 #endif        for(niterf=10;niterf<=30;niterf+=10){
   }          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
   return res;          tmf = *localtime(&forecast_time.tv_sec);
 }  /*      asctime_r(&tmf,strfor); */
           strcpy(strfor,asctime(&tmf));
 /************** Inverse of matrix **************/          itmp = strlen(strfor);
 void ludcmp(double **a, int n, int *indx, double *d)          if(strfor[itmp-1]=='\n')
 {          strfor[itmp-1]='\0';
   int i,imax,j,k;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   double big,dum,sum,temp;          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);
   double *vv;        }
        }
   vv=vector(1,n);      for (i=1;i<=n;i++) { 
   *d=1.0;        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
   for (i=1;i<=n;i++) {        fptt=(*fret); 
     big=0.0;  #ifdef DEBUG
     for (j=1;j<=n;j++)        printf("fret=%lf \n",*fret);
       if ((temp=fabs(a[i][j])) > big) big=temp;        fprintf(ficlog,"fret=%lf \n",*fret);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  #endif
     vv[i]=1.0/big;        printf("%d",i);fflush(stdout);
   }        fprintf(ficlog,"%d",i);fflush(ficlog);
   for (j=1;j<=n;j++) {        linmin(p,xit,n,fret,func); 
     for (i=1;i<j;i++) {        if (fabs(fptt-(*fret)) > del) { 
       sum=a[i][j];          del=fabs(fptt-(*fret)); 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];          ibig=i; 
       a[i][j]=sum;        } 
     }  #ifdef DEBUG
     big=0.0;        printf("%d %.12e",i,(*fret));
     for (i=j;i<=n;i++) {        fprintf(ficlog,"%d %.12e",i,(*fret));
       sum=a[i][j];        for (j=1;j<=n;j++) {
       for (k=1;k<j;k++)          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
         sum -= a[i][k]*a[k][j];          printf(" x(%d)=%.12e",j,xit[j]);
       a[i][j]=sum;          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
       if ( (dum=vv[i]*fabs(sum)) >= big) {        }
         big=dum;        for(j=1;j<=n;j++) {
         imax=i;          printf(" p=%.12e",p[j]);
       }          fprintf(ficlog," p=%.12e",p[j]);
     }        }
     if (j != imax) {        printf("\n");
       for (k=1;k<=n;k++) {        fprintf(ficlog,"\n");
         dum=a[imax][k];  #endif
         a[imax][k]=a[j][k];      } 
         a[j][k]=dum;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
       }  #ifdef DEBUG
       *d = -(*d);        int k[2],l;
       vv[imax]=vv[j];        k[0]=1;
     }        k[1]=-1;
     indx[j]=imax;        printf("Max: %.12e",(*func)(p));
     if (a[j][j] == 0.0) a[j][j]=TINY;        fprintf(ficlog,"Max: %.12e",(*func)(p));
     if (j != n) {        for (j=1;j<=n;j++) {
       dum=1.0/(a[j][j]);          printf(" %.12e",p[j]);
       for (i=j+1;i<=n;i++) a[i][j] *= dum;          fprintf(ficlog," %.12e",p[j]);
     }        }
   }        printf("\n");
   free_vector(vv,1,n);  /* Doesn't work */        fprintf(ficlog,"\n");
 ;        for(l=0;l<=1;l++) {
 }          for (j=1;j<=n;j++) {
             ptt[j]=p[j]+(p[j]-pt[j])*k[l];
 void lubksb(double **a, int n, int *indx, double b[])            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
 {            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   int i,ii=0,ip,j;          }
   double sum;          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)));
   for (i=1;i<=n;i++) {        }
     ip=indx[i];  #endif
     sum=b[ip];  
     b[ip]=b[i];  
     if (ii)        free_vector(xit,1,n); 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];        free_vector(xits,1,n); 
     else if (sum) ii=i;        free_vector(ptt,1,n); 
     b[i]=sum;        free_vector(pt,1,n); 
   }        return; 
   for (i=n;i>=1;i--) {      } 
     sum=b[i];      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];      for (j=1;j<=n;j++) { 
     b[i]=sum/a[i][i];        ptt[j]=2.0*p[j]-pt[j]; 
   }        xit[j]=p[j]-pt[j]; 
 }        pt[j]=p[j]; 
       } 
 /************ Frequencies ********************/      fptt=(*func)(ptt); 
 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)      if (fptt < fp) { 
 {  /* Some frequencies */        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
          if (t < 0.0) { 
   int i, m, jk, k1,i1, j1, bool, z1,z2,j;          linmin(p,xit,n,fret,func); 
   double ***freq; /* Frequencies */          for (j=1;j<=n;j++) { 
   double *pp;            xi[j][ibig]=xi[j][n]; 
   double pos, k2, dateintsum=0,k2cpt=0;            xi[j][n]=xit[j]; 
   FILE *ficresp;          }
   char fileresp[FILENAMELENGTH];  #ifdef DEBUG
            printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   pp=vector(1,nlstate);          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);          for(j=1;j<=n;j++){
   strcpy(fileresp,"p");            printf(" %.12e",xit[j]);
   strcat(fileresp,fileres);            fprintf(ficlog," %.12e",xit[j]);
   if((ficresp=fopen(fileresp,"w"))==NULL) {          }
     printf("Problem with prevalence resultfile: %s\n", fileresp);          printf("\n");
     exit(0);          fprintf(ficlog,"\n");
   }  #endif
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);        }
   j1=0;      } 
      } 
   j=cptcoveff;  } 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  
    /**** Prevalence limit (stable or period prevalence)  ****************/
   for(k1=1; k1<=j;k1++){  
     for(i1=1; i1<=ncodemax[k1];i1++){  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       j1++;  {
       /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
         scanf("%d", i);*/       matrix by transitions matrix until convergence is reached */
       for (i=-1; i<=nlstate+ndeath; i++)    
         for (jk=-1; jk<=nlstate+ndeath; jk++)      int i, ii,j,k;
           for(m=agemin; m <= agemax+3; m++)    double min, max, maxmin, maxmax,sumnew=0.;
             freq[i][jk][m]=0;    double **matprod2();
          double **out, cov[NCOVMAX+1], **pmij();
       dateintsum=0;    double **newm;
       k2cpt=0;    double agefin, delaymax=50 ; /* Max number of years to converge */
       for (i=1; i<=imx; i++) {  
         bool=1;    for (ii=1;ii<=nlstate+ndeath;ii++)
         if  (cptcovn>0) {      for (j=1;j<=nlstate+ndeath;j++){
           for (z1=1; z1<=cptcoveff; z1++)        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])      }
               bool=0;  
         }     cov[1]=1.;
         if (bool==1) {   
           for(m=firstpass; m<=lastpass; m++){   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
             k2=anint[m][i]+(mint[m][i]/12.);    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
             if ((k2>=dateprev1) && (k2<=dateprev2)) {      newm=savm;
               if(agev[m][i]==0) agev[m][i]=agemax+1;      /* Covariates have to be included here again */
               if(agev[m][i]==1) agev[m][i]=agemax+2;       cov[2]=agefin;
               if (m<lastpass) {    
                 freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];        for (k=1; k<=cptcovn;k++) {
                 freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
               }          /*      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]]);*/
                      }
               if ((agev[m][i]>1) && (agev[m][i]< (agemax+3))) {        for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
                 dateintsum=dateintsum+k2;        for (k=1; k<=cptcovprod;k++)
                 k2cpt++;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
               }  
             }        /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
           }        /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
         }        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       }      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
          
       fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      savm=oldm;
       oldm=newm;
       if  (cptcovn>0) {      maxmax=0.;
         fprintf(ficresp, "\n#********** Variable ");      for(j=1;j<=nlstate;j++){
         for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);        min=1.;
         fprintf(ficresp, "**********\n#");        max=0.;
       }        for(i=1; i<=nlstate; i++) {
       for(i=1; i<=nlstate;i++)          sumnew=0;
         fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
       fprintf(ficresp, "\n");          prlim[i][j]= newm[i][j]/(1-sumnew);
                max=FMAX(max,prlim[i][j]);
       for(i=(int)agemin; i <= (int)agemax+3; i++){          min=FMIN(min,prlim[i][j]);
         if(i==(int)agemax+3)        }
           printf("Total");        maxmin=max-min;
         else        maxmax=FMAX(maxmax,maxmin);
           printf("Age %d", i);      }
         for(jk=1; jk <=nlstate ; jk++){      if(maxmax < ftolpl){
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)        return prlim;
             pp[jk] += freq[jk][m][i];      }
         }    }
         for(jk=1; jk <=nlstate ; jk++){  }
           for(m=-1, pos=0; m <=0 ; m++)  
             pos += freq[jk][m][i];  /*************** transition probabilities ***************/ 
           if(pp[jk]>=1.e-10)  
             printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
           else  {
             printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);    double s1, s2;
         }    /*double t34;*/
     int i,j,j1, nc, ii, jj;
         for(jk=1; jk <=nlstate ; jk++){  
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)      for(i=1; i<= nlstate; i++){
             pp[jk] += freq[jk][m][i];        for(j=1; j<i;j++){
         }          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
             /*s2 += param[i][j][nc]*cov[nc];*/
         for(jk=1,pos=0; jk <=nlstate ; jk++)            s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
           pos += pp[jk];  /*       printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2); */
         for(jk=1; jk <=nlstate ; jk++){          }
           if(pos>=1.e-5)          ps[i][j]=s2;
             printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);  /*      printf("s1=%.17e, s2=%.17e\n",s1,s2); */
           else        }
             printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);        for(j=i+1; j<=nlstate+ndeath;j++){
           if( i <= (int) agemax){          for (nc=1, s2=0.;nc <=ncovmodel; nc++){
             if(pos>=1.e-5){            s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];
               fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);  /*        printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2); */
               probs[i][jk][j1]= pp[jk]/pos;          }
               /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/          ps[i][j]=s2;
             }        }
             else      }
               fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);      /*ps[3][2]=1;*/
           }      
         }      for(i=1; i<= nlstate; i++){
                s1=0;
         for(jk=-1; jk <=nlstate+ndeath; jk++)        for(j=1; j<i; j++){
           for(m=-1; m <=nlstate+ndeath; m++)          s1+=exp(ps[i][j]);
             if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         if(i <= (int) agemax)        }
           fprintf(ficresp,"\n");        for(j=i+1; j<=nlstate+ndeath; j++){
         printf("\n");          s1+=exp(ps[i][j]);
       }          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
     }        }
   }        ps[i][i]=1./(s1+1.);
   dateintmean=dateintsum/k2cpt;        for(j=1; j<i; j++)
            ps[i][j]= exp(ps[i][j])*ps[i][i];
   fclose(ficresp);        for(j=i+1; j<=nlstate+ndeath; j++)
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);          ps[i][j]= exp(ps[i][j])*ps[i][i];
   free_vector(pp,1,nlstate);        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
        } /* end i */
   /* End of Freq */      
 }      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         for(jj=1; jj<= nlstate+ndeath; jj++){
 /************ Prevalence ********************/          ps[ii][jj]=0;
 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)          ps[ii][ii]=1;
 {  /* Some frequencies */        }
        }
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;      
   double ***freq; /* Frequencies */  
   double *pp;  /*        for(ii=1; ii<= nlstate+ndeath; ii++){ */
   double pos, k2;  /*       for(jj=1; jj<= nlstate+ndeath; jj++){ */
   /*         printf("ddd %lf ",ps[ii][jj]); */
   pp=vector(1,nlstate);  /*       } */
   probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);  /*       printf("\n "); */
    /*        } */
   freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);  /*        printf("\n ");printf("%lf ",cov[2]); */
   j1=0;         /*
          for(i=1; i<= npar; i++) printf("%f ",x[i]);
   j=cptcoveff;        goto end;*/
   if (cptcovn<1) {j=1;ncodemax[1]=1;}      return ps;
    }
   for(k1=1; k1<=j;k1++){  
     for(i1=1; i1<=ncodemax[k1];i1++){  /**************** Product of 2 matrices ******************/
       j1++;  
        double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
       for (i=-1; i<=nlstate+ndeath; i++)    {
         for (jk=-1; jk<=nlstate+ndeath; jk++)      /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
           for(m=agemin; m <= agemax+3; m++)       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
             freq[i][jk][m]=0;    /* in, b, out are matrice of pointers which should have been initialized 
             before: only the contents of out is modified. The function returns
       for (i=1; i<=imx; i++) {       a pointer to pointers identical to out */
         bool=1;    long i, j, k;
         if  (cptcovn>0) {    for(i=nrl; i<= nrh; i++)
           for (z1=1; z1<=cptcoveff; z1++)      for(k=ncolol; k<=ncoloh; k++)
             if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]])        for(j=ncl,out[i][k]=0.; j<=nch; j++)
               bool=0;          out[i][k] +=in[i][j]*b[j][k];
         }  
         if (bool==1) {    return out;
           for(m=firstpass; m<=lastpass; m++){  }
             k2=anint[m][i]+(mint[m][i]/12.);  
             if ((k2>=dateprev1) && (k2<=dateprev2)) {  
               if(agev[m][i]==0) agev[m][i]=agemax+1;  /************* Higher Matrix Product ***************/
               if(agev[m][i]==1) agev[m][i]=agemax+2;  
               if (m<lastpass) {  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
                 if (calagedate>0)  {
                   freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i];    /* Computes the transition matrix starting at age 'age' over 
                 else       'nhstepm*hstepm*stepm' months (i.e. until
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
                 freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i];       nhstepm*hstepm matrices. 
               }       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 the memory).
         }       Model is determined by parameters x and covariates have to be 
       }       included manually here. 
       for(i=(int)agemin; i <= (int)agemax+3; i++){  
         for(jk=1; jk <=nlstate ; jk++){       */
           for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  
             pp[jk] += freq[jk][m][i];    int i, j, d, h, k;
         }    double **out, cov[NCOVMAX+1];
         for(jk=1; jk <=nlstate ; jk++){    double **newm;
           for(m=-1, pos=0; m <=0 ; m++)  
             pos += freq[jk][m][i];    /* Hstepm could be zero and should return the unit matrix */
         }    for (i=1;i<=nlstate+ndeath;i++)
              for (j=1;j<=nlstate+ndeath;j++){
         for(jk=1; jk <=nlstate ; jk++){        oldm[i][j]=(i==j ? 1.0 : 0.0);
           for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)        po[i][j][0]=(i==j ? 1.0 : 0.0);
             pp[jk] += freq[jk][m][i];      }
         }    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
            for(h=1; h <=nhstepm; h++){
         for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk];      for(d=1; d <=hstepm; d++){
                newm=savm;
         for(jk=1; jk <=nlstate ; jk++){            /* Covariates have to be included here again */
           if( i <= (int) agemax){        cov[1]=1.;
             if(pos>=1.e-5){        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
               probs[i][jk][j1]= pp[jk]/pos;        for (k=1; k<=cptcovn;k++) 
             }          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
           }        for (k=1; k<=cptcovage;k++)
         }          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
                for (k=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]]];
     }  
   }  
         /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
          /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
   free_vector(pp,1,nlstate);                     pmij(pmmij,cov,ncovmodel,x,nlstate));
          savm=oldm;
 }  /* End of Freq */        oldm=newm;
       }
 /************* Waves Concatenation ***************/      for(i=1; i<=nlstate+ndeath; i++)
         for(j=1;j<=nlstate+ndeath;j++) {
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)          po[i][j][h]=newm[i][j];
 {          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        }
      Death is a valid wave (if date is known).      /*printf("h=%d ",h);*/
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    } /* end h */
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]  /*     printf("\n H=%d \n",h); */
      and mw[mi+1][i]. dh depends on stepm.    return po;
      */  }
   
   int i, mi, m;  
   /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;  /*************** log-likelihood *************/
      double sum=0., jmean=0.;*/  double func( double *x)
   {
   int j, k=0,jk, ju, jl;    int i, ii, j, k, mi, d, kk;
   double sum=0.;    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
   jmin=1e+5;    double **out;
   jmax=-1;    double sw; /* Sum of weights */
   jmean=0.;    double lli; /* Individual log likelihood */
   for(i=1; i<=imx; i++){    int s1, s2;
     mi=0;    double bbh, survp;
     m=firstpass;    long ipmx;
     while(s[m][i] <= nlstate){    /*extern weight */
       if(s[m][i]>=1)    /* We are differentiating ll according to initial status */
         mw[++mi][i]=m;    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
       if(m >=lastpass)    /*for(i=1;i<imx;i++) 
         break;      printf(" %d\n",s[4][i]);
       else    */
         m++;    cov[1]=1.;
     }/* end while */  
     if (s[m][i] > nlstate){    for(k=1; k<=nlstate; k++) ll[k]=0.;
       mi++;     /* Death is another wave */  
       /* if(mi==0)  never been interviewed correctly before death */    if(mle==1){
          /* Only death is a correct wave */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
       mw[mi][i]=m;        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     }        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
     wav[i]=mi;            for (j=1;j<=nlstate+ndeath;j++){
     if(mi==0)              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   }            }
           for(d=0; d<dh[mi][i]; d++){
   for(i=1; i<=imx; i++){            newm=savm;
     for(mi=1; mi<wav[i];mi++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
       if (stepm <=0)            for (kk=1; kk<=cptcovage;kk++) {
         dh[mi][i]=1;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       else{            }
         if (s[mw[mi+1][i]][i] > nlstate) {            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           if (agedc[i] < 2*AGESUP) {                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);            savm=oldm;
           if(j==0) j=1;  /* Survives at least one month after exam */            oldm=newm;
           k=k+1;          } /* end mult */
           if (j >= jmax) jmax=j;        
           if (j <= jmin) jmin=j;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
           sum=sum+j;          /* But now since version 0.9 we anticipate for bias at large stepm.
           /*if (j<0) printf("j=%d num=%d \n",j,i); */           * If stepm is larger than one month (smallest stepm) and if the exact delay 
           }           * (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
         else{           * we keep into memory the bias bh[mi][i] and also the previous matrix product
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
           k=k+1;           * probability in order to take into account the bias as a fraction of the way
           if (j >= jmax) jmax=j;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
           else if (j <= jmin)jmin=j;           * -stepm/2 to stepm/2 .
           /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */           * For stepm=1 the results are the same as for previous versions of Imach.
           sum=sum+j;           * For stepm > 1 the results are less biased than in previous versions. 
         }           */
         jk= j/stepm;          s1=s[mw[mi][i]][i];
         jl= j -jk*stepm;          s2=s[mw[mi+1][i]][i];
         ju= j -(jk+1)*stepm;          bbh=(double)bh[mi][i]/(double)stepm; 
         if(jl <= -ju)          /* bias bh is positive if real duration
           dh[mi][i]=jk;           * is higher than the multiple of stepm and negative otherwise.
         else           */
           dh[mi][i]=jk+1;          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
         if(dh[mi][i]==0)          if( s2 > nlstate){ 
           dh[mi][i]=1; /* At least one step */            /* i.e. if s2 is a death state and if the date of death is known 
       }               then the contribution to the likelihood is the probability to 
     }               die between last step unit time and current  step unit time, 
   }               which is also equal to probability to die before dh 
   jmean=sum/k;               minus probability to die before dh-stepm . 
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,jmean);               In version up to 0.92 likelihood was computed
  }          as if date of death was unknown. Death was treated as any other
 /*********** Tricode ****************************/          health state: the date of the interview describes the actual state
 void tricode(int *Tvar, int **nbcode, int imx)          and not the date of a change in health state. The former idea was
 {          to consider that at each interview the state was recorded
   int Ndum[20],ij=1, k, j, i;          (healthy, disable or death) and IMaCh was corrected; but when we
   int cptcode=0;          introduced the exact date of death then we should have modified
   cptcoveff=0;          the contribution of an exact death to the likelihood. This new
            contribution is smaller and very dependent of the step unit
   for (k=0; k<19; k++) Ndum[k]=0;          stepm. It is no more the probability to die between last interview
   for (k=1; k<=7; k++) ncodemax[k]=0;          and month of death but the probability to survive from last
           interview up to one month before death multiplied by the
   for (j=1; j<=(cptcovn+2*cptcovprod); j++) {          probability to die within a month. Thanks to Chris
     for (i=1; i<=imx; i++) {          Jackson for correcting this bug.  Former versions increased
       ij=(int)(covar[Tvar[j]][i]);          mortality artificially. The bad side is that we add another loop
       Ndum[ij]++;          which slows down the processing. The difference can be up to 10%
       /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/          lower mortality.
       if (ij > cptcode) cptcode=ij;            */
     }            lli=log(out[s1][s2] - savm[s1][s2]);
   
     for (i=0; i<=cptcode; i++) {  
       if(Ndum[i]!=0) ncodemax[j]++;          } else if  (s2==-2) {
     }            for (j=1,survp=0. ; j<=nlstate; j++) 
     ij=1;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             /*survp += out[s1][j]; */
             lli= log(survp);
     for (i=1; i<=ncodemax[j]; i++) {          }
       for (k=0; k<=19; k++) {          
         if (Ndum[k] != 0) {          else if  (s2==-4) { 
           nbcode[Tvar[j]][ij]=k;            for (j=3,survp=0. ; j<=nlstate; j++)  
                        survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           ij++;            lli= log(survp); 
         }          } 
         if (ij > ncodemax[j]) break;  
       }            else if  (s2==-5) { 
     }            for (j=1,survp=0. ; j<=2; j++)  
   }                survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             lli= log(survp); 
  for (k=0; k<19; k++) Ndum[k]=0;          } 
           
  for (i=1; i<=ncovmodel-2; i++) {          else{
       ij=Tvar[i];            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       Ndum[ij]++;            /*  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 */
     }          } 
           /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
  ij=1;          /*if(lli ==000.0)*/
  for (i=1; i<=10; i++) {          /*printf("bbh= %f lli=%f savm=%f out=%f %d\n",bbh,lli,savm[s1][s2], out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]],i); */
    if((Ndum[i]!=0) && (i<=ncovcol)){          ipmx +=1;
      Tvaraff[ij]=i;          sw += weight[i];
      ij++;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    }        } /* end of wave */
  }      } /* end of individual */
      }  else if(mle==2){
     cptcoveff=ij-1;      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++){
 /*********** Health Expectancies ****************/          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
 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 )              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
               savm[ii][j]=(ii==j ? 1.0 : 0.0);
 {            }
   /* Health expectancies */          for(d=0; d<=dh[mi][i]; d++){
   int i, j, nhstepm, hstepm, h, nstepm, k, cptj;            newm=savm;
   double age, agelim, hf;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   double ***p3mat,***varhe;            for (kk=1; kk<=cptcovage;kk++) {
   double **dnewm,**doldm;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
   double *xp;            }
   double **gp, **gm;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   double ***gradg, ***trgradg;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   int theta;            savm=oldm;
             oldm=newm;
   varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage);          } /* end mult */
   xp=vector(1,npar);        
   dnewm=matrix(1,nlstate*2,1,npar);          s1=s[mw[mi][i]][i];
   doldm=matrix(1,nlstate*2,1,nlstate*2);          s2=s[mw[mi+1][i]][i];
            bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficreseij,"# Health expectancies\n");          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
   fprintf(ficreseij,"# Age");          ipmx +=1;
   for(i=1; i<=nlstate;i++)          sw += weight[i];
     for(j=1; j<=nlstate;j++)          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       fprintf(ficreseij," %1d-%1d (SE)",i,j);        } /* end of wave */
   fprintf(ficreseij,"\n");      } /* end of individual */
     }  else if(mle==3){  /* exponential inter-extrapolation */
   if(estepm < stepm){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     printf ("Problem %d lower than %d\n",estepm, stepm);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   }        for(mi=1; mi<= wav[i]-1; mi++){
   else  hstepm=estepm;            for (ii=1;ii<=nlstate+ndeath;ii++)
   /* We compute the life expectancy from trapezoids spaced every estepm months            for (j=1;j<=nlstate+ndeath;j++){
    * This is mainly to measure the difference between two models: for example              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
    * if stepm=24 months pijx are given only every 2 years and by summing them              savm[ii][j]=(ii==j ? 1.0 : 0.0);
    * we are calculating an estimate of the Life Expectancy assuming a linear            }
    * progression inbetween and thus overestimating or underestimating according          for(d=0; d<dh[mi][i]; d++){
    * to the curvature of the survival function. If, for the same date, we            newm=savm;
    * estimate the model with stepm=1 month, we can keep estepm to 24 months            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
    * to compare the new estimate of Life expectancy with the same linear            for (kk=1; kk<=cptcovage;kk++) {
    * hypothesis. A more precise result, taking into account a more precise              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
    * curvature will be obtained if estepm is as small as stepm. */            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   /* For example we decided to compute the life expectancy with the smallest unit */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.            savm=oldm;
      nhstepm is the number of hstepm from age to agelim            oldm=newm;
      nstepm is the number of stepm from age to agelin.          } /* end mult */
      Look at hpijx to understand the reason of that which relies in memory size        
      and note for a fixed period like estepm months */          s1=s[mw[mi][i]][i];
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the          s2=s[mw[mi+1][i]][i];
      survival function given by stepm (the optimization length). Unfortunately it          bbh=(double)bh[mi][i]/(double)stepm; 
      means that if the survival funtion is printed only each two years of age and if          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 */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same          ipmx +=1;
      results. So we changed our mind and took the option of the best precision.          sw += weight[i];
   */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */        } /* end of wave */
       } /* end of individual */
   agelim=AGESUP;    }else if (mle==4){  /* ml=4 no inter-extrapolation */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     /* nhstepm age range expressed in number of stepm */        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     nstepm=(int) rint((agelim-age)*YEARM/stepm);        for(mi=1; mi<= wav[i]-1; mi++){
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */          for (ii=1;ii<=nlstate+ndeath;ii++)
     /* if (stepm >= YEARM) hstepm=1;*/            for (j=1;j<=nlstate+ndeath;j++){
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2);            }
     gp=matrix(0,nhstepm,1,nlstate*2);          for(d=0; d<dh[mi][i]; d++){
     gm=matrix(0,nhstepm,1,nlstate*2);            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     /* Computed by stepm unit matrices, product of hstepm matrices, stored            for (kk=1; kk<=cptcovage;kk++) {
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);              }
            
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
     /* Computing Variances of health expectancies */            oldm=newm;
           } /* end mult */
      for(theta=1; theta <=npar; theta++){        
       for(i=1; i<=npar; i++){          s1=s[mw[mi][i]][i];
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          s2=s[mw[mi+1][i]][i];
       }          if( s2 > nlstate){ 
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              lli=log(out[s1][s2] - savm[s1][s2]);
            }else{
       cptj=0;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       for(j=1; j<= nlstate; j++){          }
         for(i=1; i<=nlstate; i++){          ipmx +=1;
           cptj=cptj+1;          sw += weight[i];
           for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
             gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;  /*      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 */
         }      } /* end of individual */
       }    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
            for (i=1,ipmx=0, sw=0.; i<=imx; i++){
              for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
       for(i=1; i<=npar; i++)        for(mi=1; mi<= wav[i]-1; mi++){
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          for (ii=1;ii<=nlstate+ndeath;ii++)
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);              for (j=1;j<=nlstate+ndeath;j++){
                    oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       cptj=0;              savm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<= nlstate; j++){            }
         for(i=1;i<=nlstate;i++){          for(d=0; d<dh[mi][i]; d++){
           cptj=cptj+1;            newm=savm;
           for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
             gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.;            for (kk=1; kk<=cptcovage;kk++) {
           }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         }            }
       }          
                  out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                             1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
       for(j=1; j<= nlstate*2; j++)            oldm=newm;
         for(h=0; h<=nhstepm-1; h++){          } /* end mult */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        
         }          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
      }          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
              ipmx +=1;
 /* End theta */          sw += weight[i];
           ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
      trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar);          /*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(h=0; h<=nhstepm-1; h++)      } /* end of individual */
       for(j=1; j<=nlstate*2;j++)    } /* End of if */
         for(theta=1; theta <=npar; theta++)    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         trgradg[h][j][theta]=gradg[h][theta][j];    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
     return -l;
      for(i=1;i<=nlstate*2;i++)  }
       for(j=1;j<=nlstate*2;j++)  
         varhe[i][j][(int)age] =0.;  /*************** log-likelihood *************/
   double funcone( double *x)
      printf("%d|",(int)age);fflush(stdout);  {
     for(h=0;h<=nhstepm-1;h++){    /* Same as likeli but slower because of a lot of printf and if */
       for(k=0;k<=nhstepm-1;k++){    int i, ii, j, k, mi, d, kk;
         matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov);    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
         matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]);    double **out;
         for(i=1;i<=nlstate*2;i++)    double lli; /* Individual log likelihood */
           for(j=1;j<=nlstate*2;j++)    double llt;
             varhe[i][j][(int)age] += doldm[i][j]*hf*hf;    int s1, s2;
       }    double bbh, survp;
     }    /*extern weight */
     /* We are differentiating ll according to initial status */
          /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     /* Computing expectancies */    /*for(i=1;i<imx;i++) 
     for(i=1; i<=nlstate;i++)      printf(" %d\n",s[4][i]);
       for(j=1; j<=nlstate;j++)    */
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){    cov[1]=1.;
           eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;  
              for(k=1; k<=nlstate; k++) ll[k]=0.;
 /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/  
     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++){
     fprintf(ficreseij,"%3.0f",age );        for (ii=1;ii<=nlstate+ndeath;ii++)
     cptj=0;          for (j=1;j<=nlstate+ndeath;j++){
     for(i=1; i<=nlstate;i++)            oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       for(j=1; j<=nlstate;j++){            savm[ii][j]=(ii==j ? 1.0 : 0.0);
         cptj++;          }
         fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) );        for(d=0; d<dh[mi][i]; d++){
       }          newm=savm;
     fprintf(ficreseij,"\n");          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
              for (kk=1; kk<=cptcovage;kk++) {
     free_matrix(gm,0,nhstepm,1,nlstate*2);            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     free_matrix(gp,0,nhstepm,1,nlstate*2);          }
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2);          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar);                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          savm=oldm;
   }          oldm=newm;
   free_vector(xp,1,npar);        } /* end mult */
   free_matrix(dnewm,1,nlstate*2,1,npar);        
   free_matrix(doldm,1,nlstate*2,1,nlstate*2);        s1=s[mw[mi][i]][i];
   free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage);        s2=s[mw[mi+1][i]][i];
 }        bbh=(double)bh[mi][i]/(double)stepm; 
         /* bias is positive if real duration
 /************ Variance ******************/         * is higher than the multiple of stepm and negative otherwise.
 void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm)         */
 {        if( s2 > nlstate && (mle <5) ){  /* Jackson */
   /* Variance of health expectancies */          lli=log(out[s1][s2] - savm[s1][s2]);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        } else if  (s2==-2) {
   double **newm;          for (j=1,survp=0. ; j<=nlstate; j++) 
   double **dnewm,**doldm;            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   int i, j, nhstepm, hstepm, h, nstepm ;          lli= log(survp);
   int k, cptcode;        }else if (mle==1){
   double *xp;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   double **gp, **gm;        } else if(mle==2){
   double ***gradg, ***trgradg;          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 */
   double ***p3mat;        } else if(mle==3){  /* exponential inter-extrapolation */
   double age,agelim, hf;          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 */
   int theta;        } else if (mle==4){  /* mle=4 no inter-extrapolation */
           lli=log(out[s1][s2]); /* Original formula */
   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");        } else{  /* mle=0 back to 1 */
   fprintf(ficresvij,"# Age");          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   for(i=1; i<=nlstate;i++)          /*lli=log(out[s1][s2]); */ /* Original formula */
     for(j=1; j<=nlstate;j++)        } /* End of if */
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);        ipmx +=1;
   fprintf(ficresvij,"\n");        sw += weight[i];
         ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   xp=vector(1,npar);        /*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]); */
   dnewm=matrix(1,nlstate,1,npar);        if(globpr){
   doldm=matrix(1,nlstate,1,nlstate);          fprintf(ficresilk,"%9d %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
     %11.6f %11.6f %11.6f ", \
   if(estepm < stepm){                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
     printf ("Problem %d lower than %d\n",estepm, stepm);                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
   }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
   else  hstepm=estepm;              llt +=ll[k]*gipmx/gsw;
   /* For example we decided to compute the life expectancy with the smallest unit */            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
   /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm.          }
      nhstepm is the number of hstepm from age to agelim          fprintf(ficresilk," %10.6f\n", -llt);
      nstepm is the number of stepm from age to agelin.        }
      Look at hpijx to understand the reason of that which relies in memory size      } /* end of wave */
      and note for a fixed period like k years */    } /* end of individual */
   /* We decided (b) to get a life expectancy respecting the most precise curvature of the    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      survival function given by stepm (the optimization length). Unfortunately it    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
      means that if the survival funtion is printed only each two years of age and if    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
      you sum them up and add 1 year (area under the trapezoids) you won't get the same    if(globpr==0){ /* First time we count the contributions and weights */
      results. So we changed our mind and took the option of the best precision.      gipmx=ipmx;
   */      gsw=sw;
   hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */    }
   agelim = AGESUP;    return -l;
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  }
     nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */  
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */  
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  /*************** function likelione ***********/
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
     gp=matrix(0,nhstepm,1,nlstate);  {
     gm=matrix(0,nhstepm,1,nlstate);    /* This routine should help understanding what is done with 
        the selection of individuals/waves and
     for(theta=1; theta <=npar; theta++){       to check the exact contribution to the likelihood.
       for(i=1; i<=npar; i++){ /* Computes gradient */       Plotting could be done.
         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);    if(*globpri !=0){ /* Just counts and sums, no printings */
       strcpy(fileresilk,"ilk"); 
       if (popbased==1) {      strcat(fileresilk,fileres);
         for(i=1; i<=nlstate;i++)      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
           prlim[i][i]=probs[(int)age][i][ij];        printf("Problem with resultfile: %s\n", fileresilk);
       }        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
        }
       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(h=0; h<=nhstepm; h++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      for(k=1; k<=nlstate; k++) 
         }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       }      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
        }
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    *fretone=(*funcone)(p);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);      if(*globpri !=0){
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      fclose(ficresilk);
        fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
       if (popbased==1) {      fflush(fichtm); 
         for(i=1; i<=nlstate;i++)    } 
           prlim[i][i]=probs[(int)age][i][ij];    return;
       }  }
   
       for(j=1; j<= nlstate; j++){  
         for(h=0; h<=nhstepm; h++){  /*********** Maximum Likelihood Estimation ***************/
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
         }  {
       }    int i,j, iter;
     double **xi;
       for(j=1; j<= nlstate; j++)    double fret;
         for(h=0; h<=nhstepm; h++){    double fretone; /* Only one call to likelihood */
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];    /*  char filerespow[FILENAMELENGTH];*/
         }    xi=matrix(1,npar,1,npar);
     } /* End theta */    for (i=1;i<=npar;i++)
       for (j=1;j<=npar;j++)
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        xi[i][j]=(i==j ? 1.0 : 0.0);
     printf("Powell\n");  fprintf(ficlog,"Powell\n");
     for(h=0; h<=nhstepm; h++)    strcpy(filerespow,"pow"); 
       for(j=1; j<=nlstate;j++)    strcat(filerespow,fileres);
         for(theta=1; theta <=npar; theta++)    if((ficrespow=fopen(filerespow,"w"))==NULL) {
           trgradg[h][j][theta]=gradg[h][theta][j];      printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */    }
     for(i=1;i<=nlstate;i++)    fprintf(ficrespow,"# Powell\n# iter -2*LL");
       for(j=1;j<=nlstate;j++)    for (i=1;i<=nlstate;i++)
         vareij[i][j][(int)age] =0.;      for(j=1;j<=nlstate+ndeath;j++)
         if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
     for(h=0;h<=nhstepm;h++){    fprintf(ficrespow,"\n");
       for(k=0;k<=nhstepm;k++){  
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);    powell(p,xi,npar,ftol,&iter,&fret,func);
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);  
         for(i=1;i<=nlstate;i++)    free_matrix(xi,1,npar,1,npar);
           for(j=1;j<=nlstate;j++)    fclose(ficrespow);
             vareij[i][j][(int)age] += doldm[i][j]*hf*hf;    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
       }    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
     }    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
   
     fprintf(ficresvij,"%.0f ",age );  }
     for(i=1; i<=nlstate;i++)  
       for(j=1; j<=nlstate;j++){  /**** Computes Hessian and covariance matrix ***/
         fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
       }  {
     fprintf(ficresvij,"\n");    double  **a,**y,*x,pd;
     free_matrix(gp,0,nhstepm,1,nlstate);    double **hess;
     free_matrix(gm,0,nhstepm,1,nlstate);    int i, j,jk;
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);    int *indx;
     free_ma3x(trgradg,0,nhstepm,1,nlstate,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);
   } /* End age */    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
      void lubksb(double **a, int npar, int *indx, double b[]) ;
   free_vector(xp,1,npar);    void ludcmp(double **a, int npar, int *indx, double *d) ;
   free_matrix(doldm,1,nlstate,1,npar);    double gompertz(double p[]);
   free_matrix(dnewm,1,nlstate,1,nlstate);    hess=matrix(1,npar,1,npar);
   
 }    printf("\nCalculation of the hessian matrix. Wait...\n");
     fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
 /************ Variance of prevlim ******************/    for (i=1;i<=npar;i++){
 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)      printf("%d",i);fflush(stdout);
 {      fprintf(ficlog,"%d",i);fflush(ficlog);
   /* Variance of prevalence limit */     
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   double **newm;      
   double **dnewm,**doldm;      /*  printf(" %f ",p[i]);
   int i, j, nhstepm, hstepm;          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
   int k, cptcode;    }
   double *xp;    
   double *gp, *gm;    for (i=1;i<=npar;i++) {
   double **gradg, **trgradg;      for (j=1;j<=npar;j++)  {
   double age,agelim;        if (j>i) { 
   int theta;          printf(".%d%d",i,j);fflush(stdout);
              fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
   fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n");          hess[i][j]=hessij(p,delti,i,j,func,npar);
   fprintf(ficresvpl,"# Age");          
   for(i=1; i<=nlstate;i++)          hess[j][i]=hess[i][j];    
       fprintf(ficresvpl," %1d-%1d",i,i);          /*printf(" %lf ",hess[i][j]);*/
   fprintf(ficresvpl,"\n");        }
       }
   xp=vector(1,npar);    }
   dnewm=matrix(1,nlstate,1,npar);    printf("\n");
   doldm=matrix(1,nlstate,1,nlstate);    fprintf(ficlog,"\n");
    
   hstepm=1*YEARM; /* Every year of age */    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
   agelim = AGESUP;    
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */    a=matrix(1,npar,1,npar);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    y=matrix(1,npar,1,npar);
     if (stepm >= YEARM) hstepm=1;    x=vector(1,npar);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    indx=ivector(1,npar);
     gradg=matrix(1,npar,1,nlstate);    for (i=1;i<=npar;i++)
     gp=vector(1,nlstate);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     gm=vector(1,nlstate);    ludcmp(a,npar,indx,&pd);
   
     for(theta=1; theta <=npar; theta++){    for (j=1;j<=npar;j++) {
       for(i=1; i<=npar; i++){ /* Computes gradient */      for (i=1;i<=npar;i++) x[i]=0;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      x[j]=1;
       }      lubksb(a,npar,indx,x);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (i=1;i<=npar;i++){ 
       for(i=1;i<=nlstate;i++)        matcov[i][j]=x[i];
         gp[i] = prlim[i][i];      }
        }
       for(i=1; i<=npar; i++) /* Computes gradient */  
         xp[i] = x[i] - (i==theta ?delti[theta]:0);    printf("\n#Hessian matrix#\n");
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);    fprintf(ficlog,"\n#Hessian matrix#\n");
       for(i=1;i<=nlstate;i++)    for (i=1;i<=npar;i++) { 
         gm[i] = prlim[i][i];      for (j=1;j<=npar;j++) { 
         printf("%.3e ",hess[i][j]);
       for(i=1;i<=nlstate;i++)        fprintf(ficlog,"%.3e ",hess[i][j]);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];      }
     } /* End theta */      printf("\n");
       fprintf(ficlog,"\n");
     trgradg =matrix(1,nlstate,1,npar);    }
   
     for(j=1; j<=nlstate;j++)    /* Recompute Inverse */
       for(theta=1; theta <=npar; theta++)    for (i=1;i<=npar;i++)
         trgradg[j][theta]=gradg[theta][j];      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     ludcmp(a,npar,indx,&pd);
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] =0.;    /*  printf("\n#Hessian matrix recomputed#\n");
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);  
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);    for (j=1;j<=npar;j++) {
     for(i=1;i<=nlstate;i++)      for (i=1;i<=npar;i++) x[i]=0;
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */      x[j]=1;
       lubksb(a,npar,indx,x);
     fprintf(ficresvpl,"%.0f ",age );      for (i=1;i<=npar;i++){ 
     for(i=1; i<=nlstate;i++)        y[i][j]=x[i];
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));        printf("%.3e ",y[i][j]);
     fprintf(ficresvpl,"\n");        fprintf(ficlog,"%.3e ",y[i][j]);
     free_vector(gp,1,nlstate);      }
     free_vector(gm,1,nlstate);      printf("\n");
     free_matrix(gradg,1,npar,1,nlstate);      fprintf(ficlog,"\n");
     free_matrix(trgradg,1,nlstate,1,npar);    }
   } /* End age */    */
   
   free_vector(xp,1,npar);    free_matrix(a,1,npar,1,npar);
   free_matrix(doldm,1,nlstate,1,npar);    free_matrix(y,1,npar,1,npar);
   free_matrix(dnewm,1,nlstate,1,nlstate);    free_vector(x,1,npar);
     free_ivector(indx,1,npar);
 }    free_matrix(hess,1,npar,1,npar);
   
 /************ Variance of one-step probabilities  ******************/  
 void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax)  }
 {  
   int i, j, i1, k1, j1, z1;  /*************** hessian matrix ****************/
   int k=0, cptcode;  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
   double **dnewm,**doldm;  {
   double *xp;    int i;
   double *gp, *gm;    int l=1, lmax=20;
   double **gradg, **trgradg;    double k1,k2;
   double age,agelim, cov[NCOVMAX];    double p2[MAXPARM+1]; /* identical to x */
   int theta;    double res;
   char fileresprob[FILENAMELENGTH];    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
     double fx;
   strcpy(fileresprob,"prob");    int k=0,kmax=10;
   strcat(fileresprob,fileres);    double l1;
   if((ficresprob=fopen(fileresprob,"w"))==NULL) {  
     printf("Problem with resultfile: %s\n", fileresprob);    fx=func(x);
   }    for (i=1;i<=npar;i++) p2[i]=x[i];
   printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);    for(l=0 ; l <=lmax; l++){
        l1=pow(10,l);
 fprintf(ficresprob,"#One-step probabilities and standard deviation in parentheses\n");      delts=delt;
   fprintf(ficresprob,"# Age");      for(k=1 ; k <kmax; k=k+1){
   for(i=1; i<=nlstate;i++)        delt = delta*(l1*k);
     for(j=1; j<=(nlstate+ndeath);j++)        p2[theta]=x[theta] +delt;
       fprintf(ficresprob," p%1d-%1d (SE)",i,j);        k1=func(p2)-fx;
         p2[theta]=x[theta]-delt;
         k2=func(p2)-fx;
   fprintf(ficresprob,"\n");        /*res= (k1-2.0*fx+k2)/delt/delt; */
         res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
         
   xp=vector(1,npar);  #ifdef DEBUGHESS
   dnewm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        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);
   doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath));        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
    #endif
   cov[1]=1;        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
   j=cptcoveff;        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
   if (cptcovn<1) {j=1;ncodemax[1]=1;}          k=kmax;
   j1=0;        }
   for(k1=1; k1<=1;k1++){        else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
     for(i1=1; i1<=ncodemax[k1];i1++){          k=kmax; l=lmax*10.;
     j1++;        }
         else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
     if  (cptcovn>0) {          delts=delt;
       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#");    }
     }    delti[theta]=delts;
        return res; 
       for (age=bage; age<=fage; age ++){    
         cov[2]=age;  }
         for (k=1; k<=cptcovn;k++) {  
           cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
            {
         }    int i;
         for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];    int l=1, l1, lmax=20;
         for (k=1; k<=cptcovprod;k++)    double k1,k2,k3,k4,res,fx;
           cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];    double p2[MAXPARM+1];
            int k;
         gradg=matrix(1,npar,1,9);  
         trgradg=matrix(1,9,1,npar);    fx=func(x);
         gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath));    for (k=1; k<=2; k++) {
         gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath));      for (i=1;i<=npar;i++) p2[i]=x[i];
          p2[thetai]=x[thetai]+delti[thetai]/k;
         for(theta=1; theta <=npar; theta++){      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
           for(i=1; i<=npar; i++)      k1=func(p2)-fx;
             xp[i] = x[i] + (i==theta ?delti[theta]:0);    
                p2[thetai]=x[thetai]+delti[thetai]/k;
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                k2=func(p2)-fx;
           k=0;    
           for(i=1; i<= (nlstate+ndeath); i++){      p2[thetai]=x[thetai]-delti[thetai]/k;
             for(j=1; j<=(nlstate+ndeath);j++){      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
               k=k+1;      k3=func(p2)-fx;
               gp[k]=pmmij[i][j];    
             }      p2[thetai]=x[thetai]-delti[thetai]/k;
           }      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                k4=func(p2)-fx;
           for(i=1; i<=npar; i++)      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
             xp[i] = x[i] - (i==theta ?delti[theta]:0);  #ifdef DEBUG
          printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
           pmij(pmmij,cov,ncovmodel,xp,nlstate);      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);
           k=0;  #endif
           for(i=1; i<=(nlstate+ndeath); i++){    }
             for(j=1; j<=(nlstate+ndeath);j++){    return res;
               k=k+1;  }
               gm[k]=pmmij[i][j];  
             }  /************** Inverse of matrix **************/
           }  void ludcmp(double **a, int n, int *indx, double *d) 
        { 
           for(i=1; i<= (nlstate+ndeath)*(nlstate+ndeath); i++)    int i,imax,j,k; 
             gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta];      double big,dum,sum,temp; 
         }    double *vv; 
    
         for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++)    vv=vector(1,n); 
           for(theta=1; theta <=npar; theta++)    *d=1.0; 
             trgradg[j][theta]=gradg[theta][j];    for (i=1;i<=n;i++) { 
              big=0.0; 
         matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov);      for (j=1;j<=n;j++) 
         matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg);        if ((temp=fabs(a[i][j])) > big) big=temp; 
              if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
         pmij(pmmij,cov,ncovmodel,x,nlstate);      vv[i]=1.0/big; 
            } 
         k=0;    for (j=1;j<=n;j++) { 
         for(i=1; i<=(nlstate+ndeath); i++){      for (i=1;i<j;i++) { 
           for(j=1; j<=(nlstate+ndeath);j++){        sum=a[i][j]; 
             k=k+1;        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
             gm[k]=pmmij[i][j];        a[i][j]=sum; 
           }      } 
         }      big=0.0; 
            for (i=j;i<=n;i++) { 
      /*printf("\n%d ",(int)age);        sum=a[i][j]; 
      for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){        for (k=1;k<j;k++) 
        printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));          sum -= a[i][k]*a[k][j]; 
      }*/        a[i][j]=sum; 
         if ( (dum=vv[i]*fabs(sum)) >= big) { 
         fprintf(ficresprob,"\n%d ",(int)age);          big=dum; 
           imax=i; 
         for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++)        } 
           fprintf(ficresprob,"%.3e (%.3e) ",gm[i],sqrt(doldm[i][i]));      } 
        if (j != imax) { 
       }        for (k=1;k<=n;k++) { 
     }          dum=a[imax][k]; 
     free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));          a[imax][k]=a[j][k]; 
     free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));          a[j][k]=dum; 
     free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        } 
     free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);        *d = -(*d); 
   }        vv[imax]=vv[j]; 
   free_vector(xp,1,npar);      } 
   fclose(ficresprob);      indx[j]=imax; 
        if (a[j][j] == 0.0) a[j][j]=TINY; 
 }      if (j != n) { 
         dum=1.0/(a[j][j]); 
 /******************* Printing html file ***********/        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
 void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \      } 
                   int lastpass, int stepm, int weightopt, char model[],\    } 
                   int imx,int jmin, int jmax, double jmeanint,char optionfile[], \    free_vector(vv,1,n);  /* Doesn't work */
                   char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\  ;
                   char version[], int popforecast, int estepm ,/* \ */  } 
                   double jprev1, double mprev1,double anprev1, \  
                   double jprev2, double mprev2,double anprev2){  void lubksb(double **a, int n, int *indx, double b[]) 
   int jj1, k1, i1, cpt;  { 
   FILE *fichtm;    int i,ii=0,ip,j; 
   /*char optionfilehtm[FILENAMELENGTH];*/    double sum; 
    
   strcpy(optionfilehtm,optionfile);    for (i=1;i<=n;i++) { 
   strcat(optionfilehtm,".htm");      ip=indx[i]; 
   if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {      sum=b[ip]; 
     printf("Problem with %s \n",optionfilehtm), exit(0);      b[ip]=b[i]; 
   }      if (ii) 
         for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
   fprintf(fichtm,"<body> <font size=\"2\">%s </font> <hr size=\"2\" color=\"#EC5E5E\"> \n      else if (sum) ii=i; 
 Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n      b[i]=sum; 
 \n    } 
 Total number of observations=%d <br>\n    for (i=n;i>=1;i--) { 
 Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n      sum=b[i]; 
 <hr  size=\"2\" color=\"#EC5E5E\">      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
  <ul><li>Parameter files<br>\n      b[i]=sum/a[i][i]; 
  - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n    } 
  - Gnuplot file name: <a href=\"%s\">%s</a><br></ul>\n",version,title,datafile,firstpass,lastpass,stepm, weightopt,model,imx,jmin,jmax,jmean,fileres,fileres,optionfilegnuplot,optionfilegnuplot);  } 
   
    fprintf(fichtm,"<ul><li>Result files (first order: no variance)<br>\n  void pstamp(FILE *fichier)
  - 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  {
  - Estimated transition probabilities over %d (stepm) months: <a href=\"pij%s\">pij%s</a><br>\n    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
  - 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):  
    <a href=\"e%s\">e%s</a> <br>\n</li>", \  /************ Frequencies ********************/
   jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,fileres,fileres,stepm,fileres,fileres,fileres,fileres,estepm,fileres,fileres);  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[])
   {  /* Some frequencies */
  fprintf(fichtm,"\n<li> Result files (second order: variances)<br>\n    
  - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n    int i, m, jk, k1,i1, j1, bool, z1,j;
  - Variance of one-step probabilities: <a href=\"prob%s\">prob%s</a> <br>\n    int first;
  - Variances and covariances of life expectancies by age and initial health status (estepm=%d months): <a href=\"v%s\">v%s</a><br>\n    double ***freq; /* Frequencies */
  - Health expectancies with their variances (no covariance): <a href=\"t%s\">t%s</a> <br>\n    double *pp, **prop;
  - Standard deviation of stable prevalences: <a href=\"vpl%s\">vpl%s</a> <br>\n",rfileres,rfileres,fileres,fileres, estepm, fileres,fileres,fileres,fileres,fileres,fileres);    double pos,posprop, k2, dateintsum=0,k2cpt=0;
     char fileresp[FILENAMELENGTH];
  if(popforecast==1) fprintf(fichtm,"\n    
  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n    pp=vector(1,nlstate);
  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n    prop=matrix(1,nlstate,iagemin,iagemax+3);
         <br>",fileres,fileres,fileres,fileres);    strcpy(fileresp,"p");
  else    strcat(fileresp,fileres);
    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);    if((ficresp=fopen(fileresp,"w"))==NULL) {
 fprintf(fichtm," <li>Graphs</li><p>");      printf("Problem with prevalence resultfile: %s\n", fileresp);
       fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
  m=cptcoveff;      exit(0);
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    }
     freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
  jj1=0;    j1=0;
  for(k1=1; k1<=m;k1++){    
    for(i1=1; i1<=ncodemax[k1];i1++){    j=cptcoveff;
        jj1++;    if (cptcovn<1) {j=1;ncodemax[1]=1;}
        if (cptcovn > 0) {  
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");    first=1;
          for (cpt=1; cpt<=cptcoveff;cpt++)  
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);    for(k1=1; k1<=j;k1++){
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");      for(i1=1; i1<=ncodemax[k1];i1++){
        }        j1++;
        /* Pij */        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
        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>          scanf("%d", i);*/
 <img src=\"pe%s%d1.png\">",strtok(optionfile, "."),jj1,stepm,strtok(optionfile, "."),jj1);            for (i=-5; i<=nlstate+ndeath; i++)  
        /* Quasi-incidences */          for (jk=-5; jk<=nlstate+ndeath; jk++)  
        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>            for(m=iagemin; m <= iagemax+3; m++)
 <img src=\"pe%s%d2.png\">",strtok(optionfile, "."),jj1,stepm,strtok(optionfile, "."),jj1);                  freq[i][jk][m]=0;
        /* Stable prevalence in each health state */  
        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(m=iagemin; m <= iagemax+3; m++)
 <img src=\"p%s%d%d.png\">",strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);          prop[i][m]=0;
        }        
     for(cpt=1; cpt<=nlstate;cpt++) {        dateintsum=0;
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident        k2cpt=0;
 interval) in state (%d): v%s%d%d.png <br>        for (i=1; i<=imx; i++) {
 <img src=\"v%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);            bool=1;
      }          if  (cptcovn>0) {
      for(cpt=1; cpt<=nlstate;cpt++) {            for (z1=1; z1<=cptcoveff; z1++) 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.png <br>              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
 <img src=\"exp%s%d%d.png\">",cpt,strtok(optionfile, "."),cpt,jj1,strtok(optionfile, "."),cpt,jj1);                bool=0;
      }          }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and          if (bool==1){
 health expectancies in states (1) and (2): e%s%d.png<br>            for(m=firstpass; m<=lastpass; m++){
 <img src=\"e%s%d.png\">",strtok(optionfile, "."),jj1,strtok(optionfile, "."),jj1);              k2=anint[m][i]+(mint[m][i]/12.);
 fprintf(fichtm,"\n</body>");              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
    }                if(agev[m][i]==0) agev[m][i]=iagemax+1;
    }                if(agev[m][i]==1) agev[m][i]=iagemax+2;
 fclose(fichtm);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
 }                if (m<lastpass) {
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
 /******************* Gnuplot file **************/                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
 void printinggnuplot(char fileres[],char optionfilefiname[],char optionfile[],char optionfilegnuplot[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){                }
                 
   int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
   int ng;                  dateintsum=dateintsum+k2;
   strcpy(optionfilegnuplot,optionfilefiname);                  k2cpt++;
   strcat(optionfilegnuplot,".gp.txt");                }
   if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {                /*}*/
     printf("Problem with file %s",optionfilegnuplot);            }
   }          }
         }
 #ifdef windows         
     fprintf(ficgp,"cd \"%s\" \n",pathc);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
 #endif        pstamp(ficresp);
 m=pow(2,cptcoveff);        if  (cptcovn>0) {
            fprintf(ficresp, "\n#********** Variable "); 
  /* 1eme*/          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   for (cpt=1; cpt<= nlstate ; cpt ++) {          fprintf(ficresp, "**********\n#");
    for (k1=1; k1<= m ; k1 ++) {        }
         for(i=1; i<=nlstate;i++) 
 #ifdef windows          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
      fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);        fprintf(ficresp, "\n");
      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);        
 #endif        for(i=iagemin; i <= iagemax+3; i++){
 #ifdef unix          if(i==iagemax+3){
 fprintf(ficgp,"\nset out \"v%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);            fprintf(ficlog,"Total");
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",ageminpar,fage,fileres);          }else{
 #endif            if(first==1){
               first=0;
 for (i=1; i<= nlstate ; i ++) {              printf("See log file for details...\n");
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            }
   else fprintf(ficgp," \%%*lf (\%%*lf)");            fprintf(ficlog,"Age %d", i);
 }          }
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);          for(jk=1; jk <=nlstate ; jk++){
     for (i=1; i<= nlstate ; i ++) {            for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");              pp[jk] += freq[jk][m][i]; 
   else fprintf(ficgp," \%%*lf (\%%*lf)");          }
 }          for(jk=1; jk <=nlstate ; jk++){
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);            for(m=-1, pos=0; m <=0 ; m++)
      for (i=1; i<= nlstate ; i ++) {              pos += freq[jk][m][i];
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");            if(pp[jk]>=1.e-10){
   else fprintf(ficgp," \%%*lf (\%%*lf)");              if(first==1){
 }                  printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));              }
 #ifdef unix              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
 fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\n");            }else{
 #endif              if(first==1)
    }                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   }              fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
   /*2 eme*/            }
           }
   for (k1=1; k1<= m ; k1 ++) {  
     fprintf(ficgp,"\nset out \"e%s%d.png\" \n",strtok(optionfile, "."),k1);          for(jk=1; jk <=nlstate ; jk++){
     fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);            for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
                  pp[jk] += freq[jk][m][i];
     for (i=1; i<= nlstate+1 ; i ++) {          }       
       k=2*i;          for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);            pos += pp[jk];
       for (j=1; j<= nlstate+1 ; j ++) {            posprop += prop[jk][i];
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          }
   else fprintf(ficgp," \%%*lf (\%%*lf)");          for(jk=1; jk <=nlstate ; jk++){
 }              if(pos>=1.e-5){
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");              if(first==1)
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);                printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);              fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
       for (j=1; j<= nlstate+1 ; j ++) {            }else{
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");              if(first==1)
         else fprintf(ficgp," \%%*lf (\%%*lf)");                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
 }                fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficgp,"\" t\"\" w l 0,");            }
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            if( i <= iagemax){
       for (j=1; j<= nlstate+1 ; j ++) {              if(pos>=1.e-5){
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
   else fprintf(ficgp," \%%*lf (\%%*lf)");                /*probs[i][jk][j1]= pp[jk]/pos;*/
 }                  /*printf("\ni=%d jk=%d j1=%d %.5f %.0f %.0f %f",i,jk,j1,pp[jk]/pos, pp[jk],pos,probs[i][jk][j1]);*/
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");              }
       else fprintf(ficgp,"\" t\"\" w l 0,");              else
     }                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
   }            }
            }
   /*3eme*/          
           for(jk=-1; jk <=nlstate+ndeath; jk++)
   for (k1=1; k1<= m ; k1 ++) {            for(m=-1; m <=nlstate+ndeath; m++)
     for (cpt=1; cpt<= nlstate ; cpt ++) {              if(freq[jk][m][i] !=0 ) {
       k=2+nlstate*(2*cpt-2);              if(first==1)
       fprintf(ficgp,"\nset out \"exp%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);                printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
       fprintf(ficgp,"set ter png small\nset size 0.65,0.65\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,fileres,k1-1,k1-1,k,cpt);                fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
       /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);              }
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");          if(i <= iagemax)
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);            fprintf(ficresp,"\n");
 fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);          if(first==1)
  for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");            printf("Others in log...\n");
 fprintf(ficgp,"\" t \"e%d1\" w l",cpt);          fprintf(ficlog,"\n");
         }
 */      }
       for (i=1; i< nlstate ; i ++) {    }
         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);    dateintmean=dateintsum/k2cpt; 
    
       }    fclose(ficresp);
     }    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   }    free_vector(pp,1,nlstate);
      free_matrix(prop,1,nlstate,iagemin, iagemax+3);
   /* CV preval stat */    /* End of Freq */
     for (k1=1; k1<= m ; k1 ++) {  }
     for (cpt=1; cpt<nlstate ; cpt ++) {  
       k=3;  /************ Prevalence ********************/
       fprintf(ficgp,"\nset out \"p%s%d%d.png\" \n",strtok(optionfile, "."),cpt,k1);  void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
       fprintf(ficgp,"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/($%d",ageminpar,agemaxpar,fileres,k1,k+cpt+1,k+1);  {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
       for (i=1; i< nlstate ; i ++)       in each health status at the date of interview (if between dateprev1 and dateprev2).
         fprintf(ficgp,"+$%d",k+i+1);       We still use firstpass and lastpass as another selection.
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    */
         
       l=3+(nlstate+ndeath)*cpt;    int i, m, jk, k1, i1, j1, bool, z1,j;
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    double ***freq; /* Frequencies */
       for (i=1; i< nlstate ; i ++) {    double *pp, **prop;
         l=3+(nlstate+ndeath)*cpt;    double pos,posprop; 
         fprintf(ficgp,"+$%d",l+i+1);    double  y2; /* in fractional years */
       }    int iagemin, iagemax;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);    
     }    iagemin= (int) agemin;
   }      iagemax= (int) agemax;
      /*pp=vector(1,nlstate);*/
   /* proba elementaires */    prop=matrix(1,nlstate,iagemin,iagemax+3); 
    for(i=1,jk=1; i <=nlstate; i++){    /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     for(k=1; k <=(nlstate+ndeath); k++){    j1=0;
       if (k != i) {    
         for(j=1; j <=ncovmodel; j++){    j=cptcoveff;
            if (cptcovn<1) {j=1;ncodemax[1]=1;}
           fprintf(ficgp,"p%d=%f ",jk,p[jk]);    
           jk++;    for(k1=1; k1<=j;k1++){
           fprintf(ficgp,"\n");      for(i1=1; i1<=ncodemax[k1];i1++){
         }        j1++;
       }        
     }        for (i=1; i<=nlstate; i++)  
    }          for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0.0;
    for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/       
      for(jk=1; jk <=m; jk++) {        for (i=1; i<=imx; i++) { /* Each individual */
        fprintf(ficgp,"\nset out \"pe%s%d%d.png\" \n",strtok(optionfile, "."),jk,ng);          bool=1;
        if (ng==2)          if  (cptcovn>0) {
          fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");            for (z1=1; z1<=cptcoveff; z1++) 
        else              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
          fprintf(ficgp,"\nset title \"Probability\"\n");                bool=0;
        fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);          } 
        i=1;          if (bool==1) { 
        for(k2=1; k2<=nlstate; k2++) {            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
          k3=i;              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
          for(k=1; k<=(nlstate+ndeath); k++) {              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
            if (k != k2){                if(agev[m][i]==0) agev[m][i]=iagemax+1;
              if(ng==2)                if(agev[m][i]==1) agev[m][i]=iagemax+2;
                fprintf(ficgp," %f*exp(p%d+p%d*x",stepm/YEARM,i,i+1);                if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
              else                if (s[m][i]>0 && s[m][i]<=nlstate) { 
                fprintf(ficgp," exp(p%d+p%d*x",i,i+1);                  /*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]]);*/
              ij=1;                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
              for(j=3; j <=ncovmodel; j++) {                  prop[s[m][i]][iagemax+3] += weight[i]; 
                if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {                } 
                  fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);              }
                  ij++;            } /* end selection of waves */
                }          }
                else        }
                  fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);        for(i=iagemin; i <= iagemax+3; i++){  
              }          
              fprintf(ficgp,")/(1");          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
                          posprop += prop[jk][i]; 
              for(k1=1; k1 <=nlstate; k1++){            } 
                fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);  
                ij=1;          for(jk=1; jk <=nlstate ; jk++){     
                for(j=3; j <=ncovmodel; j++){            if( i <=  iagemax){ 
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {              if(posprop>=1.e-5){ 
                    fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);                probs[i][jk][j1]= prop[jk][i]/posprop;
                    ij++;              } else
                  }                printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\n",jk,i,j1,probs[i][jk][j1]);
                  else            } 
                    fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);          }/* end jk */ 
                }        }/* end i */ 
                fprintf(ficgp,")");      } /* end i1 */
              }    } /* end k1 */
              fprintf(ficgp,") t \"p%d%d\" ", k2,k);    
              if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
              i=i+ncovmodel;    /*free_vector(pp,1,nlstate);*/
            }    free_matrix(prop,1,nlstate, iagemin,iagemax+3);
          }  }  /* End of prevalence */
        }  
      }  /************* Waves Concatenation ***************/
    }  
    fclose(ficgp);  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)
 }  /* end gnuplot */  {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        Death is a valid wave (if date is known).
 /*************** Moving average **************/       mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
 void movingaverage(double agedeb, double fage,double ageminpar, double ***mobaverage){       dh[m][i] or dh[mw[mi][i]][i] is the delay between two effective waves m=mw[mi][i]
        and mw[mi+1][i]. dh depends on stepm.
   int i, cpt, cptcod;       */
     for (agedeb=ageminpar; agedeb<=fage; agedeb++)  
       for (i=1; i<=nlstate;i++)    int i, mi, m;
         for (cptcod=1;cptcod<=ncodemax[cptcov];cptcod++)    /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
           mobaverage[(int)agedeb][i][cptcod]=0.;       double sum=0., jmean=0.;*/
        int first;
     for (agedeb=ageminpar+4; agedeb<=fage; agedeb++){    int j, k=0,jk, ju, jl;
       for (i=1; i<=nlstate;i++){    double sum=0.;
         for (cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){    first=0;
           for (cpt=0;cpt<=4;cpt++){    jmin=1e+5;
             mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]+probs[(int)agedeb-cpt][i][cptcod];    jmax=-1;
           }    jmean=0.;
           mobaverage[(int)agedeb-2][i][cptcod]=mobaverage[(int)agedeb-2][i][cptcod]/5;    for(i=1; i<=imx; i++){
         }      mi=0;
       }      m=firstpass;
     }      while(s[m][i] <= nlstate){
            if(s[m][i]>=1 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5)
 }          mw[++mi][i]=m;
         if(m >=lastpass)
           break;
 /************** Forecasting ******************/        else
 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){          m++;
        }/* end while */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;      if (s[m][i] > nlstate){
   int *popage;        mi++;     /* Death is another wave */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;        /* if(mi==0)  never been interviewed correctly before death */
   double *popeffectif,*popcount;           /* Only death is a correct wave */
   double ***p3mat;        mw[mi][i]=m;
   char fileresf[FILENAMELENGTH];      }
   
  agelim=AGESUP;      wav[i]=mi;
 calagedate=(anproj1+mproj1/12.+jproj1/365.-dateintmean)*YEARM;      if(mi==0){
         nbwarn++;
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);        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);
            first=1;
   strcpy(fileresf,"f");        }
   strcat(fileresf,fileres);        if(first==1){
   if((ficresf=fopen(fileresf,"w"))==NULL) {          fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
     printf("Problem with forecast resultfile: %s\n", fileresf);        }
   }      } /* end mi==0 */
   printf("Computing forecasting: result on file '%s' \n", fileresf);    } /* End individuals */
   
   if (cptcoveff==0) ncodemax[cptcoveff]=1;    for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
   if (mobilav==1) {        if (stepm <=0)
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);          dh[mi][i]=1;
     movingaverage(agedeb, fage, ageminpar, mobaverage);        else{
   }          if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
             if (agedc[i] < 2*AGESUP) {
   stepsize=(int) (stepm+YEARM-1)/YEARM;              j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
   if (stepm<=12) stepsize=1;              if(j==0) j=1;  /* Survives at least one month after exam */
                else if(j<0){
   agelim=AGESUP;                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]);
   hstepm=1;                j=1; /* Temporary Dangerous patch */
   hstepm=hstepm/stepm;                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);
   yp1=modf(dateintmean,&yp);                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]);
   anprojmean=yp;                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);
   yp2=modf((yp1*12),&yp);              }
   mprojmean=yp;              k=k+1;
   yp1=modf((yp2*30.5),&yp);              if (j >= jmax){
   jprojmean=yp;                jmax=j;
   if(jprojmean==0) jprojmean=1;                ijmax=i;
   if(mprojmean==0) jprojmean=1;              }
                if (j <= jmin){
   fprintf(ficresf,"# Estimated date of observed prevalence: %.lf/%.lf/%.lf ",jprojmean,mprojmean,anprojmean);                jmin=j;
                  ijmin=i;
   for(cptcov=1;cptcov<=i2;cptcov++){              }
     for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){              sum=sum+j;
       k=k+1;              /*if (j<0) printf("j=%d num=%d \n",j,i);*/
       fprintf(ficresf,"\n#******");              /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
       for(j=1;j<=cptcoveff;j++) {            }
         fprintf(ficresf," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          }
       }          else{
       fprintf(ficresf,"******\n");            j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
       fprintf(ficresf,"# StartingAge FinalAge");  /*        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]); */
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficresf," P.%d",j);  
                  k=k+1;
                  if (j >= jmax) {
       for (cpt=0; cpt<=(anproj2-anproj1);cpt++) {              jmax=j;
         fprintf(ficresf,"\n");              ijmax=i;
         fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+cpt);              }
             else if (j <= jmin){
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){              jmin=j;
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);              ijmin=i;
           nhstepm = nhstepm/hstepm;            }
                      /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            /*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]);*/
           oldm=oldms;savm=savms;            if(j<0){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                nberr++;
                      printf("Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
           for (h=0; h<=nhstepm; h++){              fprintf(ficlog,"Error! Negative delay (%d) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
             if (h==(int) (calagedate+YEARM*cpt)) {            }
               fprintf(ficresf,"\n %.f %.f ",anproj1+cpt,agedeb+h*hstepm/YEARM*stepm);            sum=sum+j;
             }          }
             for(j=1; j<=nlstate+ndeath;j++) {          jk= j/stepm;
               kk1=0.;kk2=0;          jl= j -jk*stepm;
               for(i=1; i<=nlstate;i++) {                        ju= j -(jk+1)*stepm;
                 if (mobilav==1)          if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];            if(jl==0){
                 else {              dh[mi][i]=jk;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];              bh[mi][i]=0;
                 }            }else{ /* We want a negative bias in order to only have interpolation ie
                                    * to avoid the price of an extra matrix product in likelihood */
               }              dh[mi][i]=jk+1;
               if (h==(int)(calagedate+12*cpt)){              bh[mi][i]=ju;
                 fprintf(ficresf," %.3f", kk1);            }
                                  }else{
               }            if(jl <= -ju){
             }              dh[mi][i]=jk;
           }              bh[mi][i]=jl;       /* bias is positive if real duration
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                                   * is higher than the multiple of stepm and negative otherwise.
         }                                   */
       }            }
     }            else{
   }              dh[mi][i]=jk+1;
                      bh[mi][i]=ju;
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);            }
             if(dh[mi][i]==0){
   fclose(ficresf);              dh[mi][i]=1; /* At least one step */
 }              bh[mi][i]=ju; /* At least one step */
 /************** Forecasting ******************/              /*  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);*/
 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){            }
            } /* end if mle */
   int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;        }
   int *popage;      } /* end wave */
   double calagedate, agelim, kk1, kk2, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;    }
   double *popeffectif,*popcount;    jmean=sum/k;
   double ***p3mat,***tabpop,***tabpopprev;    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);
   char filerespop[FILENAMELENGTH];    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);
    }
   tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  /*********** Tricode ****************************/
   agelim=AGESUP;  void tricode(int *Tvar, int **nbcode, int imx)
   calagedate=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;  {
      /* Uses cptcovn+2*cptcovprod as the number of covariates */
   prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);    /*      Tvar[i]=atoi(stre); /* find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 */
    
      int Ndum[20],ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
   strcpy(filerespop,"pop");    int modmaxcovj=0; /* Modality max of covariates j */
   strcat(filerespop,fileres);    cptcoveff=0; 
   if((ficrespop=fopen(filerespop,"w"))==NULL) {   
     printf("Problem with forecast resultfile: %s\n", filerespop);    for (k=0; k<maxncov; k++) Ndum[k]=0;
   }    for (k=1; k<=7; k++) ncodemax[k]=0; /* Horrible constant again */
   printf("Computing forecasting: result on file '%s' \n", filerespop);  
     for (j=1; j<=(cptcovn+2*cptcovprod); j++) { /* For each covariate j */
   if (cptcoveff==0) ncodemax[cptcoveff]=1;      for (i=1; i<=imx; i++) { /*reads the data file to get the maximum value of the 
                                  modality of this covariate Vj*/ 
   if (mobilav==1) {        ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Finds for covariate j, n=Tvar[j] of Vn . ij is the
     mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);                                        modality of the nth covariate of individual i. */
     movingaverage(agedeb, fage, ageminpar, mobaverage);        Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
   }        /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         if (ij > modmaxcovj) modmaxcovj=ij; 
   stepsize=(int) (stepm+YEARM-1)/YEARM;        /* getting the maximum value of the modality of the covariate
   if (stepm<=12) stepsize=1;           (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
             female is 1, then modmaxcovj=1.*/
   agelim=AGESUP;      }
    
   hstepm=1;      for (i=0; i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*/
   hstepm=hstepm/stepm;        if( Ndum[i] != 0 )
            ncodemax[j]++; 
   if (popforecast==1) {        /* Number of modalities of the j th covariate. In fact
     if((ficpop=fopen(popfile,"r"))==NULL) {           ncodemax[j]=2 (dichotom. variables only) but it could be more for
       printf("Problem with population file : %s\n",popfile);exit(0);           historical reasons */
     }      } /* Ndum[-1] number of undefined modalities */
     popage=ivector(0,AGESUP);  
     popeffectif=vector(0,AGESUP);      /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
     popcount=vector(0,AGESUP);      ij=1; 
          for (i=1; i<=ncodemax[j]; i++) { /* i= 1 to 2 for dichotomous */
     i=1;          for (k=0; k<= maxncov; k++) { /* k=-1 ? NCOVMAX*/
     while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;          if (Ndum[k] != 0) { /* If at least one individual responded to this modality k */
                nbcode[Tvar[j]][ij]=k;  /* stores the modality in an array nbcode. 
     imx=i;                                       k is a modality. If we have model=V1+V1*sex 
     for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];                                       then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
   }            ij++;
           }
   for(cptcov=1;cptcov<=i2;cptcov++){          if (ij > ncodemax[j]) break; 
    for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){        }  
       k=k+1;      } 
       fprintf(ficrespop,"\n#******");    }  
       for(j=1;j<=cptcoveff;j++) {  
         fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);   for (k=0; k< maxncov; k++) Ndum[k]=0;
       }  
       fprintf(ficrespop,"******\n");   for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */
       fprintf(ficrespop,"# Age");     /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/
       for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);     ij=Tvar[i]; /* Tvar might be -1 if status was unknown */
       if (popforecast==1)  fprintf(ficrespop," [Population]");     Ndum[ij]++;
         }
       for (cpt=0; cpt<=0;cpt++) {  
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);     ij=1;
           for (i=1; i<= maxncov; i++) {
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     if((Ndum[i]!=0) && (i<=ncovcol)){
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);       Tvaraff[ij]=i; /*For printing */
           nhstepm = nhstepm/hstepm;       ij++;
               }
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);   }
           oldm=oldms;savm=savms;   ij--;
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);     cptcoveff=ij; /*Number of simple covariates*/
          }
           for (h=0; h<=nhstepm; h++){  
             if (h==(int) (calagedate+YEARM*cpt)) {  /*********** Health Expectancies ****************/
               fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);  
             }  void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
             for(j=1; j<=nlstate+ndeath;j++) {  
               kk1=0.;kk2=0;  {
               for(i=1; i<=nlstate;i++) {                  /* Health expectancies, no variances */
                 if (mobilav==1)    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2;
                   kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];    int nhstepma, nstepma; /* Decreasing with age */
                 else {    double age, agelim, hf;
                   kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];    double ***p3mat;
                 }    double eip;
               }  
               if (h==(int)(calagedate+12*cpt)){    pstamp(ficreseij);
                 tabpop[(int)(agedeb)][j][cptcod]=kk1;    fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
                   /*fprintf(ficrespop," %.3f", kk1);    fprintf(ficreseij,"# Age");
                     if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/    for(i=1; i<=nlstate;i++){
               }      for(j=1; j<=nlstate;j++){
             }        fprintf(ficreseij," e%1d%1d ",i,j);
             for(i=1; i<=nlstate;i++){      }
               kk1=0.;      fprintf(ficreseij," e%1d. ",i);
                 for(j=1; j<=nlstate;j++){    }
                   kk1= kk1+tabpop[(int)(agedeb)][j][cptcod];    fprintf(ficreseij,"\n");
                 }  
                   tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedate+12*cpt)*hstepm/YEARM*stepm-1)];    
             }    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
             if (h==(int)(calagedate+12*cpt)) for(j=1; j<=nlstate;j++)    }
               fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);    else  hstepm=estepm;   
           }    /* We compute the life expectancy from trapezoids spaced every estepm months
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);     * 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
       }     * we are calculating an estimate of the Life Expectancy assuming a linear 
       * progression in between and thus overestimating or underestimating according
   /******/     * to the curvature of the survival function. If, for the same date, we 
      * estimate the model with stepm=1 month, we can keep estepm to 24 months
       for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) {     * to compare the new estimate of Life expectancy with the same linear 
         fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);       * hypothesis. A more precise result, taking into account a more precise
         for (agedeb=(fage-((int)calagedate %12/12.)); agedeb>=(ageminpar-((int)calagedate %12)/12.); agedeb--){     * curvature will be obtained if estepm is as small as stepm. */
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm);  
           nhstepm = nhstepm/hstepm;    /* For example we decided to compute the life expectancy with the smallest unit */
              /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);       nhstepm is the number of hstepm from age to agelim 
           oldm=oldms;savm=savms;       nstepm is the number of stepm from age to agelin. 
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);         Look at hpijx to understand the reason of that which relies in memory size
           for (h=0; h<=nhstepm; h++){       and note for a fixed period like estepm months */
             if (h==(int) (calagedate+YEARM*cpt)) {    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
               fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);       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
             for(j=1; j<=nlstate+ndeath;j++) {       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
               kk1=0.;kk2=0;       results. So we changed our mind and took the option of the best precision.
               for(i=1; i<=nlstate;i++) {                  */
                 kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];        hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
               }  
               if (h==(int)(calagedate+12*cpt)) fprintf(ficresf," %15.2f", kk1);    agelim=AGESUP;
             }    /* If stepm=6 months */
           }      /* Computed by stepm unit matrices, product of hstepm matrices, stored
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);         in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
         }      
       }  /* nhstepm age range expressed in number of stepm */
    }    nstepm=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   }    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
      /* if (stepm >= YEARM) hstepm=1;*/
   if (mobilav==1) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   if (popforecast==1) {  
     free_ivector(popage,0,AGESUP);    for (age=bage; age<=fage; age ++){ 
     free_vector(popeffectif,0,AGESUP);      nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
     free_vector(popcount,0,AGESUP);      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   }      /* if (stepm >= YEARM) hstepm=1;*/
   free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);      nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);  
   fclose(ficrespop);      /* If stepm=6 months */
 }      /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
 /***********************************************/      
 /**************** Main Program *****************/      hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
 /***********************************************/      
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
 int main(int argc, char *argv[])      
 {      printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
   int i,j, k, n=MAXN,iter,m,size,cptcode, cptcod;      
   double agedeb, agefin,hf;      /* Computing expectancies */
   double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;      for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
   double fret;          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
   double **xi,tmp,delta;            eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
   double dum; /* Dummy variable */            /* 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]);*/
   double ***p3mat;  
   int *indx;          }
   char line[MAXLINE], linepar[MAXLINE];  
   char title[MAXLINE];      fprintf(ficreseij,"%3.0f",age );
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];      for(i=1; i<=nlstate;i++){
   char optionfilext[10], optionfilefiname[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilegnuplot[FILENAMELENGTH], plotcmd[FILENAMELENGTH];        eip=0;
          for(j=1; j<=nlstate;j++){
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];          eip +=eij[i][j][(int)age];
           fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
   char filerest[FILENAMELENGTH];        }
   char fileregp[FILENAMELENGTH];        fprintf(ficreseij,"%9.4f", eip );
   char popfile[FILENAMELENGTH];      }
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];      fprintf(ficreseij,"\n");
   int firstobs=1, lastobs=10;      
   int sdeb, sfin; /* Status at beginning and end */    }
   int c,  h , cpt,l;    free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   int ju,jl, mi;    printf("\n");
   int i1,j1, k1,k2,k3,jk,aa,bb, stepsize, ij;    fprintf(ficlog,"\n");
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;    
   int mobilav=0,popforecast=0;  }
   int hstepm, nhstepm;  
   double jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,jpyram, mpyram,anpyram,jpyram1, mpyram1,anpyram1, calagedate;  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[] )
   
   double bage, fage, age, agelim, agebase;  {
   double ftolpl=FTOL;    /* Covariances of health expectancies eij and of total life expectancies according
   double **prlim;     to initial status i, ei. .
   double *severity;    */
   double ***param; /* Matrix of parameters */    int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
   double  *p;    int nhstepma, nstepma; /* Decreasing with age */
   double **matcov; /* Matrix of covariance */    double age, agelim, hf;
   double ***delti3; /* Scale */    double ***p3matp, ***p3matm, ***varhe;
   double *delti; /* Scale */    double **dnewm,**doldm;
   double ***eij, ***vareij;    double *xp, *xm;
   double **varpl; /* Variances of prevalence limits by age */    double **gp, **gm;
   double *epj, vepp;    double ***gradg, ***trgradg;
   double kk1, kk2;    int theta;
   double dateprev1, dateprev2,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2;  
      double eip, vip;
   
   char version[80]="Imach version 0.8d, May 2002, INED-EUROREVES ";    varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
   char *alph[]={"a","a","b","c","d","e"}, str[4];    xp=vector(1,npar);
     xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
   char z[1]="c", occ;    doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
 #include <sys/time.h>    
 #include <time.h>    pstamp(ficresstdeij);
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];    fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
      fprintf(ficresstdeij,"# Age");
   /* long total_usecs;    for(i=1; i<=nlstate;i++){
   struct timeval start_time, end_time;      for(j=1; j<=nlstate;j++)
          fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */      fprintf(ficresstdeij," e%1d. ",i);
   getcwd(pathcd, size);    }
     fprintf(ficresstdeij,"\n");
   printf("\n%s",version);  
   if(argc <=1){    pstamp(ficrescveij);
     printf("\nEnter the parameter file name: ");    fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
     scanf("%s",pathtot);    fprintf(ficrescveij,"# Age");
   }    for(i=1; i<=nlstate;i++)
   else{      for(j=1; j<=nlstate;j++){
     strcpy(pathtot,argv[1]);        cptj= (j-1)*nlstate+i;
   }        for(i2=1; i2<=nlstate;i2++)
   /*if(getcwd(pathcd, 80)!= NULL)printf ("Error pathcd\n");*/          for(j2=1; j2<=nlstate;j2++){
   /*cygwin_split_path(pathtot,path,optionfile);            cptj2= (j2-1)*nlstate+i2;
     printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/            if(cptj2 <= cptj)
   /* cutv(path,optionfile,pathtot,'\\');*/              fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
   split(pathtot,path,optionfile,optionfilext,optionfilefiname);      }
    printf("pathtot=%s, path=%s, optionfile=%s optionfilext=%s optionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);    fprintf(ficrescveij,"\n");
   chdir(path);    
   replace(pathc,path);    if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
 /*-------- arguments in the command line --------*/    }
     else  hstepm=estepm;   
   strcpy(fileres,"r");    /* We compute the life expectancy from trapezoids spaced every estepm months
   strcat(fileres, optionfilefiname);     * This is mainly to measure the difference between two models: for example
   strcat(fileres,".txt");    /* Other files have txt extension */     * if stepm=24 months pijx are given only every 2 years and by summing them
      * we are calculating an estimate of the Life Expectancy assuming a linear 
   /*---------arguments file --------*/     * progression in between and thus overestimating or underestimating according
      * to the curvature of the survival function. If, for the same date, we 
   if((ficpar=fopen(optionfile,"r"))==NULL)    {     * estimate the model with stepm=1 month, we can keep estepm to 24 months
     printf("Problem with optionfile %s\n",optionfile);     * to compare the new estimate of Life expectancy with the same linear 
     goto end;     * hypothesis. A more precise result, taking into account a more precise
   }     * curvature will be obtained if estepm is as small as stepm. */
   
   strcpy(filereso,"o");    /* For example we decided to compute the life expectancy with the smallest unit */
   strcat(filereso,fileres);    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
   if((ficparo=fopen(filereso,"w"))==NULL) {       nhstepm is the number of hstepm from age to agelim 
     printf("Problem with Output resultfile: %s\n", filereso);goto end;       nstepm is the number of stepm from age to agelin. 
   }       Look at hpijx to understand the reason of that which relies in memory size
        and note for a fixed period like estepm months */
   /* Reads comments: lines beginning with '#' */    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
   while((c=getc(ficpar))=='#' && c!= EOF){       survival function given by stepm (the optimization length). Unfortunately it
     ungetc(c,ficpar);       means that if the survival funtion is printed only each two years of age and if
     fgets(line, MAXLINE, ficpar);       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
     puts(line);       results. So we changed our mind and took the option of the best precision.
     fputs(line,ficparo);    */
   }    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   ungetc(c,ficpar);  
     /* If stepm=6 months */
   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\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);    /* nhstepm age range expressed in number of stepm */
   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);    agelim=AGESUP;
   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);    nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
 while((c=getc(ficpar))=='#' && c!= EOF){    /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     ungetc(c,ficpar);    /* if (stepm >= YEARM) hstepm=1;*/
     fgets(line, MAXLINE, ficpar);    nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     puts(line);    
     fputs(line,ficparo);    p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   }    p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   ungetc(c,ficpar);    gradg=ma3x(0,nhstepm,1,npar,1,nlstate*nlstate);
      trgradg =ma3x(0,nhstepm,1,nlstate*nlstate,1,npar);
        gp=matrix(0,nhstepm,1,nlstate*nlstate);
   covar=matrix(0,NCOVMAX,1,n);    gm=matrix(0,nhstepm,1,nlstate*nlstate);
   cptcovn=0;  
   if (strlen(model)>1) cptcovn=nbocc(model,'+')+1;    for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
   ncovmodel=2+cptcovn;      /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      /* if (stepm >= YEARM) hstepm=1;*/
        nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   /* Read guess parameters */  
   /* Reads comments: lines beginning with '#' */      /* If stepm=6 months */
   while((c=getc(ficpar))=='#' && c!= EOF){      /* Computed by stepm unit matrices, product of hstepma matrices, stored
     ungetc(c,ficpar);         in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
     fgets(line, MAXLINE, ficpar);      
     puts(line);      hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
     fputs(line,ficparo);  
   }      /* Computing  Variances of health expectancies */
   ungetc(c,ficpar);      /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
           decrease memory allocation */
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      for(theta=1; theta <=npar; theta++){
     for(i=1; i <=nlstate; i++)        for(i=1; i<=npar; i++){ 
     for(j=1; j <=nlstate+ndeath-1; j++){          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       fscanf(ficpar,"%1d%1d",&i1,&j1);          xm[i] = x[i] - (i==theta ?delti[theta]:0);
       fprintf(ficparo,"%1d%1d",i1,j1);        }
       printf("%1d%1d",i,j);        hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
       for(k=1; k<=ncovmodel;k++){        hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
         fscanf(ficpar," %lf",&param[i][j][k]);    
         printf(" %lf",param[i][j][k]);        for(j=1; j<= nlstate; j++){
         fprintf(ficparo," %lf",param[i][j][k]);          for(i=1; i<=nlstate; i++){
       }            for(h=0; h<=nhstepm-1; h++){
       fscanf(ficpar,"\n");              gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
       printf("\n");              gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
       fprintf(ficparo,"\n");            }
     }          }
          }
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel;       
         for(ij=1; ij<= nlstate*nlstate; ij++)
   p=param[1][1];          for(h=0; h<=nhstepm-1; h++){
              gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
   /* Reads comments: lines beginning with '#' */          }
   while((c=getc(ficpar))=='#' && c!= EOF){      }/* End theta */
     ungetc(c,ficpar);      
     fgets(line, MAXLINE, ficpar);      
     puts(line);      for(h=0; h<=nhstepm-1; h++)
     fputs(line,ficparo);        for(j=1; j<=nlstate*nlstate;j++)
   }          for(theta=1; theta <=npar; theta++)
   ungetc(c,ficpar);            trgradg[h][j][theta]=gradg[h][theta][j];
       
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);  
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */       for(ij=1;ij<=nlstate*nlstate;ij++)
   for(i=1; i <=nlstate; i++){        for(ji=1;ji<=nlstate*nlstate;ji++)
     for(j=1; j <=nlstate+ndeath-1; j++){          varhe[ij][ji][(int)age] =0.;
       fscanf(ficpar,"%1d%1d",&i1,&j1);  
       printf("%1d%1d",i,j);       printf("%d|",(int)age);fflush(stdout);
       fprintf(ficparo,"%1d%1d",i1,j1);       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       for(k=1; k<=ncovmodel;k++){       for(h=0;h<=nhstepm-1;h++){
         fscanf(ficpar,"%le",&delti3[i][j][k]);        for(k=0;k<=nhstepm-1;k++){
         printf(" %le",delti3[i][j][k]);          matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
         fprintf(ficparo," %le",delti3[i][j][k]);          matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
       }          for(ij=1;ij<=nlstate*nlstate;ij++)
       fscanf(ficpar,"\n");            for(ji=1;ji<=nlstate*nlstate;ji++)
       printf("\n");              varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
       fprintf(ficparo,"\n");        }
     }      }
   }  
   delti=delti3[1][1];      /* Computing expectancies */
        hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
   /* Reads comments: lines beginning with '#' */      for(i=1; i<=nlstate;i++)
   while((c=getc(ficpar))=='#' && c!= EOF){        for(j=1; j<=nlstate;j++)
     ungetc(c,ficpar);          for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
     fgets(line, MAXLINE, ficpar);            eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
     puts(line);            
     fputs(line,ficparo);            /* 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]);*/
   }  
   ungetc(c,ficpar);          }
    
   matcov=matrix(1,npar,1,npar);      fprintf(ficresstdeij,"%3.0f",age );
   for(i=1; i <=npar; i++){      for(i=1; i<=nlstate;i++){
     fscanf(ficpar,"%s",&str);        eip=0.;
     printf("%s",str);        vip=0.;
     fprintf(ficparo,"%s",str);        for(j=1; j<=nlstate;j++){
     for(j=1; j <=i; j++){          eip += eij[i][j][(int)age];
       fscanf(ficpar," %le",&matcov[i][j]);          for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
       printf(" %.5le",matcov[i][j]);            vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
       fprintf(ficparo," %.5le",matcov[i][j]);          fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
     }        }
     fscanf(ficpar,"\n");        fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
     printf("\n");      }
     fprintf(ficparo,"\n");      fprintf(ficresstdeij,"\n");
   }  
   for(i=1; i <=npar; i++)      fprintf(ficrescveij,"%3.0f",age );
     for(j=i+1;j<=npar;j++)      for(i=1; i<=nlstate;i++)
       matcov[i][j]=matcov[j][i];        for(j=1; j<=nlstate;j++){
              cptj= (j-1)*nlstate+i;
   printf("\n");          for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
     /*-------- Rewriting paramater file ----------*/              if(cptj2 <= cptj)
      strcpy(rfileres,"r");    /* "Rparameterfile */                fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
      strcat(rfileres,optionfilefiname);    /* Parameter file first name*/            }
      strcat(rfileres,".");    /* */        }
      strcat(rfileres,optionfilext);    /* Other files have txt extension */      fprintf(ficrescveij,"\n");
     if((ficres =fopen(rfileres,"w"))==NULL) {     
       printf("Problem writing new parameter file: %s\n", fileres);goto end;    }
     }    free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     fprintf(ficres,"#%s\n",version);    free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
        free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     /*-------- data file ----------*/    free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     if((fic=fopen(datafile,"r"))==NULL)    {    free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       printf("Problem with datafile: %s\n", datafile);goto end;    free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     }    printf("\n");
     fprintf(ficlog,"\n");
     n= lastobs;  
     severity = vector(1,maxwav);    free_vector(xm,1,npar);
     outcome=imatrix(1,maxwav+1,1,n);    free_vector(xp,1,npar);
     num=ivector(1,n);    free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     moisnais=vector(1,n);    free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     annais=vector(1,n);    free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
     moisdc=vector(1,n);  }
     andc=vector(1,n);  
     agedc=vector(1,n);  /************ Variance ******************/
     cod=ivector(1,n);  void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
     weight=vector(1,n);  {
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    /* Variance of health expectancies */
     mint=matrix(1,maxwav,1,n);    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     anint=matrix(1,maxwav,1,n);    /* double **newm;*/
     s=imatrix(1,maxwav+1,1,n);    double **dnewm,**doldm;
     adl=imatrix(1,maxwav+1,1,n);        double **dnewmp,**doldmp;
     tab=ivector(1,NCOVMAX);    int i, j, nhstepm, hstepm, h, nstepm ;
     ncodemax=ivector(1,8);    int k, cptcode;
     double *xp;
     i=1;    double **gp, **gm;  /* for var eij */
     while (fgets(line, MAXLINE, fic) != NULL)    {    double ***gradg, ***trgradg; /*for var eij */
       if ((i >= firstobs) && (i <=lastobs)) {    double **gradgp, **trgradgp; /* for var p point j */
            double *gpp, *gmp; /* for var p point j */
         for (j=maxwav;j>=1;j--){    double **varppt; /* for var p point j nlstate to nlstate+ndeath */
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);    double ***p3mat;
           strcpy(line,stra);    double age,agelim, hf;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    double ***mobaverage;
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    int theta;
         }    char digit[4];
            char digitp[25];
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);  
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);    char fileresprobmorprev[FILENAMELENGTH];
   
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);    if(popbased==1){
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);      if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);      else strcpy(digitp,"-populbased-nomobil-");
         for (j=ncovcol;j>=1;j--){    }
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);    else 
         }      strcpy(digitp,"-stablbased-");
         num[i]=atol(stra);  
            if (mobilav!=0) {
         /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){      mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           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;}*/      if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         i=i+1;        printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }      }
     }    }
     /* printf("ii=%d", ij);  
        scanf("%d",i);*/    strcpy(fileresprobmorprev,"prmorprev"); 
   imx=i-1; /* Number of individuals */    sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
   /* for (i=1; i<=imx; i++){    strcat(fileresprobmorprev,digit); /* Tvar to be done */
     if ((s[1][i]==3) && (s[2][i]==2)) s[2][i]=3;    strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     if ((s[2][i]==3) && (s[3][i]==2)) s[3][i]=3;    strcat(fileresprobmorprev,fileres);
     if ((s[3][i]==3) && (s[4][i]==2)) s[4][i]=3;    if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
     }*/      printf("Problem with resultfile: %s\n", fileresprobmorprev);
    /*  for (i=1; i<=imx; i++){      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
      if (s[4][i]==9)  s[4][i]=-1;    }
      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]));}*/    printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     
      fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
   /* Calculation of the number of parameter from char model*/    pstamp(ficresprobmorprev);
   Tvar=ivector(1,15);    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);
   Tprod=ivector(1,15);    fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
   Tvaraff=ivector(1,15);    for(j=nlstate+1; j<=(nlstate+ndeath);j++){
   Tvard=imatrix(1,15,1,2);      fprintf(ficresprobmorprev," p.%-d SE",j);
   Tage=ivector(1,15);            for(i=1; i<=nlstate;i++)
            fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
   if (strlen(model) >1){    }  
     j=0, j1=0, k1=1, k2=1;    fprintf(ficresprobmorprev,"\n");
     j=nbocc(model,'+');    fprintf(ficgp,"\n# Routine varevsij");
     j1=nbocc(model,'*');    /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     cptcovn=j+1;    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");
     cptcovprod=j1;    fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
      /*   } */
     strcpy(modelsav,model);    varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if ((strcmp(model,"age")==0) || (strcmp(model,"age*age")==0)){    pstamp(ficresvij);
       printf("Error. Non available option model=%s ",model);    fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
       goto end;    if(popbased==1)
     }      fprintf(ficresvij,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d\n",mobilav);
        else
     for(i=(j+1); i>=1;i--){      fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
       cutv(stra,strb,modelsav,'+');    fprintf(ficresvij,"# Age");
       if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);    for(i=1; i<=nlstate;i++)
       /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/      for(j=1; j<=nlstate;j++)
       /*scanf("%d",i);*/        fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
       if (strchr(strb,'*')) {    fprintf(ficresvij,"\n");
         cutv(strd,strc,strb,'*');  
         if (strcmp(strc,"age")==0) {    xp=vector(1,npar);
           cptcovprod--;    dnewm=matrix(1,nlstate,1,npar);
           cutv(strb,stre,strd,'V');    doldm=matrix(1,nlstate,1,nlstate);
           Tvar[i]=atoi(stre);    dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
           cptcovage++;    doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
             Tage[cptcovage]=i;  
             /*printf("stre=%s ", stre);*/    gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
         }    gpp=vector(nlstate+1,nlstate+ndeath);
         else if (strcmp(strd,"age")==0) {    gmp=vector(nlstate+1,nlstate+ndeath);
           cptcovprod--;    trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
           cutv(strb,stre,strc,'V');    
           Tvar[i]=atoi(stre);    if(estepm < stepm){
           cptcovage++;      printf ("Problem %d lower than %d\n",estepm, stepm);
           Tage[cptcovage]=i;    }
         }    else  hstepm=estepm;   
         else {    /* For example we decided to compute the life expectancy with the smallest unit */
           cutv(strb,stre,strc,'V');    /* hstepm beeing the number of stepms, if hstepm=1 the length of hstepm is stepm. 
           Tvar[i]=ncovcol+k1;       nhstepm is the number of hstepm from age to agelim 
           cutv(strb,strc,strd,'V');       nstepm is the number of stepm from age to agelin. 
           Tprod[k1]=i;       Look at function hpijx to understand why (it is linked to memory size questions) */
           Tvard[k1][1]=atoi(strc);    /* We decided (b) to get a life expectancy respecting the most precise curvature of the
           Tvard[k1][2]=atoi(stre);       survival function given by stepm (the optimization length). Unfortunately it
           Tvar[cptcovn+k2]=Tvard[k1][1];       means that if the survival funtion is printed every two years of age and if
           Tvar[cptcovn+k2+1]=Tvard[k1][2];       you sum them up and add 1 year (area under the trapezoids) you won't get the same 
           for (k=1; k<=lastobs;k++)       results. So we changed our mind and took the option of the best precision.
             covar[ncovcol+k1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];    */
           k1++;    hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
           k2=k2+2;    agelim = AGESUP;
         }    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       }      nstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       else {      nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
         /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/      p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
        /*  scanf("%d",i);*/      gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       cutv(strd,strc,strb,'V');      gp=matrix(0,nhstepm,1,nlstate);
       Tvar[i]=atoi(strc);      gm=matrix(0,nhstepm,1,nlstate);
       }  
       strcpy(modelsav,stra);    
       /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);      for(theta=1; theta <=npar; theta++){
         scanf("%d",i);*/        for(i=1; i<=npar; i++){ /* Computes gradient x + delta*/
     }          xp[i] = x[i] + (i==theta ?delti[theta]:0);
 }        }
          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
   /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   printf("cptcovprod=%d ", cptcovprod);  
   scanf("%d ",i);*/        if (popbased==1) {
     fclose(fic);          if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
     /*  if(mle==1){*/              prlim[i][i]=probs[(int)age][i][ij];
     if (weightopt != 1) { /* Maximisation without weights*/          }else{ /* mobilav */ 
       for(i=1;i<=n;i++) weight[i]=1.0;            for(i=1; i<=nlstate;i++)
     }              prlim[i][i]=mobaverage[(int)age][i][ij];
     /*-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(j=1; j<= nlstate; j++){
       for(m=2; (m<= maxwav); m++) {          for(h=0; h<=nhstepm; h++){
        if ((mint[m][i]== 99) && (s[m][i] <= nlstate)){            for(i=1, gp[h][j]=0.;i<=nlstate;i++)
          anint[m][i]=9999;              gp[h][j] += prlim[i][i]*p3mat[i][j][h];
          s[m][i]=-1;          }
        }        }
      if(moisdc[i]==99 && andc[i]==9999 & s[m][i]>nlstate) s[m][i]=-1;        /* This for computing probability of death (h=1 means
       }           computed over hstepm matrices product = hstepm*stepm months) 
     }           as a weighted average of prlim.
         */
     for (i=1; i<=imx; i++)  {        for(j=nlstate+1;j<=nlstate+ndeath;j++){
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          for(i=1,gpp[j]=0.; i<= nlstate; i++)
       for(m=1; (m<= maxwav); m++){            gpp[j] += prlim[i][i]*p3mat[i][j][1];
         if(s[m][i] >0){        }    
           if (s[m][i] >= nlstate+1) {        /* end probability of death */
             if(agedc[i]>0)  
               if(moisdc[i]!=99 && andc[i]!=9999)        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
                 agev[m][i]=agedc[i];          xp[i] = x[i] - (i==theta ?delti[theta]:0);
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/        hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
            else {        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
               if (andc[i]!=9999){   
               printf("Warning negative age at death: %d line:%d\n",num[i],i);        if (popbased==1) {
               agev[m][i]=-1;          if(mobilav ==0){
               }            for(i=1; i<=nlstate;i++)
             }              prlim[i][i]=probs[(int)age][i][ij];
           }          }else{ /* mobilav */ 
           else if(s[m][i] !=9){ /* Should no more exist */            for(i=1; i<=nlstate;i++)
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);              prlim[i][i]=mobaverage[(int)age][i][ij];
             if(mint[m][i]==99 || anint[m][i]==9999)          }
               agev[m][i]=1;        }
             else if(agev[m][i] <agemin){  
               agemin=agev[m][i];        for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/          for(h=0; h<=nhstepm; h++){
             }            for(i=1, gm[h][j]=0.;i<=nlstate;i++)
             else if(agev[m][i] >agemax){              gm[h][j] += prlim[i][i]*p3mat[i][j][h];
               agemax=agev[m][i];          }
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/        }
             }        /* This for computing probability of death (h=1 means
             /*agev[m][i]=anint[m][i]-annais[i];*/           computed over hstepm matrices product = hstepm*stepm months) 
             /*   agev[m][i] = age[i]+2*m;*/           as a weighted average of prlim.
           }        */
           else { /* =9 */        for(j=nlstate+1;j<=nlstate+ndeath;j++){
             agev[m][i]=1;          for(i=1,gmp[j]=0.; i<= nlstate; i++)
             s[m][i]=-1;           gmp[j] += prlim[i][i]*p3mat[i][j][1];
           }        }    
         }        /* end probability of death */
         else /*= 0 Unknown */  
           agev[m][i]=1;        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 (i=1; i<=imx; i++)  {  
       for(m=1; (m<= maxwav); m++){        for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
         if (s[m][i] > (nlstate+ndeath)) {          gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
           printf("Error: Wrong value in nlstate or ndeath\n");          }
           goto end;  
         }      } /* End theta */
       }  
     }      trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
     free_vector(severity,1,maxwav);          for(theta=1; theta <=npar; theta++)
     free_imatrix(outcome,1,maxwav+1,1,n);            trgradg[h][j][theta]=gradg[h][theta][j];
     free_vector(moisnais,1,n);  
     free_vector(annais,1,n);      for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
     /* free_matrix(mint,1,maxwav,1,n);        for(theta=1; theta <=npar; theta++)
        free_matrix(anint,1,maxwav,1,n);*/          trgradgp[j][theta]=gradgp[theta][j];
     free_vector(moisdc,1,n);    
     free_vector(andc,1,n);  
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
          for(i=1;i<=nlstate;i++)
     wav=ivector(1,imx);        for(j=1;j<=nlstate;j++)
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          vareij[i][j][(int)age] =0.;
     mw=imatrix(1,lastpass-firstpass+1,1,imx);  
          for(h=0;h<=nhstepm;h++){
     /* Concatenates waves */        for(k=0;k<=nhstepm;k++){
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);          matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
       Tcode=ivector(1,100);            for(j=1;j<=nlstate;j++)
       nbcode=imatrix(0,NCOVMAX,0,NCOVMAX);              vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
       ncodemax[1]=1;        }
       if (cptcovn > 0) tricode(Tvar,nbcode,imx);      }
          
    codtab=imatrix(1,100,1,10);      /* pptj */
    h=0;      matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
    m=pow(2,cptcoveff);      matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
        for(j=nlstate+1;j<=nlstate+ndeath;j++)
    for(k=1;k<=cptcoveff; k++){        for(i=nlstate+1;i<=nlstate+ndeath;i++)
      for(i=1; i <=(m/pow(2,k));i++){          varppt[j][i]=doldmp[j][i];
        for(j=1; j <= ncodemax[k]; j++){      /* end ppptj */
          for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){      /*  x centered again */
            h++;      hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
            if (h>m) h=1;codtab[h][k]=j;codtab[h][Tvar[k]]=j;      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
            /*  printf("h=%d k=%d j=%d codtab[h][k]=%d tvar[k]=%d \n",h, k,j,codtab[h][k],Tvar[k]);*/   
          }      if (popbased==1) {
        }        if(mobilav ==0){
      }          for(i=1; i<=nlstate;i++)
    }            prlim[i][i]=probs[(int)age][i][ij];
    /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]);        }else{ /* mobilav */ 
       codtab[1][2]=1;codtab[2][2]=2; */          for(i=1; i<=nlstate;i++)
    /* for(i=1; i <=m ;i++){            prlim[i][i]=mobaverage[(int)age][i][ij];
       for(k=1; k <=cptcovn; k++){        }
       printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);      }
       }               
       printf("\n");      /* This for computing probability of death (h=1 means
       }         computed over hstepm (estepm) matrices product = hstepm*stepm months) 
       scanf("%d",i);*/         as a weighted average of prlim.
          */
    /* Calculates basic frequencies. Computes observed prevalence at single age      for(j=nlstate+1;j<=nlstate+ndeath;j++){
        and prints on file fileres'p'. */        for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
          }    
          /* end probability of death */
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      for(j=nlstate+1; j<=(nlstate+ndeath);j++){
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */        for(i=1; i<=nlstate;i++){
                fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
     /* 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) */      fprintf(ficresprobmorprev,"\n");
   
     if(mle==1){      fprintf(ficresvij,"%.0f ",age );
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);      for(i=1; i<=nlstate;i++)
     }        for(j=1; j<=nlstate;j++){
              fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
     /*--------- 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(ficresvij,"\n");
        free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
    jk=1;      free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
    fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");      free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
    printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");      free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
    for(i=1,jk=1; i <=nlstate; i++){    } /* End age */
      for(k=1; k <=(nlstate+ndeath); k++){    free_vector(gpp,nlstate+1,nlstate+ndeath);
        if (k != i)    free_vector(gmp,nlstate+1,nlstate+ndeath);
          {    free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
            printf("%d%d ",i,k);    free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
            fprintf(ficres,"%1d%1d ",i,k);    fprintf(ficgp,"\nunset parametric;unset label; set ter png small;set size 0.65, 0.65");
            for(j=1; j <=ncovmodel; j++){    /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
              printf("%f ",p[jk]);    fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
              fprintf(ficres,"%f ",p[jk]);  /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
              jk++;  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
            }  /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
            printf("\n");    fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l 1 ",subdirf(fileresprobmorprev));
            fprintf(ficres,"\n");    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l 2 ",subdirf(fileresprobmorprev));
          }    fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l 2 ",subdirf(fileresprobmorprev));
      }    fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
    }    fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
  if(mle==1){    /*  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);
     /* Computing hessian and covariance matrix */  */
     ftolhess=ftol; /* Usually correct */  /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     hesscov(matcov, p, npar, delti, ftolhess, func);    fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
  }  
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");    free_vector(xp,1,npar);
     printf("# Scales (for hessian or gradient estimation)\n");    free_matrix(doldm,1,nlstate,1,nlstate);
      for(i=1,jk=1; i <=nlstate; i++){    free_matrix(dnewm,1,nlstate,1,npar);
       for(j=1; j <=nlstate+ndeath; j++){    free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
         if (j!=i) {    free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
           fprintf(ficres,"%1d%1d",i,j);    free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
           printf("%1d%1d",i,j);    if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
           for(k=1; k<=ncovmodel;k++){    fclose(ficresprobmorprev);
             printf(" %.5e",delti[jk]);    fflush(ficgp);
             fprintf(ficres," %.5e",delti[jk]);    fflush(fichtm); 
             jk++;  }  /* end varevsij */
           }  
           printf("\n");  /************ Variance of prevlim ******************/
           fprintf(ficres,"\n");  void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
         }  {
       }    /* Variance of prevalence limit */
      }    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
        double **newm;
     k=1;    double **dnewm,**doldm;
     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");    int i, j, nhstepm, hstepm;
     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");    int k, cptcode;
     for(i=1;i<=npar;i++){    double *xp;
       /*  if (k>nlstate) k=1;    double *gp, *gm;
       i1=(i-1)/(ncovmodel*nlstate)+1;    double **gradg, **trgradg;
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    double age,agelim;
       printf("%s%d%d",alph[k],i1,tab[i]);*/    int theta;
       fprintf(ficres,"%3d",i);    
       printf("%3d",i);    pstamp(ficresvpl);
       for(j=1; j<=i;j++){    fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
         fprintf(ficres," %.5e",matcov[i][j]);    fprintf(ficresvpl,"# Age");
         printf(" %.5e",matcov[i][j]);    for(i=1; i<=nlstate;i++)
       }        fprintf(ficresvpl," %1d-%1d",i,i);
       fprintf(ficres,"\n");    fprintf(ficresvpl,"\n");
       printf("\n");  
       k++;    xp=vector(1,npar);
     }    dnewm=matrix(1,nlstate,1,npar);
        doldm=matrix(1,nlstate,1,nlstate);
     while((c=getc(ficpar))=='#' && c!= EOF){    
       ungetc(c,ficpar);    hstepm=1*YEARM; /* Every year of age */
       fgets(line, MAXLINE, ficpar);    hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
       puts(line);    agelim = AGESUP;
       fputs(line,ficparo);    for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
     }      nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
     ungetc(c,ficpar);      if (stepm >= YEARM) hstepm=1;
     estepm=0;      nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);      gradg=matrix(1,npar,1,nlstate);
     if (estepm==0 || estepm < stepm) estepm=stepm;      gp=vector(1,nlstate);
     if (fage <= 2) {      gm=vector(1,nlstate);
       bage = ageminpar;  
       fage = agemaxpar;      for(theta=1; theta <=npar; theta++){
     }        for(i=1; i<=npar; i++){ /* Computes gradient */
              xp[i] = x[i] + (i==theta ?delti[theta]:0);
     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);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);        for(i=1;i<=nlstate;i++)
            gp[i] = prlim[i][i];
     while((c=getc(ficpar))=='#' && c!= EOF){      
     ungetc(c,ficpar);        for(i=1; i<=npar; i++) /* Computes gradient */
     fgets(line, MAXLINE, ficpar);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
     puts(line);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
     fputs(line,ficparo);        for(i=1;i<=nlstate;i++)
   }          gm[i] = prlim[i][i];
   ungetc(c,ficpar);  
          for(i=1;i<=nlstate;i++)
   fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2);          gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
   fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);      } /* End theta */
  fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);  
            trgradg =matrix(1,nlstate,1,npar);
   while((c=getc(ficpar))=='#' && c!= EOF){  
     ungetc(c,ficpar);      for(j=1; j<=nlstate;j++)
     fgets(line, MAXLINE, ficpar);        for(theta=1; theta <=npar; theta++)
     puts(line);          trgradg[j][theta]=gradg[theta][j];
     fputs(line,ficparo);  
   }      for(i=1;i<=nlstate;i++)
   ungetc(c,ficpar);        varpl[i][(int)age] =0.;
        matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
    dateprev1=anprev1+mprev1/12.+jprev1/365.;      for(i=1;i<=nlstate;i++)
    dateprev2=anprev2+mprev2/12.+jprev2/365.;        varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
   fscanf(ficpar,"pop_based=%d\n",&popbased);      fprintf(ficresvpl,"%.0f ",age );
   fprintf(ficparo,"pop_based=%d\n",popbased);        for(i=1; i<=nlstate;i++)
   fprintf(ficres,"pop_based=%d\n",popbased);          fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
        fprintf(ficresvpl,"\n");
   while((c=getc(ficpar))=='#' && c!= EOF){      free_vector(gp,1,nlstate);
     ungetc(c,ficpar);      free_vector(gm,1,nlstate);
     fgets(line, MAXLINE, ficpar);      free_matrix(gradg,1,npar,1,nlstate);
     puts(line);      free_matrix(trgradg,1,nlstate,1,npar);
     fputs(line,ficparo);    } /* End age */
   }  
   ungetc(c,ficpar);    free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
   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);    free_matrix(dnewm,1,nlstate,1,nlstate);
 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);  }
   
   /************ Variance of one-step probabilities  ******************/
 while((c=getc(ficpar))=='#' && c!= EOF){  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[])
     ungetc(c,ficpar);  {
     fgets(line, MAXLINE, ficpar);    int i, j=0,  i1, k1, l1, t, tj;
     puts(line);    int k2, l2, j1,  z1;
     fputs(line,ficparo);    int k=0,l, cptcode;
   }    int first=1, first1;
   ungetc(c,ficpar);    double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
   fscanf(ficpar,"popforecast=%d popfile=%s popfiledate=%lf/%lf/%lf last-popfiledate=%lf/%lf/%lf\n",&popforecast,popfile,&jpyram,&mpyram,&anpyram,&jpyram1,&mpyram1,&anpyram1);    double *xp;
   fprintf(ficparo,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    double *gp, *gm;
   fprintf(ficres,"popforecast=%d popfile=%s popfiledate=%.lf/%.lf/%.lf last-popfiledate=%.lf/%.lf/%.lf\n",popforecast,popfile,jpyram,mpyram,anpyram,jpyram1,mpyram1,anpyram1);    double **gradg, **trgradg;
     double **mu;
  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);    double age,agelim, cov[NCOVMAX];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
 /*------------ gnuplot -------------*/    int theta;
  printinggnuplot(fileres,optionfilefiname,optionfile,optionfilegnuplot, ageminpar,agemaxpar,fage, pathc,p);    char fileresprob[FILENAMELENGTH];
      char fileresprobcov[FILENAMELENGTH];
 /*------------ free_vector  -------------*/    char fileresprobcor[FILENAMELENGTH];
  chdir(path);  
      double ***varpij;
  free_ivector(wav,1,imx);  
  free_imatrix(dh,1,lastpass-firstpass+1,1,imx);    strcpy(fileresprob,"prob"); 
  free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      strcat(fileresprob,fileres);
  free_ivector(num,1,n);    if((ficresprob=fopen(fileresprob,"w"))==NULL) {
  free_vector(agedc,1,n);      printf("Problem with resultfile: %s\n", fileresprob);
  /*free_matrix(covar,1,NCOVMAX,1,n);*/      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
  fclose(ficparo);    }
  fclose(ficres);    strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
 /*--------- index.htm --------*/    if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
   printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,model,imx,jmin,jmax,jmean,optionfile,optionfilehtm,rfileres,optionfilegnuplot,version,popforecast,estepm,jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
      strcpy(fileresprobcor,"probcor"); 
   /*--------------- Prevalence limit --------------*/    strcat(fileresprobcor,fileres);
      if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
   strcpy(filerespl,"pl");      printf("Problem with resultfile: %s\n", fileresprobcor);
   strcat(filerespl,fileres);      fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    }
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   }    fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficrespl,"#Prevalence limit\n");    fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
   fprintf(ficrespl,"#Age ");    printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
   fprintf(ficrespl,"\n");    pstamp(ficresprob);
      fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
   prlim=matrix(1,nlstate,1,nlstate);    fprintf(ficresprob,"# Age");
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    pstamp(ficresprobcov);
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficresprobcov,"# Age");
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    pstamp(ficresprobcor);
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
   k=0;    fprintf(ficresprobcor,"# Age");
   agebase=ageminpar;  
   agelim=agemaxpar;  
   ftolpl=1.e-10;    for(i=1; i<=nlstate;i++)
   i1=cptcoveff;      for(j=1; j<=(nlstate+ndeath);j++){
   if (cptcovn < 1){i1=1;}        fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
   for(cptcov=1;cptcov<=i1;cptcov++){        fprintf(ficresprobcor," p%1d-%1d ",i,j);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      }  
         k=k+1;   /* fprintf(ficresprob,"\n");
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/    fprintf(ficresprobcov,"\n");
         fprintf(ficrespl,"\n#******");    fprintf(ficresprobcor,"\n");
         for(j=1;j<=cptcoveff;j++)   */
           fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);    xp=vector(1,npar);
         fprintf(ficrespl,"******\n");    dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
            doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
         for (age=agebase; age<=agelim; age++){    mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
           fprintf(ficrespl,"%.0f",age );    first=1;
           for(i=1; i<=nlstate;i++)    fprintf(ficgp,"\n# Routine varprob");
           fprintf(ficrespl," %.5f", prlim[i][i]);    fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
           fprintf(ficrespl,"\n");    fprintf(fichtm,"\n");
         }  
       }    fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     }    fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
   fclose(ficrespl);    file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   /*------------- h Pij x at various ages ------------*/  and drawn. It helps understanding how is the covariance between two incidences.\
     They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);    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. \
   if((ficrespij=fopen(filerespij,"w"))==NULL) {  It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;  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>\
   printf("Computing pij: result on file '%s' \n", filerespij);   Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
     and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   stepsize=(int) (stepm+YEARM-1)/YEARM;  To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   /*if (stepm<=24) stepsize=2;*/  
     cov[1]=1;
   agelim=AGESUP;    tj=cptcoveff;
   hstepm=stepsize*YEARM; /* Every year of age */    if (cptcovn<1) {tj=1;ncodemax[1]=1;}
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */    j1=0;
      for(t=1; t<=tj;t++){
   k=0;      for(i1=1; i1<=ncodemax[t];i1++){ 
   for(cptcov=1;cptcov<=i1;cptcov++){        j1++;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){        if  (cptcovn>0) {
       k=k+1;          fprintf(ficresprob, "\n#********** Variable "); 
         fprintf(ficrespij,"\n#****** ");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
         for(j=1;j<=cptcoveff;j++)          fprintf(ficresprob, "**********\n#\n");
           fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          fprintf(ficresprobcov, "\n#********** Variable "); 
         fprintf(ficrespij,"******\n");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
                  fprintf(ficresprobcov, "**********\n#\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 */          fprintf(ficgp, "\n#********** Variable "); 
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          fprintf(ficgp, "**********\n#\n");
           oldm=oldms;savm=savms;          
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);            
           fprintf(ficrespij,"# Age");          fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for(i=1; i<=nlstate;i++)          for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             for(j=1; j<=nlstate+ndeath;j++)          fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
               fprintf(ficrespij," %1d-%1d",i,j);          
           fprintf(ficrespij,"\n");          fprintf(ficresprobcor, "\n#********** Variable ");    
            for (h=0; h<=nhstepm; h++){          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );          fprintf(ficresprobcor, "**********\n#");    
             for(i=1; i<=nlstate;i++)        }
               for(j=1; j<=nlstate+ndeath;j++)        
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);        for (age=bage; age<=fage; age ++){ 
             fprintf(ficrespij,"\n");          cov[2]=age;
              }          for (k=1; k<=cptcovn;k++) {
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);            cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];
           fprintf(ficrespij,"\n");          }
         }          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]]];
           
   varprob(fileres, matcov, p, delti, nlstate, (int) bage, (int) fage,k,Tvar,nbcode, ncodemax);          gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
           trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
   fclose(ficrespij);          gp=vector(1,(nlstate)*(nlstate+ndeath));
           gm=vector(1,(nlstate)*(nlstate+ndeath));
       
   /*---------- Forecasting ------------------*/          for(theta=1; theta <=npar; theta++){
   if((stepm == 1) && (strcmp(model,".")==0)){            for(i=1; i<=npar; i++)
     prevforecast(fileres, anproj1,mproj1,jproj1, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anproj2,p, i1);              xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
     if (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);            
   }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   else{            
     erreur=108;            k=0;
     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);            for(i=1; i<= (nlstate); i++){
   }              for(j=1; j<=(nlstate+ndeath);j++){
                  k=k+1;
                 gp[k]=pmmij[i][j];
   /*---------- Health expectancies and variances ------------*/              }
             }
   strcpy(filerest,"t");            
   strcat(filerest,fileres);            for(i=1; i<=npar; i++)
   if((ficrest=fopen(filerest,"w"))==NULL) {              xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;      
   }            pmij(pmmij,cov,ncovmodel,xp,nlstate);
   printf("Computing Total LEs with variances: file '%s' \n", filerest);            k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
   strcpy(filerese,"e");                k=k+1;
   strcat(filerese,fileres);                gm[k]=pmmij[i][j];
   if((ficreseij=fopen(filerese,"w"))==NULL) {              }
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);            }
   }       
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);            for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
  strcpy(fileresv,"v");          }
   strcat(fileresv,fileres);  
   if((ficresvij=fopen(fileresv,"w"))==NULL) {          for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);            for(theta=1; theta <=npar; theta++)
   }              trgradg[j][theta]=gradg[theta][j];
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);          
   calagedate=-1;          matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
 prevalence(ageminpar, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax,mint,anint,dateprev1,dateprev2, calagedate);          matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
           free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
   k=0;          free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
   for(cptcov=1;cptcov<=i1;cptcov++){          free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
       k=k+1;  
       fprintf(ficrest,"\n#****** ");          pmij(pmmij,cov,ncovmodel,x,nlstate);
       for(j=1;j<=cptcoveff;j++)          
         fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);          k=0;
       fprintf(ficrest,"******\n");          for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
       fprintf(ficreseij,"\n#****** ");              k=k+1;
       for(j=1;j<=cptcoveff;j++)              mu[k][(int) age]=pmmij[i][j];
         fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);            }
       fprintf(ficreseij,"******\n");          }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
       fprintf(ficresvij,"\n#****** ");            for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
       for(j=1;j<=cptcoveff;j++)              varpij[i][j][(int)age] = doldm[i][j];
         fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficresvij,"******\n");          /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
       oldm=oldms;savm=savms;            fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov);              }*/
    
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);          fprintf(ficresprob,"\n%d ",(int)age);
       oldm=oldms;savm=savms;          fprintf(ficresprobcov,"\n%d ",(int)age);
        varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm);          fprintf(ficresprobcor,"\n%d ",(int)age);
      
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
              fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");          for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);            fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
       fprintf(ficrest,"\n");            fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
       epj=vector(1,nlstate+1);          i=0;
       for(age=bage; age <=fage ;age++){          for (k=1; k<=(nlstate);k++){
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            for (l=1; l<=(nlstate+ndeath);l++){ 
         if (popbased==1) {              i=i++;
           for(i=1; i<=nlstate;i++)              fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
             prlim[i][i]=probs[(int)age][i][k];              fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
         }              for (j=1; j<=i;j++){
                        fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
         fprintf(ficrest," %4.0f",age);                fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)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];          }/* end of loop for state */
             /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/        } /* end of loop for age */
           }  
           epj[nlstate+1] +=epj[j];        /* Confidence intervalle of pij  */
         }        /*
           fprintf(ficgp,"\nunset parametric;unset label");
         for(i=1, vepp=0.;i <=nlstate;i++)          fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           for(j=1;j <=nlstate;j++)          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
             vepp += vareij[i][j][(int)age];          fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
         fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));          fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
         for(j=1;j <=nlstate;j++){          fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));          fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         }        */
         fprintf(ficrest,"\n");  
       }        /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
     }        first1=1;
   }        for (k2=1; k2<=(nlstate);k2++){
 free_matrix(mint,1,maxwav,1,n);          for (l2=1; l2<=(nlstate+ndeath);l2++){ 
     free_matrix(anint,1,maxwav,1,n); free_imatrix(s,1,maxwav+1,1,n);            if(l2==k2) continue;
     free_vector(weight,1,n);            j=(k2-1)*(nlstate+ndeath)+l2;
   fclose(ficreseij);            for (k1=1; k1<=(nlstate);k1++){
   fclose(ficresvij);              for (l1=1; l1<=(nlstate+ndeath);l1++){ 
   fclose(ficrest);                if(l1==k1) continue;
   fclose(ficpar);                i=(k1-1)*(nlstate+ndeath)+l1;
   free_vector(epj,1,nlstate+1);                if(i<=j) continue;
                  for (age=bage; age<=fage; age ++){ 
   /*------- Variance limit prevalence------*/                    if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
   strcpy(fileresvpl,"vpl");                    v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
   strcat(fileresvpl,fileres);                    cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {                    mu1=mu[i][(int) age]/stepm*YEARM ;
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);                    mu2=mu[j][(int) age]/stepm*YEARM;
     exit(0);                    c12=cv12/sqrt(v1*v2);
   }                    /* Computing eigen value of matrix of covariance */
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);                    lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
   k=0;                    if ((lc2 <0) || (lc1 <0) ){
   for(cptcov=1;cptcov<=i1;cptcov++){                      printf("Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Continuing by making them positive: WRONG RESULTS.\n", lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){                      fprintf(ficlog,"Error: One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e\n", lc1, lc2, v1, v2, cv12);fflush(ficlog);
       k=k+1;                      lc1=fabs(lc1);
       fprintf(ficresvpl,"\n#****** ");                      lc2=fabs(lc2);
       for(j=1;j<=cptcoveff;j++)                    }
         fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);  
       fprintf(ficresvpl,"******\n");                    /* Eigen vectors */
                          v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
       varpl=matrix(1,nlstate,(int) bage, (int) fage);                    /*v21=sqrt(1.-v11*v11); *//* error */
       oldm=oldms;savm=savms;                    v21=(lc1-v1)/cv12*v11;
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);                    v12=-v21;
     }                    v22=v11;
  }                    tnalp=v21/v11;
                     if(first1==1){
   fclose(ficresvpl);                      first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
   /*---------- End : free ----------------*/                    }
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);                    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*/
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);                    /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);                    /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                      if(first==1){
                        first=0;
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);                      fprintf(ficgp,"\nset parametric;unset label");
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);                      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);
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);                      fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);                      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\">\
   free_matrix(matcov,1,npar,1,npar);  %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
   free_vector(delti,1,npar);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
   free_matrix(agev,1,maxwav,1,imx);                              subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);                      fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
   if(erreur >0)                      fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
     printf("End of Imach with error or warning %d\n",erreur);                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
   else   printf("End of Imach\n");                      fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */                      fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                                mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
   /* 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);*/                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
   /*printf("Total time was %d uSec.\n", total_usecs);*/                    }else{
   /*------ End -----------*/                      first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
  end:                      fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
 #ifdef windows                      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",\
   /* chdir(pathcd);*/                              mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
 #endif                              mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
  /*system("wgnuplot graph.plt");*/                    }/* if first */
  /*system("../gp37mgw/wgnuplot graph.plt");*/                  } /* age mod 5 */
  /*system("cd ../gp37mgw");*/                } /* end loop age */
  /* system("..\\gp37mgw\\wgnuplot graph.plt");*/                fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
  strcpy(plotcmd,GNUPLOTPROGRAM);                first=1;
  strcat(plotcmd," ");              } /*l12 */
  strcat(plotcmd,optionfilegnuplot);            } /* k12 */
  system(plotcmd);          } /*l1 */
         }/* k1 */
 #ifdef windows      } /* loop covariates */
   while (z[0] != 'q') {    }
     /* chdir(path); */    free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     printf("\nType e to edit output files, g to graph again, c to start again, and q for exiting: ");    free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     scanf("%s",z);    free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     if (z[0] == 'c') system("./imach");    free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     else if (z[0] == 'e') system(optionfilehtm);    free_vector(xp,1,npar);
     else if (z[0] == 'g') system(plotcmd);    fclose(ficresprob);
     else if (z[0] == 'q') exit(0);    fclose(ficresprobcov);
   }    fclose(ficresprobcor);
 #endif    fflush(ficgp);
 }    fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        /* Pij */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i, %d (stepm) months before: <a href=\"%s%d1.png\">%s%d1.png</a><br> \
   <img src=\"%s%d1.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1);     
        /* Quasi-incidences */
        fprintf(fichtm,"<br>- Pij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\
    before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too: <a href=\"%s%d2.png\">%s%d2.png</a><br> \
   <img src=\"%s%d2.png\">",stepm,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1,subdirf2(optionfilefiname,"pe"),jj1); 
          /* Period (stable) prevalence in each health state */
          for(cpt=1; cpt<nlstate;cpt++){
            fprintf(fichtm,"<br>- Period (stable) prevalence in each health state : <a href=\"%s%d%d.png\">%s%d%d.png</a><br> \
   <img src=\"%s%d%d.png\">",subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1,subdirf2(optionfilefiname,"p"),cpt,jj1);
          }
        for(cpt=1; cpt<=nlstate;cpt++) {
           fprintf(fichtm,"\n<br>- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1,subdirf2(optionfilefiname,"exp"),cpt,jj1);
        }
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
   
   
    fprintf(fichtm,"\
   \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\
    - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br>\n", rfileres,rfileres);
   
    fprintf(fichtm," - Variance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"prob"),subdirf2(fileres,"prob"));
    fprintf(fichtm,"\
    - Variance-covariance of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcov"),subdirf2(fileres,"probcov"));
   
    fprintf(fichtm,"\
    - Correlation matrix of one-step probabilities: <a href=\"%s\">%s</a> <br>\n",
            subdirf2(fileres,"probcor"),subdirf2(fileres,"probcor"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age and <b>initial health status</b> (cov(e<sup>ij</sup>,e<sup>kl</sup>)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"cve"),subdirf2(fileres,"cve"));
    fprintf(fichtm,"\
    - (a) Health expectancies by health status at initial age (e<sup>ij</sup>) and standard errors (in parentheses) (b) life expectancies and standard errors (e<sup>i.</sup>=e<sup>i1</sup>+e<sup>i2</sup>+...)(estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n</li>",
              estepm,subdirf2(fileres,"stde"),subdirf2(fileres,"stde"));
    fprintf(fichtm,"\
    - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), e<sup>ij</sup> are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a><br>\n",
            estepm, subdirf2(fileres,"v"),subdirf2(fileres,"v"));
    fprintf(fichtm,"\
    - Total life expectancy and total health expectancies to be spent in each health state e<sup>.j</sup> with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): <a href=\"%s\">%s</a> <br>\n",
            estepm, subdirf2(fileres,"t"),subdirf2(fileres,"t"));
    fprintf(fichtm,"\
    - Standard deviation of period (stable) prevalences: <a href=\"%s\">%s</a> <br>\n",\
            subdirf2(fileres,"vpl"),subdirf2(fileres,"vpl"));
   
   /*  if(popforecast==1) fprintf(fichtm,"\n */
   /*  - Prevalences forecasting: <a href=\"f%s\">f%s</a> <br>\n */
   /*  - Population forecasting (if popforecast=1): <a href=\"pop%s\">pop%s</a> <br>\n */
   /*      <br>",fileres,fileres,fileres,fileres); */
   /*  else  */
   /*    fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)<br><br></li>\n",popforecast, stepm, model); */
    fflush(fichtm);
    fprintf(fichtm," <ul><li><b>Graphs</b></li><p>");
   
    m=cptcoveff;
    if (cptcovn < 1) {m=1;ncodemax[1]=1;}
   
    jj1=0;
    for(k1=1; k1<=m;k1++){
      for(i1=1; i1<=ncodemax[k1];i1++){
        jj1++;
        if (cptcovn > 0) {
          fprintf(fichtm,"<hr  size=\"2\" color=\"#EC5E5E\">************ Results for covariates");
          for (cpt=1; cpt<=cptcoveff;cpt++) 
            fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtab[jj1][cpt]]);
          fprintf(fichtm," ************\n<hr size=\"2\" color=\"#EC5E5E\">");
        }
        for(cpt=1; cpt<=nlstate;cpt++) {
          fprintf(fichtm,"<br>- Observed (cross-sectional) and period (incidence based) \
   prevalence (with 95%% confidence interval) in state (%d): %s%d%d.png <br>\
   <img src=\"%s%d%d.png\">",cpt,subdirf2(optionfilefiname,"v"),cpt,jj1,subdirf2(optionfilefiname,"v"),cpt,jj1);  
        }
        fprintf(fichtm,"\n<br>- Total life expectancy by age and \
   health expectancies in states (1) and (2). If popbased=1 the smooth (due to the model) \
   true period expectancies (those weighted with period prevalences are also\
    drawn in addition to the population based expectancies computed using\
    observed and cahotic prevalences: %s%d.png<br>\
   <img src=\"%s%d.png\">",subdirf2(optionfilefiname,"e"),jj1,subdirf2(optionfilefiname,"e"),jj1);
      } /* end i1 */
    }/* End k1 */
    fprintf(fichtm,"</ul>");
    fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplot(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     for (cpt=1; cpt<= nlstate ; cpt ++) {
      for (k1=1; k1<= m ; k1 ++) {
        fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"v"),cpt,k1);
        fprintf(ficgp,"\n#set out \"v%s%d%d.png\" \n",optionfilefiname,cpt,k1);
        fprintf(ficgp,"set xlabel \"Age\" \n\
   set ylabel \"Probability\" \n\
   set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:2 \"\%%lf",ageminpar,fage,subdirf2(fileres,"vpl"),k1-1,k1-1);
   
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else        fprintf(ficgp," \%%*lf (\%%*lf)");
        }
        fprintf(ficgp,"\" t\"Period (stable) prevalence\" w l 0,\"%s\" every :::%d::%d u 1:($2+1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1);
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        } 
        fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       fprintf(ficgp,"\nset out \"%s%d.png\" \n",subdirf2(optionfilefiname,"e"),k1);
       fprintf(ficgp,"set ylabel \"Years\" \nset ter png small\nset size 0.65,0.65\nplot [%.f:%.f] ",ageminpar,fage);
       
       for (i=1; i<= nlstate+1 ; i ++) {
         k=2*i;
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:2 \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
         else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         fprintf(ficgp,"\" t\"\" w l 0,");
         fprintf(ficgp,"\"%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",subdirf2(fileres,"t"),k1-1,k1-1);
         for (j=1; j<= nlstate+1 ; j ++) {
           if (j==i) fprintf(ficgp," \%%lf (\%%lf)");
           else fprintf(ficgp," \%%*lf (\%%*lf)");
         }   
         if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
         else fprintf(ficgp,"\" t\"\" w l 0,");
       }
     }
     
     /*3eme*/
     
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<= nlstate ; cpt ++) {
         /*       k=2+nlstate*(2*cpt-2); */
         k=2+(nlstate+1)*(cpt-1);
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"exp"),cpt,k1);
         fprintf(ficgp,"set ter png small\n\
   set size 0.65,0.65\n\
   plot [%.f:%.f] \"%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",ageminpar,fage,subdirf2(fileres,"e"),k1-1,k1-1,k,cpt);
         /*fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d-2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:($%d+2*$%d) \"\%%lf ",fileres,k1-1,k1-1,k,k+1);
           for (i=1; i<= nlstate*2 ; i ++) fprintf(ficgp,"\%%lf (\%%lf) ");
           fprintf(ficgp,"\" t \"e%d1\" w l",cpt);
           
         */
         for (i=1; i< nlstate ; i ++) {
           fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+i,cpt,i+1);
           /*      fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+2*i,cpt,i+1);*/
           
         } 
         fprintf(ficgp," ,\"%s\" every :::%d::%d u 1:%d t \"e%d.\" w l",subdirf2(fileres,"e"),k1-1,k1-1,k+nlstate,cpt);
       }
     }
     
     /* CV preval stable (period) */
     for (k1=1; k1<= m ; k1 ++) { 
       for (cpt=1; cpt<=nlstate ; cpt ++) {
         k=3;
         fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"p"),cpt,k1);
         fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \n\
   set ter png small\nset size 0.65,0.65\n\
   unset log y\n\
   plot [%.f:%.f] \"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",ageminpar,agemaxpar,subdirf2(fileres,"pij"),k1,k+cpt+1,k+1);
         
         for (i=1; i< nlstate ; i ++)
           fprintf(ficgp,"+$%d",k+i+1);
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
         
         l=3+(nlstate+ndeath)*cpt;
         fprintf(ficgp,",\"%s\" u ($1==%d ? ($3):1/0):($%d/($%d",subdirf2(fileres,"pij"),k1,l+cpt+1,l+1);
         for (i=1; i< nlstate ; i ++) {
           l=3+(nlstate+ndeath)*cpt;
           fprintf(ficgp,"+$%d",l+i+1);
         }
         fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);   
       } 
     }  
     
     /* proba elementaires */
     for(i=1,jk=1; i <=nlstate; i++){
       for(k=1; k <=(nlstate+ndeath); k++){
         if (k != i) {
           for(j=1; j <=ncovmodel; j++){
             fprintf(ficgp,"p%d=%f ",jk,p[jk]);
             jk++; 
             fprintf(ficgp,"\n");
           }
         }
       }
      }
   
      for(ng=1; ng<=2;ng++){ /* Number of graphics: first is probabilities second is incidence per year*/
        for(jk=1; jk <=m; jk++) {
          fprintf(ficgp,"\nset out \"%s%d%d.png\" \n",subdirf2(optionfilefiname,"pe"),jk,ng); 
          if (ng==2)
            fprintf(ficgp,"\nset ylabel \"Quasi-incidence per year\"\n");
          else
            fprintf(ficgp,"\nset title \"Probability\"\n");
          fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65\nset log y\nplot  [%.f:%.f] ",ageminpar,agemaxpar);
          i=1;
          for(k2=1; k2<=nlstate; k2++) {
            k3=i;
            for(k=1; k<=(nlstate+ndeath); k++) {
              if (k != k2){
                if(ng==2)
                  fprintf(ficgp," %f*exp(p%d+p%d*x",YEARM/stepm,i,i+1);
                else
                  fprintf(ficgp," exp(p%d+p%d*x",i,i+1);
                ij=1;
                for(j=3; j <=ncovmodel; j++) {
                  if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                    fprintf(ficgp,"+p%d*%d*x",i+j-1,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                    ij++;
                  }
                  else
                    fprintf(ficgp,"+p%d*%d",i+j-1,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                }
                fprintf(ficgp,")/(1");
                
                for(k1=1; k1 <=nlstate; k1++){   
                  fprintf(ficgp,"+exp(p%d+p%d*x",k3+(k1-1)*ncovmodel,k3+(k1-1)*ncovmodel+1);
                  ij=1;
                  for(j=3; j <=ncovmodel; j++){
                    if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) {
                      fprintf(ficgp,"+p%d*%d*x",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][Tvar[j-2]]]);
                      ij++;
                    }
                    else
                      fprintf(ficgp,"+p%d*%d",k3+(k1-1)*ncovmodel+1+j-2,nbcode[Tvar[j-2]][codtab[jk][j-2]]);
                  }
                  fprintf(ficgp,")");
                }
                fprintf(ficgp,") t \"p%d%d\" ", k2,k);
                if ((k+k2)!= (nlstate*2+ndeath)) fprintf(ficgp,",");
                i=i+ncovmodel;
              }
            } /* end k */
          } /* end k2 */
        } /* end jk */
      } /* end ng */
      fflush(ficgp); 
   }  /* end gnuplot */
   
   
   /*************** Moving average **************/
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav){
   
     int i, cpt, cptcod;
     int modcovmax =1;
     int mobilavrange, mob;
     double age;
   
     modcovmax=2*cptcoveff;/* Max number of modalities. We suppose 
                              a covariate has 2 modalities */
     if (cptcovn<1) modcovmax=1; /* At least 1 pass */
   
     if(mobilav==1||mobilav ==3 ||mobilav==5 ||mobilav== 7){
       if(mobilav==1) mobilavrange=5; /* default */
       else mobilavrange=mobilav;
       for (age=bage; age<=fage; age++)
         for (i=1; i<=nlstate;i++)
           for (cptcod=1;cptcod<=modcovmax;cptcod++)
             mobaverage[(int)age][i][cptcod]=probs[(int)age][i][cptcod];
       /* We keep the original values on the extreme ages bage, fage and for 
          fage+1 and bage-1 we use a 3 terms moving average; for fage+2 bage+2
          we use a 5 terms etc. until the borders are no more concerned. 
       */ 
       for (mob=3;mob <=mobilavrange;mob=mob+2){
         for (age=bage+(mob-1)/2; age<=fage-(mob-1)/2; age++){
           for (i=1; i<=nlstate;i++){
             for (cptcod=1;cptcod<=modcovmax;cptcod++){
               mobaverage[(int)age][i][cptcod] =probs[(int)age][i][cptcod];
                 for (cpt=1;cpt<=(mob-1)/2;cpt++){
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age-cpt][i][cptcod];
                   mobaverage[(int)age][i][cptcod] +=probs[(int)age+cpt][i][cptcod];
                 }
               mobaverage[(int)age][i][cptcod]=mobaverage[(int)age][i][cptcod]/mob;
             }
           }
         }/* end age */
       }/* end mob */
     }else return -1;
     return 0;
   }/* End movingaverage */
   
   
   /************** Forecasting ******************/
   prevforecast(char fileres[], double anproj1, double mproj1, double jproj1, double ageminpar, double agemax, double dateprev1, double dateprev2, int mobilav, double bage, double fage, int firstpass, int lastpass, double anproj2, double p[], int cptcoveff){
     /* proj1, year, month, day of starting projection 
        agemin, agemax range of age
        dateprev1 dateprev2 range of dates during which prevalence is computed
        anproj2 year of en of projection (same day and month as proj1).
     */
     int yearp, stepsize, hstepm, nhstepm, j, k, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small\n set log y\n"); 
     fprintf(ficgp, "set size 0.65,0.65\n");
     fprintf(ficgp,"plot [%d:100] %lf*exp(%lf*(x-%d))",agegomp,p[1],p[2],agegomp);
   
   } 
   
   int readdata(char datafile[], int firstobs, int lastobs, int *imax)
   {
   
     /*-------- data file ----------*/
     FILE *fic;
     char dummy[]="                         ";
     int i, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);
             fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a status of wave %d. Setting maxwav=%d might be wrong.  Exiting.\n", strb, linei,i,line,j,maxwav);fflush(ficlog);
             return 1;
           }
         }
         s[j][i]=lval;
         
         strcpy(line,stra);
         cutv(stra, strb,line,' ');
         if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
         }
         else  if(iout=sscanf(strb,"%s.") != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of interview (mm/yyyy or .) at wave %d.  Exiting.\n",strb, linei,i, line,j);fflush(ficlog);
           return 1;
         }
         anint[j][i]= (double) year; 
         mint[j][i]= (double)month; 
         strcpy(line,stra);
       } /* ENd Waves */
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.",dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
           fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of death (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       andc[i]=(double) year; 
       moisdc[i]=(double) month; 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       if(iout=sscanf(strb,"%d/%d",&month, &year) != 0){
       }
       else  if(iout=sscanf(strb,"%s.") != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy or .).  Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
       }
       if (year==9999) {
         printf("Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given.  Exiting.\n",strb, linei,i,line);
         fprintf(ficlog,"Error reading data around '%s' at line number %ld for individual %d, '%s'\nShould be a date of birth (mm/yyyy) but at least the year of birth should be given. Exiting.\n",strb, linei,i,line);fflush(ficlog);
           return 1;
   
       }
       annais[i]=(double)(year);
       moisnais[i]=(double)(month); 
       strcpy(line,stra);
       
       cutv(stra, strb,line,' '); 
       errno=0;
       dval=strtod(strb,&endptr); 
       if( strb[0]=='\0' || (*endptr != '\0')){
         printf("Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %ld, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fflush(ficlog);
         return 1;
       }
       weight[i]=dval; 
       strcpy(line,stra);
       
       for (j=ncovcol;j>=1;j--){
         cutv(stra, strb,line,' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);
             fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\nShould be a covariate value (=0 for the reference or 1 for alternative).  Exiting.\n",lval, linei,i, line);fflush(ficlog);
             return 1;
           }
         }
         if(lval <-1 || lval >1){
           printf("Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);
           fprintf(ficlog,"Error reading data around '%d' at line number %ld for individual %d, '%s'\n \
    Should be a value of %d(nth) covariate (0 should be the value for the reference and 1\n \
    for the alternative. IMaCh does not build design variables automatically, do it yourself.\n \
    For example, for multinomial values like 1, 2 and 3,\n \
    build V1=0 V2=0 for the reference value (1),\n \
           V1=1 V2=0 for (2) \n \
    and V1=0 V2=1 for (3). V1=1 V2=1 should not exist and the corresponding\n \
    output of IMaCh is often meaningless.\n \
    Exiting.\n",lval,linei, i,line,j);fflush(ficlog);
           return 1;
         }
         covar[j][i]=(double)(lval);
         strcpy(line,stra);
       }  
       lstra=strlen(stra);
        
       if(lstra > 9){ /* More than 2**32 or max of what printf can write with %ld */
         stratrunc = &(stra[lstra-9]);
         num[i]=atol(stratrunc);
       }
       else
         num[i]=atol(stra);
       /*if((s[2][i]==2) && (s[3][i]==-1)&&(s[4][i]==9)){
         printf("%ld %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),weight[i], (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i])); ij=ij+1;}*/
       
       i=i+1;
     } /* End loop reading  data */
   
     *imax=i-1; /* Number of individuals */
     fclose(fic);
    
     return (0);
     endread:
       printf("Exiting readdata: ");
       fclose(fic);
       return (1);
   
   
   
   }
   
   int decodemodel ( char model[], int lastobs)
   {
     int i, j, k;
     int i1, j1, k1, k2;
     char modelsav[80];
      char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=1, k2=1;
       j=nbocc(model,'+'); /* j=Number of '+' */
       j1=nbocc(model,'*'); /* j1=Number of '*' */
       cptcovn=j+1; /* Number of covariates V1+V2*age+V3 =>(2 plus signs) + 1=3 
                     but the covariates which are product must be computed and stored. */
       cptcovprod=j1; /*Number of products  V1*V2 +v3*age = 2 */
       
       strcpy(modelsav,model); 
       if ((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);fflush(ficlog);
         return 1;
       }
       
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*    modelsav=V3*age+V2+V1+V4 strb=V3*age stra=V2+V1+V4 
           i=1 Tvar[1]=3 Tage[1]=1  
           i=2 Tvar[2]=2
           i=3 Tvar[3]=1
           i=4 Tvar[4]= 4
           i=5 Tvar[5]
         for (k=1; k<=cptcovn;k++) {
           cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
        */
       for(k=1; k<=(j+1);k++){
         cutv(strb,stra,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav=V3*age+V2+V1+V4 strb=V3*age stra=V2+V1+V4 
                                       */ 
         /* if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav);*/ /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /* Model includes a product V3*age+V2+V1+V4 strb=V3*age */
           cutv(strd,strc,strb,'*'); /* strd*strc  Vm*Vn: strb=V3*age strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /* Vn*age */
             cptcovprod--;
             cutv(strb,stre,strd,'V'); /* stre="V3" */
             Tvar[k]=atoi(stre);  /* V1+V3*age+V2 Tvar[2]=3, and Tvar[3]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] =2 */
             /*printf("stre=%s ", stre);*/
           }
           else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutv(strb,stre,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           }
           else {  /* Age is not in the model V1+V3*V2+V2  strb=V3*V2*/
             cutv(strb,stre,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=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]=k;  /* 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 (i=1; i<=lastobs;i++) /* Computes the new covariate which is a product of covar[n][i]* covar[m][i]
                                        and is stored at ncovol+k1 */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             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);*/
   
   
     return (0);
     endread:
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               /* printf(" 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);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax); 
   
     return (0);
     endread:
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4];
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile %s\n",optionfile);
       fprintf(ficlog,"Problem with optionfile %s\n",optionfile);
       fflush(ficlog);
       goto end;
     }
   
   
   
     strcpy(filereso,"o");
     strcat(filereso,fileres);
     if((ficparo=fopen(filereso,"w"))==NULL) { /* opened on subdirectory */
       printf("Problem with Output resultfile: %s\n", filereso);
       fprintf(ficlog,"Problem with Output resultfile: %s\n", filereso);
       fflush(ficlog);
       goto end;
     }
   
     /* Reads comments: lines beginning with '#' */
     numlinepar=0;
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
     fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d model=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);
     numlinepar++;
     printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model);
     fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fprintf(ficlog,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     fflush(ficlog);
     while((c=getc(ficpar))=='#' && c!= EOF){
       ungetc(c,ficpar);
       fgets(line, MAXLINE, ficpar);
       numlinepar++;
       puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n); 
     cptcovn=0; /*Number of covariates, i.e. number of '+' in model statement plus one, indepently of n in Vn*/
     /* v1+v2+v3+v2*v4+v5*age makes cptcovn = 5
        v1+v2*age+v2*v3 makes cptcovn = 3
     */
     if (strlen(model)>1) 
       cptcovn=nbocc(model,'+')+1;
     /* ncovprod */
     ncovmodel=2+cptcovn; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     nvar=ncovmodel-1; /* Suppressing age as a basic covariate */
     nforce= (nlstate+ndeath-1)*nlstate; /* Number of forces ij from state i to j */
     npar= nforce*ncovmodel; /* Number of parameters like aij*/
     if(npar >MAXPARM || nlstate >NLSTATEMAX || ndeath >NDEATHMAX || ncovmodel>NCOVMAX){
       printf("Too complex model for current IMaCh: npar=(nlstate+ndeath-1)*nlstate*ncovmodel=%d >= %d(MAXPARM) or nlstate=%d >= %d(NLSTATEMAX) or ndeath=%d >= %d(NDEATHMAX) or ncovmodel=(k+age+#of+signs)=%d(NCOVMAX) >= %d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fprintf(ficlog,"Too complex model for current IMaCh: %d >=%d(MAXPARM) or %d >=%d(NLSTATEMAX) or %d >=%d(NDEATHMAX) or %d(NCOVMAX) >=%d\n",npar, MAXPARM, nlstate, NLSTATEMAX, ndeath, NDEATHMAX, ncovmodel, NCOVMAX);
       fflush(stdout);
       fclose (ficlog);
       goto end;
     }
     delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     delti=delti3[1][1];
     /*delti=vector(1,npar); *//* Scale of each paramater (output from hesscov)*/
     if(mle==-1){ /* Print a wizard for help writing covariance matrix */
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-1, look at file %s for a template of covariance matrix \n",filereso);
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       fclose (ficparo);
       fclose (ficlog);
       goto end;
       exit(0);
     }
     else if(mle==-3) {
       prwizard(ncovmodel, nlstate, ndeath, model, ficparo);
       printf(" You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       fprintf(ficlog," You choose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       matcov=matrix(1,npar,1,npar);
     }
     else{
       /* Read guess parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
       
       param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
       for(i=1; i <=nlstate; i++){
         j=0;
         for(jj=1; jj <=nlstate+ndeath; jj++){
           if(jj==i) continue;
           j++;
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1 != i) && (j1 != j)){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n \
   It might be a problem of design; if ncovcol and the model are correct\n \
   run imach with mle=-1 to get a correct template of the parameter file.\n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           fprintf(ficparo,"%1d%1d",i1,j1);
           if(mle==1)
             printf("%1d%1d",i,j);
           fprintf(ficlog,"%1d%1d",i,j);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar," %lf",&param[i][j][k]);
             if(mle==1){
               printf(" %lf",param[i][j][k]);
               fprintf(ficlog," %lf",param[i][j][k]);
             }
             else
               fprintf(ficlog," %lf",param[i][j][k]);
             fprintf(ficparo," %lf",param[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           if(mle==1)
             printf("\n");
           fprintf(ficlog,"\n");
           fprintf(ficparo,"\n");
         }
       }  
       fflush(ficlog);
   
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
   
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath-1; j++){
           fscanf(ficpar,"%1d%1d",&i1,&j1);
           if ((i1-i)*(j1-j)!=0){
             printf("Error in line parameters number %d, %1d%1d instead of %1d%1d \n",numlinepar, i,j, i1, j1);
             exit(1);
           }
           printf("%1d%1d",i,j);
           fprintf(ficparo,"%1d%1d",i1,j1);
           fprintf(ficlog,"%1d%1d",i1,j1);
           for(k=1; k<=ncovmodel;k++){
             fscanf(ficpar,"%le",&delti3[i][j][k]);
             printf(" %le",delti3[i][j][k]);
             fprintf(ficparo," %le",delti3[i][j][k]);
             fprintf(ficlog," %le",delti3[i][j][k]);
           }
           fscanf(ficpar,"\n");
           numlinepar++;
           printf("\n");
           fprintf(ficparo,"\n");
           fprintf(ficlog,"\n");
         }
       }
       fflush(ficlog);
   
       delti=delti3[1][1];
   
   
       /* free_ma3x(delti3,1,nlstate,1,nlstate+ndeath-1,1,ncovmodel); */ /* Hasn't to to freed here otherwise delti is no more allocated */
     
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         puts(line);
         fputs(line,ficparo);
         fputs(line,ficlog);
       }
       ungetc(c,ficpar);
     
       matcov=matrix(1,npar,1,npar);
       for(i=1; i <=npar; i++)
         for(j=1; j <=npar; j++) matcov[i][j]=0.;
         
       for(i=1; i <=npar; i++){
         fscanf(ficpar,"%s",&str);
         if(mle==1)
           printf("%s",str);
         fprintf(ficlog,"%s",str);
         fprintf(ficparo,"%s",str);
         for(j=1; j <=i; j++){
           fscanf(ficpar," %le",&matcov[i][j]);
           if(mle==1){
             printf(" %.5le",matcov[i][j]);
           }
           fprintf(ficlog," %.5le",matcov[i][j]);
           fprintf(ficparo," %.5le",matcov[i][j]);
         }
         fscanf(ficpar,"\n");
         numlinepar++;
         if(mle==1)
           printf("\n");
         fprintf(ficlog,"\n");
         fprintf(ficparo,"\n");
       }
       for(i=1; i <=npar; i++)
         for(j=i+1;j<=npar;j++)
           matcov[i][j]=matcov[j][i];
       
       if(mle==1)
         printf("\n");
       fprintf(ficlog,"\n");
       
       fflush(ficlog);
       
       /*-------- Rewriting parameter file ----------*/
       strcpy(rfileres,"r");    /* "Rparameterfile */
       strcat(rfileres,optionfilefiname);    /* Parameter file first name*/
       strcat(rfileres,".");    /* */
       strcat(rfileres,optionfilext);    /* Other files have txt extension */
       if((ficres =fopen(rfileres,"w"))==NULL) {
         printf("Problem writing new parameter file: %s\n", fileres);goto end;
         fprintf(ficlog,"Problem writing new parameter file: %s\n", fileres);goto end;
       }
       fprintf(ficres,"#%s\n",version);
     }    /* End of mle != -3 */
   
   
     n= lastobs;
     num=lvector(1,n);
     moisnais=vector(1,n);
     annais=vector(1,n);
     moisdc=vector(1,n);
     andc=vector(1,n);
     agedc=vector(1,n);
     cod=ivector(1,n);
     weight=vector(1,n);
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
     mint=matrix(1,maxwav,1,n);
     anint=matrix(1,maxwav,1,n);
     s=imatrix(1,maxwav+1,1,n); /* s[i][j] health state for wave i and individual j */ 
     tab=ivector(1,NCOVMAX);
     ncodemax=ivector(1,8);
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. 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(decodemodel(model, lastobs) == 1)
       goto end;
   
       /*  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);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
   
      
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
   
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     if (cptcovn > 0) tricode(Tvar,nbcode,imx);
         
     codtab=imatrix(1,100,1,10); /* Cross tabulation to get the order of 
                                    the estimations*/
     h=0;
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=(m/pow(2,k));i++){ /* i=1 to 8/1=8; i=1 to 8/2=4; i=1 to 8/8=1 */ 
         for(j=1; j <= ncodemax[k]; j++){ /* For each modality of this covariate */
           for(cpt=1; cpt <=(m/pow(2,cptcoveff+1-k)); cpt++){  /* cpt=1 to 8/2**(3+1-1 or 3+1-3) =1 or 4 */ 
             h++;
             if (h>m) {
               h=1;
               codtab[h][k]=j;
               codtab[h][Tvar[k]]=j;
             }
             printf("h=%d k=%d j=%d codtab[h][k]=%d Tvar[k]=%d codtab[h][Tvar[k]]=%d \n",h, k,j,codtab[h][k],Tvar[k],codtab[h][Tvar[k]]);
           } 
         }
       }
     } 
     /* printf("codtab[1][2]=%d codtab[2][2]=%d",codtab[1][2],codtab[2][2]); 
        codtab[1][2]=1;codtab[2][2]=2; */
     /* for(i=1; i <=m ;i++){ 
        for(k=1; k <=cptcovn; k++){
          printf("i=%d k=%d %d %d ",i,k,codtab[i][k], cptcoveff);
        }
        printf("\n");
        }
        scanf("%d",i);*/
       
     /*------------ gnuplot -------------*/
     strcpy(optionfilegnuplot,optionfilefiname);
     if(mle==-3)
       strcat(optionfilegnuplot,"-mort");
     strcat(optionfilegnuplot,".gp");
   
     if((ficgp=fopen(optionfilegnuplot,"w"))==NULL) {
       printf("Problem with file %s",optionfilegnuplot);
     }
     else{
       fprintf(ficgp,"\n# %s\n", version); 
       fprintf(ficgp,"# %s\n", optionfilegnuplot); 
       fprintf(ficgp,"set missing 'NaNq'\n");
     }
     /*  fclose(ficgp);*/
     /*--------- index.htm --------*/
   
     strcpy(optionfilehtm,optionfilefiname); /* Main html file */
     if(mle==-3)
       strcat(optionfilehtm,"-mort");
     strcat(optionfilehtm,".htm");
     if((fichtm=fopen(optionfilehtm,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtm);
       exit(0);
     }
   
     strcpy(optionfilehtmcov,optionfilefiname); /* Only for matrix of covariance */
     strcat(optionfilehtmcov,"-cov.htm");
     if((fichtmcov=fopen(optionfilehtmcov,"w"))==NULL)    {
       printf("Problem with %s \n",optionfilehtmcov), exit(0);
     }
     else{
     fprintf(fichtmcov,"<html><head>\n<title>IMaCh Cov %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n",\
             optionfilehtmcov,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model);
     }
   
     fprintf(fichtm,"<html><head>\n<title>IMaCh %s</title></head>\n <body><font size=\"2\">%s <br> %s</font> \
   <hr size=\"2\" color=\"#EC5E5E\"> \n\
   Title=%s <br>Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s<br>\n\
   \n\
   <hr  size=\"2\" color=\"#EC5E5E\">\
    <ul><li><h4>Parameter files</h4>\n\
    - Parameter file: <a href=\"%s.%s\">%s.%s</a><br>\n\
    - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>\n\
    - Log file of the run: <a href=\"%s\">%s</a><br>\n\
    - Gnuplot file name: <a href=\"%s\">%s</a><br>\n\
    - Date and time at start: %s</ul>\n",\
             optionfilehtm,version,fullversion,title,datafile,firstpass,lastpass,stepm, weightopt, model,\
             optionfilefiname,optionfilext,optionfilefiname,optionfilext,\
             fileres,fileres,\
             filelog,filelog,optionfilegnuplot,optionfilegnuplot,strstart);
     fflush(fichtm);
   
     strcpy(pathr,path);
     strcat(pathr,optionfilefiname);
     chdir(optionfilefiname); /* Move to directory named optionfile */
     
     /* Calculates basic frequencies. Computes observed prevalence at single age
        and prints on file fileres'p'. */
     freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint,strstart);
   
     fprintf(fichtm,"\n");
     fprintf(fichtm,"<br>Total number of observations=%d <br>\n\
   Youngest age at first (selected) pass %.2f, oldest age %.2f<br>\n\
   Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf<br>\n",\
             imx,agemin,agemax,jmin,jmax,jmean);
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
       oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
       
      
     /* For Powell, parameters are in a vector p[] starting at p[1]
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
   
     globpr=0; /* To get the number ipmx of contributions and the sum of weights*/
   
     if (mle==-3){
       ximort=matrix(1,NDIM,1,NDIM); 
   /*     ximort=gsl_matrix_alloc(1,NDIM,1,NDIM); */
       cens=ivector(1,n);
       ageexmed=vector(1,n);
       agecens=vector(1,n);
       dcwave=ivector(1,n);
    
       for (i=1; i<=imx; i++){
         dcwave[i]=-1;
         for (m=firstpass; m<=lastpass; m++)
           if (s[m][i]>nlstate) {
             dcwave[i]=m;
             /*    printf("i=%d j=%d s=%d dcwave=%d\n",i,j, s[j][i],dcwave[i]);*/
             break;
           }
       }
   
       for (i=1; i<=imx; i++) {
         if (wav[i]>0){
           ageexmed[i]=agev[mw[1][i]][i];
           j=wav[i];
           agecens[i]=1.; 
   
           if (ageexmed[i]> 1 && wav[i] > 0){
             agecens[i]=agev[mw[j][i]][i];
             cens[i]= 1;
           }else if (ageexmed[i]< 1) 
             cens[i]= -1;
           if (agedc[i]< AGESUP && agedc[i]>1 && dcwave[i]>firstpass && dcwave[i]<=lastpass)
             cens[i]=0 ;
         }
         else cens[i]=-1;
       }
       
       for (i=1;i<=NDIM;i++) {
         for (j=1;j<=NDIM;j++)
           ximort[i][j]=(i == j ? 1.0 : 0.0);
       }
       
       p[1]=0.0268; p[NDIM]=0.083;
       /*printf("%lf %lf", p[1], p[2]);*/
       
       
   #ifdef GSL
       printf("GSL optimization\n");  fprintf(ficlog,"Powell\n");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       estepm=0;
       fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf estepm=%d\n",&ageminpar,&agemaxpar, &bage, &fage, &estepm);
       if (estepm==0 || estepm < stepm) estepm=stepm;
       if (fage <= 2) {
         bage = ageminpar;
         fage = agemaxpar;
       }
       
       fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
       fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f estepm=%d\n",ageminpar,agemaxpar,bage,fage, estepm);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"begin-prev-date=%lf/%lf/%lf end-prev-date=%lf/%lf/%lf mov_average=%d\n",&jprev1, &mprev1,&anprev1,&jprev2, &mprev2,&anprev2,&mobilav);
       fprintf(ficparo,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficres,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       printf("begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       fprintf(ficlog,"begin-prev-date=%.lf/%.lf/%.lf end-prev-date=%.lf/%.lf/%.lf mov_average=%d\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,mobilav);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       
       dateprev1=anprev1+(mprev1-1)/12.+(jprev1-1)/365.;
       dateprev2=anprev2+(mprev2-1)/12.+(jprev2-1)/365.;
       
       fscanf(ficpar,"pop_based=%d\n",&popbased);
       fprintf(ficparo,"pop_based=%d\n",popbased);   
       fprintf(ficres,"pop_based=%d\n",popbased);   
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         puts(line);
         fputs(line,ficparo);
       }
       ungetc(c,ficpar);
       
       fscanf(ficpar,"prevforecast=%d starting-proj-date=%lf/%lf/%lf final-proj-date=%lf/%lf/%lf mobil_average=%d\n",&prevfcast,&jproj1,&mproj1,&anproj1,&jproj2,&mproj2,&anproj2,&mobilavproj);
       fprintf(ficparo,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       printf("prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficlog,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       fprintf(ficres,"prevforecast=%d starting-proj-date=%.lf/%.lf/%.lf final-proj-date=%.lf/%.lf/%.lf mobil_average=%d\n",prevfcast,jproj1,mproj1,anproj1,jproj2,mproj2,anproj2,mobilavproj);
       /* day and month of proj2 are not used but only year anproj2.*/
       
       
       
       /*  freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvaraff,nbcode, ncodemax,mint,anint);*/
       /*,dateprev1,dateprev2,jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplot(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtml(fileres,title,datafile, firstpass, lastpass, stepm, weightopt,\
                    model,imx,jmin,jmax,jmean,rfileres,popforecast,estepm,\
                    jprev1,mprev1,anprev1,jprev2,mprev2,anprev2);
         
      /*------------ free_vector  -------------*/
      /*  chdir(path); */
    
       free_ivector(wav,1,imx);
       free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(bh,1,lastpass-firstpass+1,1,imx);
       free_imatrix(mw,1,lastpass-firstpass+1,1,imx);   
       free_lvector(num,1,n);
       free_vector(agedc,1,n);
       /*free_matrix(covar,0,NCOVMAX,1,n);*/
       /*free_matrix(covar,1,NCOVMAX,1,n);*/
       fclose(ficparo);
       fclose(ficres);
   
   
       /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     
       strcpy(filerespl,"pl");
       strcat(filerespl,fileres);
       if((ficrespl=fopen(filerespl,"w"))==NULL) {
         printf("Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
         fprintf(ficlog,"Problem with period (stable) prevalence resultfile: %s\n", filerespl);goto end;
       }
       printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
       pstamp(ficrespl);
       fprintf(ficrespl,"# Period (stable) prevalence \n");
       fprintf(ficrespl,"#Age ");
       for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
       fprintf(ficrespl,"\n");
     
       prlim=matrix(1,nlstate,1,nlstate);
   
       agebase=ageminpar;
       agelim=agemaxpar;
       ftolpl=1.e-10;
       i1=cptcoveff;
       if (cptcovn < 1){i1=1;}
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           /* to clean */
           printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,codtab[cptcod][cptcov],nbcode);
           fprintf(ficrespl,"\n#******");
           printf("\n#******");
           fprintf(ficlog,"\n#******");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficrespl," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             printf(" V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficlog," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficrespl,"******\n");
           printf("******\n");
           fprintf(ficlog,"******\n");
           
           for (age=agebase; age<=agelim; age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
             fprintf(ficrespl,"%.0f ",age );
             for(j=1;j<=cptcoveff;j++)
               fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             for(i=1; i<=nlstate;i++)
               fprintf(ficrespl," %.5f", prlim[i][i]);
             fprintf(ficrespl,"\n");
           }
         }
       }
       fclose(ficrespl);
   
       /*------------- h Pij x at various ages ------------*/
     
       strcpy(filerespij,"pij");  strcat(filerespij,fileres);
       if((ficrespij=fopen(filerespij,"w"))==NULL) {
         printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
         fprintf(ficlog,"Problem with Pij resultfile: %s\n", filerespij);goto end;
       }
       printf("Computing pij: result on file '%s' \n", filerespij);
       fprintf(ficlog,"Computing pij: result on file '%s' \n", filerespij);
     
       stepsize=(int) (stepm+YEARM-1)/YEARM;
       /*if (stepm<=24) stepsize=2;*/
   
       agelim=AGESUP;
       hstepm=stepsize*YEARM; /* Every year of age */
       hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
   
       /* hstepm=1;   aff par mois*/
       pstamp(ficrespij);
       fprintf(ficrespij,"#****** h Pij x Probability to be in state j at age x+h being in i at x ");
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficrespij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrespij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrespij,"******\n");
           
           for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
             nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
   
             /*      nhstepm=nhstepm*YEARM; aff par mois*/
   
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             fprintf(ficrespij,"# Cov Agex agex+h hpijx with i,j=");
             for(i=1; i<=nlstate;i++)
               for(j=1; j<=nlstate+ndeath;j++)
                 fprintf(ficrespij," %1d-%1d",i,j);
             fprintf(ficrespij,"\n");
             for (h=0; h<=nhstepm; h++){
               fprintf(ficrespij,"%d %3.f %3.f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );
               for(i=1; i<=nlstate;i++)
                 for(j=1; j<=nlstate+ndeath;j++)
                   fprintf(ficrespij," %.5f", p3mat[i][j][h]);
               fprintf(ficrespij,"\n");
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             fprintf(ficrespij,"\n");
           }
         }
       }
   
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
       fclose(ficrespij);
   
       probs= ma3x(1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
       for(i=1;i<=AGESUP;i++)
         for(j=1;j<=NCOVMAX;j++)
           for(k=1;k<=NCOVMAX;k++)
             probs[i][j][k]=0.;
   
       /*---------- Forecasting ------------------*/
       /*if((stepm == 1) && (strcmp(model,".")==0)){*/
       if(prevfcast==1){
         /*    if(stepm ==1){*/
         prevforecast(fileres, anproj1, mproj1, jproj1, agemin, agemax, dateprev1, dateprev2, mobilavproj, bage, fage, firstpass, lastpass, anproj2, p, cptcoveff);
         /* (popforecast==1) populforecast(fileres, anpyram,mpyram,jpyram, agemin,agemax, dateprev1, dateprev2,mobilav, agedeb, fage, popforecast, popfile, anpyram1,p, i1);*/
         /*      }  */
         /*      else{ */
         /*        erreur=108; */
         /*        printf("Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*        fprintf(ficlog,"Warning %d!! You can only forecast the prevalences if the optimization\n  has been performed with stepm = 1 (month) instead of %d or model=. instead of '%s'\n", erreur, stepm, model); */
         /*      } */
       }
     
   
       /* Computes prevalence between agemin (i.e minimal age computed) and no more ageminpar */
   
       prevalence(probs, agemin, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
       /*  printf("ageminpar=%f, agemax=%f, s[lastpass][imx]=%d, agev[lastpass][imx]=%f, nlstate=%d, imx=%d,  mint[lastpass][imx]=%f, anint[lastpass][imx]=%f,dateprev1=%f, dateprev2=%f, firstpass=%d, lastpass=%d\n",\
           ageminpar, agemax, s[lastpass][imx], agev[lastpass][imx], nlstate, imx, mint[lastpass][imx],anint[lastpass][imx], dateprev1, dateprev2, firstpass, lastpass);
       */
   
       if (mobilav!=0) {
         mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
         if (movingaverage(probs, bage, fage, mobaverage,mobilav)!=0){
           fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
           printf(" Error in movingaverage mobilav=%d\n",mobilav);
         }
       }
   
   
       /*---------- Health expectancies, no variances ------------*/
   
       strcpy(filerese,"e");
       strcat(filerese,fileres);
       if((ficreseij=fopen(filerese,"w"))==NULL) {
         printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
         fprintf(ficlog,"Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
       }
       printf("Computing Health Expectancies: result on file '%s' \n", filerese);
       fprintf(ficlog,"Computing Health Expectancies: result on file '%s' \n", filerese);
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficreseij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficreseij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficreseij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           evsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, strstart);  
         
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
         }
       }
       fclose(ficreseij);
   
   
       /*---------- Health expectancies and variances ------------*/
   
   
       strcpy(filerest,"t");
       strcat(filerest,fileres);
       if((ficrest=fopen(filerest,"w"))==NULL) {
         printf("Problem with total LE resultfile: %s\n", filerest);goto end;
         fprintf(ficlog,"Problem with total LE resultfile: %s\n", filerest);goto end;
       }
       printf("Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
       fprintf(ficlog,"Computing Total Life expectancies with their standard errors: file '%s' \n", filerest); 
   
   
       strcpy(fileresstde,"stde");
       strcat(fileresstde,fileres);
       if((ficresstdeij=fopen(fileresstde,"w"))==NULL) {
         printf("Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
         fprintf(ficlog,"Problem with Health Exp. and std errors resultfile: %s\n", fileresstde); exit(0);
       }
       printf("Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
       fprintf(ficlog,"Computing Health Expectancies and standard errors: result on file '%s' \n", fileresstde);
   
       strcpy(filerescve,"cve");
       strcat(filerescve,fileres);
       if((ficrescveij=fopen(filerescve,"w"))==NULL) {
         printf("Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
         fprintf(ficlog,"Problem with Covar. Health Exp. resultfile: %s\n", filerescve); exit(0);
       }
       printf("Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
       fprintf(ficlog,"Computing Covar. of Health Expectancies: result on file '%s' \n", filerescve);
   
       strcpy(fileresv,"v");
       strcat(fileresv,fileres);
       if((ficresvij=fopen(fileresv,"w"))==NULL) {
         printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
         fprintf(ficlog,"Problem with variance resultfile: %s\n", fileresv);exit(0);
       }
       printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
       fprintf(ficlog,"Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1; 
           fprintf(ficrest,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficrest,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficrest,"******\n");
   
           fprintf(ficresstdeij,"\n#****** ");
           fprintf(ficrescveij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) {
             fprintf(ficresstdeij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
             fprintf(ficrescveij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           }
           fprintf(ficresstdeij,"******\n");
           fprintf(ficrescveij,"******\n");
   
           fprintf(ficresvij,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvij,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvij,"******\n");
   
           eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           cvevsij(eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k, estepm, delti, matcov, strstart);  
    
           vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
           pstamp(ficrest);
           for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
             oldm=oldms;savm=savms;
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);   fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         }
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,15,1,2);
       free_imatrix(s,1,maxwav+1,1,n);
       free_matrix(anint,1,maxwav,1,n); 
       free_matrix(mint,1,maxwav,1,n);
       free_ivector(cod,1,n);
       free_ivector(tab,1,NCOVMAX);
       fclose(ficresstdeij);
       fclose(ficrescveij);
       fclose(ficresvij);
       fclose(ficrest);
       fclose(ficpar);
     
       /*------- Variance of period (stable) prevalence------*/   
   
       strcpy(fileresvpl,"vpl");
       strcat(fileresvpl,fileres);
       if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
         printf("Problem with variance of period (stable) prevalence  resultfile: %s\n", fileresvpl);
         exit(0);
       }
       printf("Computing Variance-covariance of period (stable) prevalence: file '%s' \n", fileresvpl);
   
       for(cptcov=1,k=0;cptcov<=i1;cptcov++){
         for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){
           k=k+1;
           fprintf(ficresvpl,"\n#****** ");
           for(j=1;j<=cptcoveff;j++) 
             fprintf(ficresvpl,"V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
           fprintf(ficresvpl,"******\n");
         
           varpl=matrix(1,nlstate,(int) bage, (int) fage);
           oldm=oldms;savm=savms;
           varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);
           free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
         }
       }
   
       fclose(ficresvpl);
   
       /*---------- End : free ----------------*/
       if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       free_ma3x(probs,1,AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     }  /* mle==-3 arrives here for freeing */
    endfree:
     free_matrix(prlim,1,nlstate,1,nlstate);
       free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
       free_matrix(covar,0,NCOVMAX,1,n);
       free_matrix(matcov,1,npar,1,npar);
       /*free_vector(delti,1,npar);*/
       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
       free_matrix(agev,1,maxwav,1,imx);
       free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);
   
       free_ivector(ncodemax,1,8);
       free_ivector(Tvar,1,15);
       free_ivector(Tprod,1,15);
       free_ivector(Tvaraff,1,15);
       free_ivector(Tage,1,15);
   
       free_imatrix(nbcode,0,NCOVMAX,0,NCOVMAX);
       free_imatrix(codtab,1,100,1,10);
     fflush(fichtm);
     fflush(ficgp);
     
   
     if((nberr >0) || (nbwarn>0)){
       printf("End of Imach with %d errors and/or %d warnings\n",nberr,nbwarn);
       fprintf(ficlog,"End of Imach with %d errors and/or warnings %d\n",nberr,nbwarn);
     }else{
       printf("End of Imach\n");
       fprintf(ficlog,"End of Imach\n");
     }
     printf("See log file on %s\n",filelog);
     /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
     (void) gettimeofday(&end_time,&tzp);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %d Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error gnuplot program not found: %s Environment GNUPLOTBIN not set.\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #ifdef UNIX
       strcpy(plotcmd,GNUPLOTPROGRAM);
       if(!stat(plotcmd,&info)){
         printf("Error gnuplot program not found: %s\n",plotcmd);fflush(stdout);
       }else
         strcpy(pplotcmd,plotcmd);
   #endif
     }else
       strcpy(pplotcmd,plotcmd);
     
     sprintf(plotcmd,"%s %s",pplotcmd, optionfilegnuplot);
     printf("Starting graphs with: %s\n",plotcmd);fflush(stdout);
   
     if((outcmd=system(plotcmd)) != 0){
       printf("\n Problem with gnuplot\n");
     }
     printf(" Wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit output files, g to graph again and q for exiting: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
         printf("Starting browser with: %s",optionfilehtm);fflush(stdout);
         system(optionfilehtm);
       }
       else if (z[0] == 'g') system(plotcmd);
       else if (z[0] == 'q') exit(0);
     }
     end:
     while (z[0] != 'q') {
       printf("\nType  q for exiting: ");
       scanf("%s",z);
     }
   }
   
   
   

Removed from v.1.43  
changed lines
  Added in v.1.136


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