Diff for /imach/src/imach.c between versions 1.4 and 1.168

version 1.4, 2001/05/02 17:34:41 version 1.168, 2014/12/22 15:17:42
Line 1 Line 1
      /* $Id$
 /*********************** Imach **************************************            $State$
   This program computes Healthy Life Expectancies from cross-longitudinal    $Log$
   data. Cross-longitudinal consist in a first survey ("cross") where    Revision 1.168  2014/12/22 15:17:42  brouard
   individuals from different ages are interviewed on their health status    Summary: udate
   or degree of  disability. At least a second wave of interviews  
   ("longitudinal") should  measure each new individual health status.    Revision 1.167  2014/12/22 13:50:56  brouard
   Health expectancies are computed from the transistions observed between    Summary: Testing uname and compiler version and if compiled 32 or 64
   waves and are computed for each degree of severity of disability (number  
   of life states). More degrees you consider, more time is necessary to    Testing on Linux 64
   reach the Maximum Likelihood of the parameters involved in the model.  
   The simplest model is the multinomial logistic model where pij is    Revision 1.166  2014/12/22 11:40:47  brouard
   the probabibility to be observed in state j at the second wave conditional    *** empty log message ***
   to be observed in state i at the first wave. Therefore the model is:  
   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex'    Revision 1.165  2014/12/16 11:20:36  brouard
   is a covariate. If you want to have a more complex model than "constant and    Summary: After compiling on Visual C
   age", you should modify the program where the markup  
     *Covariates have to be included here again* invites you to do it.    * imach.c (Module): Merging 1.61 to 1.162
   More covariates you add, less is the speed of the convergence.  
     Revision 1.164  2014/12/16 10:52:11  brouard
   The advantage that this computer programme claims, comes from that if the    Summary: Merging with Visual C after suppressing some warnings for unused variables. Also fixing Saito's bug 0.98Xn
   delay between waves is not identical for each individual, or if some  
   individual missed an interview, the information is not rounded or lost, but    * imach.c (Module): Merging 1.61 to 1.162
   taken into account using an interpolation or extrapolation.  
   hPijx is the probability to be    Revision 1.163  2014/12/16 10:30:11  brouard
   observed in state i at age x+h conditional to the observed state i at age    * imach.c (Module): Merging 1.61 to 1.162
   x. The delay 'h' can be split into an exact number (nh*stepm) of  
   unobserved intermediate  states. This elementary transition (by month or    Revision 1.162  2014/09/25 11:43:39  brouard
   quarter trimester, semester or year) is model as a multinomial logistic.    Summary: temporary backup 0.99!
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices  
   and the contribution of each individual to the likelihood is simply hPijx.    Revision 1.1  2014/09/16 11:06:58  brouard
     Summary: With some code (wrong) for nlopt
   Also this programme outputs the covariance matrix of the parameters but also  
   of the life expectancies. It also computes the prevalence limits.    Author:
    
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    Revision 1.161  2014/09/15 20:41:41  brouard
            Institut national d'études démographiques, Paris.    Summary: Problem with macro SQR on Intel compiler
   This software have been partly granted by Euro-REVES, a concerted action  
   from the European Union.    Revision 1.160  2014/09/02 09:24:05  brouard
   It is copyrighted identically to a GNU software product, ie programme and    *** empty log message ***
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Revision 1.159  2014/09/01 10:34:10  brouard
   **********************************************************************/    Summary: WIN32
      Author: Brouard
 #include <math.h>  
 #include <stdio.h>    Revision 1.158  2014/08/27 17:11:51  brouard
 #include <stdlib.h>    *** empty log message ***
 #include <unistd.h>  
     Revision 1.157  2014/08/27 16:26:55  brouard
 #define MAXLINE 256    Summary: Preparing windows Visual studio version
 #define FILENAMELENGTH 80    Author: Brouard
 /*#define DEBUG*/  
 #define windows    In order to compile on Visual studio, time.h is now correct and time_t
     and tm struct should be used. difftime should be used but sometimes I
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    just make the differences in raw time format (time(&now).
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */    Trying to suppress #ifdef LINUX
     Add xdg-open for __linux in order to open default browser.
 #define NINTERVMAX 8  
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */    Revision 1.156  2014/08/25 20:10:10  brouard
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    *** empty log message ***
 #define NCOVMAX 8 /* Maximum number of covariates */  
 #define MAXN 20000    Revision 1.155  2014/08/25 18:32:34  brouard
 #define YEARM 12. /* Number of months per year */    Summary: New compile, minor changes
 #define AGESUP 130    Author: Brouard
 #define AGEBASE 40  
     Revision 1.154  2014/06/20 17:32:08  brouard
     Summary: Outputs now all graphs of convergence to period prevalence
 int nvar;  
 static int cptcov;    Revision 1.153  2014/06/20 16:45:46  brouard
 int cptcovn;    Summary: If 3 live state, convergence to period prevalence on same graph
 int npar=NPARMAX;    Author: Brouard
 int nlstate=2; /* Number of live states */  
 int ndeath=1; /* Number of dead states */    Revision 1.152  2014/06/18 17:54:09  brouard
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   
 int *wav; /* Number of waves for this individuual 0 is possible */    Revision 1.151  2014/06/18 16:43:30  brouard
 int maxwav; /* Maxim number of waves */    *** empty log message ***
 int mle, weightopt;  
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    Revision 1.150  2014/06/18 16:42:35  brouard
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Author: brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */  
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    Revision 1.149  2014/06/18 15:51:14  brouard
 FILE *ficgp, *fichtm;    Summary: Some fixes in parameter files errors
 FILE *ficreseij;    Author: Nicolas Brouard
   char filerese[FILENAMELENGTH];  
  FILE  *ficresvij;    Revision 1.148  2014/06/17 17:38:48  brouard
   char fileresv[FILENAMELENGTH];    Summary: Nothing new
  FILE  *ficresvpl;    Author: Brouard
   char fileresvpl[FILENAMELENGTH];  
     Just a new packaging for OS/X version 0.98nS
   
     Revision 1.147  2014/06/16 10:33:11  brouard
     *** empty log message ***
 #define NR_END 1  
 #define FREE_ARG char*    Revision 1.146  2014/06/16 10:20:28  brouard
 #define FTOL 1.0e-10    Summary: Merge
     Author: Brouard
 #define NRANSI  
 #define ITMAX 200    Merge, before building revised version.
   
 #define TOL 2.0e-4    Revision 1.145  2014/06/10 21:23:15  brouard
     Summary: Debugging with valgrind
 #define CGOLD 0.3819660    Author: Nicolas Brouard
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Lot of changes in order to output the results with some covariates
     After the Edimburgh REVES conference 2014, it seems mandatory to
 #define GOLD 1.618034    improve the code.
 #define GLIMIT 100.0    No more memory valgrind error but a lot has to be done in order to
 #define TINY 1.0e-20    continue the work of splitting the code into subroutines.
     Also, decodemodel has been improved. Tricode is still not
 static double maxarg1,maxarg2;    optimal. nbcode should be improved. Documentation has been added in
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))    the source code.
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))  
      Revision 1.143  2014/01/26 09:45:38  brouard
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 #define rint(a) floor(a+0.5)  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 static double sqrarg;    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)  
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    Revision 1.142  2014/01/26 03:57:36  brouard
     Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 int imx;  
 int stepm;    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 /* Stepm, step in month: minimum step interpolation*/  
     Revision 1.141  2014/01/26 02:42:01  brouard
 int m,nb;    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Revision 1.140  2011/09/02 10:37:54  brouard
 double **pmmij;    Summary: times.h is ok with mingw32 now.
   
 double *weight;    Revision 1.139  2010/06/14 07:50:17  brouard
 int **s; /* Status */    After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 double *agedc, **covar, idx;    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 int **nbcode, *Tcode, *Tvar, **codtab;  
     Revision 1.138  2010/04/30 18:19:40  brouard
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    *** empty log message ***
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.137  2010/04/29 18:11:38  brouard
     (Module): Checking covariates for more complex models
 /******************************************/    than V1+V2. A lot of change to be done. Unstable.
   
 void replace(char *s, char*t)    Revision 1.136  2010/04/26 20:30:53  brouard
 {    (Module): merging some libgsl code. Fixing computation
   int i;    of likelione (using inter/intrapolation if mle = 0) in order to
   int lg=20;    get same likelihood as if mle=1.
   i=0;    Some cleaning of code and comments added.
   lg=strlen(t);  
   for(i=0; i<= lg; i++) {    Revision 1.135  2009/10/29 15:33:14  brouard
     (s[i] = t[i]);    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
     if (t[i]== '\\') s[i]='/';  
   }    Revision 1.134  2009/10/29 13:18:53  brouard
 }    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   
 int nbocc(char *s, char occ)    Revision 1.133  2009/07/06 10:21:25  brouard
 {    just nforces
   int i,j=0;  
   int lg=20;    Revision 1.132  2009/07/06 08:22:05  brouard
   i=0;    Many tings
   lg=strlen(s);  
   for(i=0; i<= lg; i++) {    Revision 1.131  2009/06/20 16:22:47  brouard
   if  (s[i] == occ ) j++;    Some dimensions resccaled
   }  
   return j;    Revision 1.130  2009/05/26 06:44:34  brouard
 }    (Module): Max Covariate is now set to 20 instead of 8. A
     lot of cleaning with variables initialized to 0. Trying to make
 void cutv(char *u,char *v, char*t, char occ)    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 {  
   int i,lg,j,p;    Revision 1.129  2007/08/31 13:49:27  lievre
   i=0;    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
   for(j=0; j<=strlen(t)-1; j++) {  
     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1;    Revision 1.128  2006/06/30 13:02:05  brouard
   }    (Module): Clarifications on computing e.j
   
   lg=strlen(t);    Revision 1.127  2006/04/28 18:11:50  brouard
   for(j=0; j<p; j++) {    (Module): Yes the sum of survivors was wrong since
     (u[j] = t[j]);    imach-114 because nhstepm was no more computed in the age
     u[p]='\0';    loop. Now we define nhstepma in the age loop.
   }    (Module): In order to speed up (in case of numerous covariates) we
     compute health expectancies (without variances) in a first step
    for(j=0; j<= lg; j++) {    and then all the health expectancies with variances or standard
     if (j>=(p+1))(v[j-p-1] = t[j]);    deviation (needs data from the Hessian matrices) which slows the
   }    computation.
 }    In the future we should be able to stop the program is only health
     expectancies and graph are needed without standard deviations.
 /********************** nrerror ********************/  
     Revision 1.126  2006/04/28 17:23:28  brouard
 void nrerror(char error_text[])    (Module): Yes the sum of survivors was wrong since
 {    imach-114 because nhstepm was no more computed in the age
   fprintf(stderr,"ERREUR ...\n");    loop. Now we define nhstepma in the age loop.
   fprintf(stderr,"%s\n",error_text);    Version 0.98h
   exit(1);  
 }    Revision 1.125  2006/04/04 15:20:31  lievre
 /*********************** vector *******************/    Errors in calculation of health expectancies. Age was not initialized.
 double *vector(int nl, int nh)    Forecasting file added.
 {  
   double *v;    Revision 1.124  2006/03/22 17:13:53  lievre
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    Parameters are printed with %lf instead of %f (more numbers after the comma).
   if (!v) nrerror("allocation failure in vector");    The log-likelihood is printed in the log file
   return v-nl+NR_END;  
 }    Revision 1.123  2006/03/20 10:52:43  brouard
     * imach.c (Module): <title> changed, corresponds to .htm file
 /************************ free vector ******************/    name. <head> headers where missing.
 void free_vector(double*v, int nl, int nh)  
 {    * imach.c (Module): Weights can have a decimal point as for
   free((FREE_ARG)(v+nl-NR_END));    English (a comma might work with a correct LC_NUMERIC environment,
 }    otherwise the weight is truncated).
     Modification of warning when the covariates values are not 0 or
 /************************ivector *******************************/    1.
 int *ivector(long nl,long nh)    Version 0.98g
 {  
   int *v;    Revision 1.122  2006/03/20 09:45:41  brouard
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));    (Module): Weights can have a decimal point as for
   if (!v) nrerror("allocation failure in ivector");    English (a comma might work with a correct LC_NUMERIC environment,
   return v-nl+NR_END;    otherwise the weight is truncated).
 }    Modification of warning when the covariates values are not 0 or
     1.
 /******************free ivector **************************/    Version 0.98g
 void free_ivector(int *v, long nl, long nh)  
 {    Revision 1.121  2006/03/16 17:45:01  lievre
   free((FREE_ARG)(v+nl-NR_END));    * imach.c (Module): Comments concerning covariates added
 }  
     * imach.c (Module): refinements in the computation of lli if
 /******************* imatrix *******************************/    status=-2 in order to have more reliable computation if stepm is
 int **imatrix(long nrl, long nrh, long ncl, long nch)    not 1 month. Version 0.98f
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {    Revision 1.120  2006/03/16 15:10:38  lievre
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    (Module): refinements in the computation of lli if
   int **m;    status=-2 in order to have more reliable computation if stepm is
      not 1 month. Version 0.98f
   /* allocate pointers to rows */  
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));    Revision 1.119  2006/03/15 17:42:26  brouard
   if (!m) nrerror("allocation failure 1 in matrix()");    (Module): Bug if status = -2, the loglikelihood was
   m += NR_END;    computed as likelihood omitting the logarithm. Version O.98e
   m -= nrl;  
      Revision 1.118  2006/03/14 18:20:07  brouard
      (Module): varevsij Comments added explaining the second
   /* allocate rows and set pointers to them */    table of variances if popbased=1 .
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    (Module): Function pstamp added
   m[nrl] += NR_END;    (Module): Version 0.98d
   m[nrl] -= ncl;  
      Revision 1.117  2006/03/14 17:16:22  brouard
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;    (Module): varevsij Comments added explaining the second
      table of variances if popbased=1 .
   /* return pointer to array of pointers to rows */    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
   return m;    (Module): Function pstamp added
 }    (Module): Version 0.98d
   
 /****************** free_imatrix *************************/    Revision 1.116  2006/03/06 10:29:27  brouard
 void free_imatrix(m,nrl,nrh,ncl,nch)    (Module): Variance-covariance wrong links and
       int **m;    varian-covariance of ej. is needed (Saito).
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */    Revision 1.115  2006/02/27 12:17:45  brouard
 {    (Module): One freematrix added in mlikeli! 0.98c
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));    Revision 1.114  2006/02/26 12:57:58  brouard
 }    (Module): Some improvements in processing parameter
     filename with strsep.
 /******************* matrix *******************************/  
 double **matrix(long nrl, long nrh, long ncl, long nch)    Revision 1.113  2006/02/24 14:20:24  brouard
 {    (Module): Memory leaks checks with valgrind and:
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    datafile was not closed, some imatrix were not freed and on matrix
   double **m;    allocation too.
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Revision 1.112  2006/01/30 09:55:26  brouard
   if (!m) nrerror("allocation failure 1 in matrix()");    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   m += NR_END;  
   m -= nrl;    Revision 1.111  2006/01/25 20:38:18  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    (Module): Comments can be added in data file. Missing date values
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    can be a simple dot '.'.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.110  2006/01/25 00:51:50  brouard
     (Module): Lots of cleaning and bugs added (Gompertz)
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
   return m;    Revision 1.109  2006/01/24 19:37:15  brouard
 }    (Module): Comments (lines starting with a #) are allowed in data.
   
 /*************************free matrix ************************/    Revision 1.108  2006/01/19 18:05:42  lievre
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    Gnuplot problem appeared...
 {    To be fixed
   free((FREE_ARG)(m[nrl]+ncl-NR_END));  
   free((FREE_ARG)(m+nrl-NR_END));    Revision 1.107  2006/01/19 16:20:37  brouard
 }    Test existence of gnuplot in imach path
   
 /******************* ma3x *******************************/    Revision 1.106  2006/01/19 13:24:36  brouard
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    Some cleaning and links added in html output
 {  
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    Revision 1.105  2006/01/05 20:23:19  lievre
   double ***m;    *** empty log message ***
   
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Revision 1.104  2005/09/30 16:11:43  lievre
   if (!m) nrerror("allocation failure 1 in matrix()");    (Module): sump fixed, loop imx fixed, and simplifications.
   m += NR_END;    (Module): If the status is missing at the last wave but we know
   m -= nrl;    that the person is alive, then we can code his/her status as -2
     (instead of missing=-1 in earlier versions) and his/her
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    contributions to the likelihood is 1 - Prob of dying from last
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   m[nrl] += NR_END;    the healthy state at last known wave). Version is 0.98
   m[nrl] -= ncl;  
     Revision 1.103  2005/09/30 15:54:49  lievre
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    (Module): sump fixed, loop imx fixed, and simplifications.
   
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    Revision 1.102  2004/09/15 17:31:30  brouard
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    Add the possibility to read data file including tab characters.
   m[nrl][ncl] += NR_END;  
   m[nrl][ncl] -= nll;    Revision 1.101  2004/09/15 10:38:38  brouard
   for (j=ncl+1; j<=nch; j++)    Fix on curr_time
     m[nrl][j]=m[nrl][j-1]+nlay;  
      Revision 1.100  2004/07/12 18:29:06  brouard
   for (i=nrl+1; i<=nrh; i++) {    Add version for Mac OS X. Just define UNIX in Makefile
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;  
     for (j=ncl+1; j<=nch; j++)    Revision 1.99  2004/06/05 08:57:40  brouard
       m[i][j]=m[i][j-1]+nlay;    *** empty log message ***
   }  
   return m;    Revision 1.98  2004/05/16 15:05:56  brouard
 }    New version 0.97 . First attempt to estimate force of mortality
     directly from the data i.e. without the need of knowing the health
 /*************************free ma3x ************************/    state at each age, but using a Gompertz model: log u =a + b*age .
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    This is the basic analysis of mortality and should be done before any
 {    other analysis, in order to test if the mortality estimated from the
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));    cross-longitudinal survey is different from the mortality estimated
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    from other sources like vital statistic data.
   free((FREE_ARG)(m+nrl-NR_END));  
 }    The same imach parameter file can be used but the option for mle should be -3.
   
 /***************** f1dim *************************/    Agnès, who wrote this part of the code, tried to keep most of the
 extern int ncom;    former routines in order to include the new code within the former code.
 extern double *pcom,*xicom;  
 extern double (*nrfunc)(double []);    The output is very simple: only an estimate of the intercept and of
      the slope with 95% confident intervals.
 double f1dim(double x)  
 {    Current limitations:
   int j;    A) Even if you enter covariates, i.e. with the
   double f;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   double *xt;    B) There is no computation of Life Expectancy nor Life Table.
    
   xt=vector(1,ncom);    Revision 1.97  2004/02/20 13:25:42  lievre
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    Version 0.96d. Population forecasting command line is (temporarily)
   f=(*nrfunc)(xt);    suppressed.
   free_vector(xt,1,ncom);  
   return f;    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.
 /*****************brent *************************/  
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    Revision 1.95  2003/07/08 07:54:34  brouard
 {    * imach.c (Repository):
   int iter;    (Repository): Using imachwizard code to output a more meaningful covariance
   double a,b,d,etemp;    matrix (cov(a12,c31) instead of numbers.
   double fu,fv,fw,fx;  
   double ftemp;    Revision 1.94  2003/06/27 13:00:02  brouard
   double p,q,r,tol1,tol2,u,v,w,x,xm;    Just cleaning
   double e=0.0;  
      Revision 1.93  2003/06/25 16:33:55  brouard
   a=(ax < cx ? ax : cx);    (Module): On windows (cygwin) function asctime_r doesn't
   b=(ax > cx ? ax : cx);    exist so I changed back to asctime which exists.
   x=w=v=bx;    (Module): Version 0.96b
   fw=fv=fx=(*f)(x);  
   for (iter=1;iter<=ITMAX;iter++) {    Revision 1.92  2003/06/25 16:30:45  brouard
     xm=0.5*(a+b);    (Module): On windows (cygwin) function asctime_r doesn't
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    exist so I changed back to asctime which exists.
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/  
     printf(".");fflush(stdout);    Revision 1.91  2003/06/25 15:30:29  brouard
 #ifdef DEBUG    * imach.c (Repository): Duplicated warning errors corrected.
     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);    (Repository): Elapsed time after each iteration is now output. It
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    helps to forecast when convergence will be reached. Elapsed time
 #endif    is stamped in powell.  We created a new html file for the graphs
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    concerning matrix of covariance. It has extension -cov.htm.
       *xmin=x;  
       return fx;    Revision 1.90  2003/06/24 12:34:15  brouard
     }    (Module): Some bugs corrected for windows. Also, when
     ftemp=fu;    mle=-1 a template is output in file "or"mypar.txt with the design
     if (fabs(e) > tol1) {    of the covariance matrix to be input.
       r=(x-w)*(fx-fv);  
       q=(x-v)*(fx-fw);    Revision 1.89  2003/06/24 12:30:52  brouard
       p=(x-v)*q-(x-w)*r;    (Module): Some bugs corrected for windows. Also, when
       q=2.0*(q-r);    mle=-1 a template is output in file "or"mypar.txt with the design
       if (q > 0.0) p = -p;    of the covariance matrix to be input.
       q=fabs(q);  
       etemp=e;    Revision 1.88  2003/06/23 17:54:56  brouard
       e=d;    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))  
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    Revision 1.87  2003/06/18 12:26:01  brouard
       else {    Version 0.96
         d=p/q;  
         u=x+d;    Revision 1.86  2003/06/17 20:04:08  brouard
         if (u-a < tol2 || b-u < tol2)    (Module): Change position of html and gnuplot routines and added
           d=SIGN(tol1,xm-x);    routine fileappend.
       }  
     } else {    Revision 1.85  2003/06/17 13:12:43  brouard
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    * imach.c (Repository): Check when date of death was earlier that
     }    current date of interview. It may happen when the death was just
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    prior to the death. In this case, dh was negative and likelihood
     fu=(*f)(u);    was wrong (infinity). We still send an "Error" but patch by
     if (fu <= fx) {    assuming that the date of death was just one stepm after the
       if (u >= x) a=x; else b=x;    interview.
       SHFT(v,w,x,u)    (Repository): Because some people have very long ID (first column)
         SHFT(fv,fw,fx,fu)    we changed int to long in num[] and we added a new lvector for
         } else {    memory allocation. But we also truncated to 8 characters (left
           if (u < x) a=u; else b=u;    truncation)
           if (fu <= fw || w == x) {    (Repository): No more line truncation errors.
             v=w;  
             w=u;    Revision 1.84  2003/06/13 21:44:43  brouard
             fv=fw;    * imach.c (Repository): Replace "freqsummary" at a correct
             fw=fu;    place. It differs from routine "prevalence" which may be called
           } else if (fu <= fv || v == x || v == w) {    many times. Probs is memory consuming and must be used with
             v=u;    parcimony.
             fv=fu;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
           }  
         }    Revision 1.83  2003/06/10 13:39:11  lievre
   }    *** empty log message ***
   nrerror("Too many iterations in brent");  
   *xmin=x;    Revision 1.82  2003/06/05 15:57:20  brouard
   return fx;    Add log in  imach.c and  fullversion number is now printed.
 }  
   */
 /****************** mnbrak ***********************/  /*
      Interpolated Markov Chain
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,  
             double (*func)(double))    Short summary of the programme:
 {    
   double ulim,u,r,q, dum;    This program computes Healthy Life Expectancies from
   double fu;    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
      first survey ("cross") where individuals from different ages are
   *fa=(*func)(*ax);    interviewed on their health status or degree of disability (in the
   *fb=(*func)(*bx);    case of a health survey which is our main interest) -2- at least a
   if (*fb > *fa) {    second wave of interviews ("longitudinal") which measure each change
     SHFT(dum,*ax,*bx,dum)    (if any) in individual health status.  Health expectancies are
       SHFT(dum,*fb,*fa,dum)    computed from the time spent in each health state according to a
       }    model. More health states you consider, more time is necessary to reach the
   *cx=(*bx)+GOLD*(*bx-*ax);    Maximum Likelihood of the parameters involved in the model.  The
   *fc=(*func)(*cx);    simplest model is the multinomial logistic model where pij is the
   while (*fb > *fc) {    probability to be observed in state j at the second wave
     r=(*bx-*ax)*(*fb-*fc);    conditional to be observed in state i at the first wave. Therefore
     q=(*bx-*cx)*(*fb-*fa);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/    'age' is age and 'sex' is a covariate. If you want to have a more
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));    complex model than "constant and age", you should modify the program
     ulim=(*bx)+GLIMIT*(*cx-*bx);    where the markup *Covariates have to be included here again* invites
     if ((*bx-u)*(u-*cx) > 0.0) {    you to do it.  More covariates you add, slower the
       fu=(*func)(u);    convergence.
     } else if ((*cx-u)*(u-ulim) > 0.0) {  
       fu=(*func)(u);    The advantage of this computer programme, compared to a simple
       if (fu < *fc) {    multinomial logistic model, is clear when the delay between waves is not
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    identical for each individual. Also, if a individual missed an
           SHFT(*fb,*fc,fu,(*func)(u))    intermediate interview, the information is lost, but taken into
           }    account using an interpolation or extrapolation.  
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {  
       u=ulim;    hPijx is the probability to be observed in state i at age x+h
       fu=(*func)(u);    conditional to the observed state i at age x. The delay 'h' can be
     } else {    split into an exact number (nh*stepm) of unobserved intermediate
       u=(*cx)+GOLD*(*cx-*bx);    states. This elementary transition (by month, quarter,
       fu=(*func)(u);    semester or year) is modelled as a multinomial logistic.  The hPx
     }    matrix is simply the matrix product of nh*stepm elementary matrices
     SHFT(*ax,*bx,*cx,u)    and the contribution of each individual to the likelihood is simply
       SHFT(*fa,*fb,*fc,fu)    hPijx.
       }  
 }    Also this programme outputs the covariance matrix of the parameters but also
     of the life expectancies. It also computes the period (stable) prevalence. 
 /*************** linmin ************************/    
     Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
 int ncom;             Institut national d'études démographiques, Paris.
 double *pcom,*xicom;    This software have been partly granted by Euro-REVES, a concerted action
 double (*nrfunc)(double []);    from the European Union.
      It is copyrighted identically to a GNU software product, ie programme and
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))    software can be distributed freely for non commercial use. Latest version
 {    can be accessed at http://euroreves.ined.fr/imach .
   double brent(double ax, double bx, double cx,  
                double (*f)(double), double tol, double *xmin);    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
   double f1dim(double x);    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,    
               double *fc, double (*func)(double));    **********************************************************************/
   int j;  /*
   double xx,xmin,bx,ax;    main
   double fx,fb,fa;    read parameterfile
      read datafile
   ncom=n;    concatwav
   pcom=vector(1,n);    freqsummary
   xicom=vector(1,n);    if (mle >= 1)
   nrfunc=func;      mlikeli
   for (j=1;j<=n;j++) {    print results files
     pcom[j]=p[j];    if mle==1 
     xicom[j]=xi[j];       computes hessian
   }    read end of parameter file: agemin, agemax, bage, fage, estepm
   ax=0.0;        begin-prev-date,...
   xx=1.0;    open gnuplot file
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);    open html file
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
 #ifdef DEBUG     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
 #endif      freexexit2 possible for memory heap.
   for (j=1;j<=n;j++) {  
     xi[j] *= xmin;    h Pij x                         | pij_nom  ficrestpij
     p[j] += xi[j];     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
   }         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
   free_vector(xicom,1,n);         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
   free_vector(pcom,1,n);  
 }         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
          1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
 /*************** powell ************************/    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
             double (*func)(double []))     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
 {  
   void linmin(double p[], double xi[], int n, double *fret,    forecasting if prevfcast==1 prevforecast call prevalence()
               double (*func)(double []));    health expectancies
   int i,ibig,j;    Variance-covariance of DFLE
   double del,t,*pt,*ptt,*xit;    prevalence()
   double fp,fptt;     movingaverage()
   double *xits;    varevsij() 
   pt=vector(1,n);    if popbased==1 varevsij(,popbased)
   ptt=vector(1,n);    total life expectancies
   xit=vector(1,n);    Variance of period (stable) prevalence
   xits=vector(1,n);   end
   *fret=(*func)(p);  */
   for (j=1;j<=n;j++) pt[j]=p[j];  
   for (*iter=1;;++(*iter)) {  #define POWELL /* Instead of NLOPT */
     fp=(*fret);  
     ibig=0;  #include <math.h>
     del=0.0;  #include <stdio.h>
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  #include <stdlib.h>
     for (i=1;i<=n;i++)  #include <string.h>
       printf(" %d %.12f",i, p[i]);  
     printf("\n");  #ifdef _WIN32
     for (i=1;i<=n;i++) {  #include <io.h>
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  #else
       fptt=(*fret);  #include <unistd.h>
 #ifdef DEBUG  #endif
       printf("fret=%lf \n",*fret);  
 #endif  #include <limits.h>
       printf("%d",i);fflush(stdout);  #include <sys/types.h>
       linmin(p,xit,n,fret,func);  #include <sys/utsname.h>
       if (fabs(fptt-(*fret)) > del) {  #include <sys/stat.h>
         del=fabs(fptt-(*fret));  #include <errno.h>
         ibig=i;  /* extern int errno; */
       }  
 #ifdef DEBUG  /* #ifdef LINUX */
       printf("%d %.12e",i,(*fret));  /* #include <time.h> */
       for (j=1;j<=n;j++) {  /* #include "timeval.h" */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  /* #else */
         printf(" x(%d)=%.12e",j,xit[j]);  /* #include <sys/time.h> */
       }  /* #endif */
       for(j=1;j<=n;j++)  
         printf(" p=%.12e",p[j]);  #include <time.h>
       printf("\n");  
 #endif  #ifdef GSL
     }  #include <gsl/gsl_errno.h>
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  #include <gsl/gsl_multimin.h>
 #ifdef DEBUG  #endif
       int k[2],l;  
       k[0]=1;  
       k[1]=-1;  #ifdef NLOPT
       printf("Max: %.12e",(*func)(p));  #include <nlopt.h>
       for (j=1;j<=n;j++)  typedef struct {
         printf(" %.12e",p[j]);    double (* function)(double [] );
       printf("\n");  } myfunc_data ;
       for(l=0;l<=1;l++) {  #endif
         for (j=1;j<=n;j++) {  
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  /* #include <libintl.h> */
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  /* #define _(String) gettext (String) */
         }  
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
       }  
 #endif  #define GNUPLOTPROGRAM "gnuplot"
   /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   #define FILENAMELENGTH 132
       free_vector(xit,1,n);  
       free_vector(xits,1,n);  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
       free_vector(ptt,1,n);  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
       free_vector(pt,1,n);  
       return;  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
     }  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  
     for (j=1;j<=n;j++) {  #define NINTERVMAX 8
       ptt[j]=2.0*p[j]-pt[j];  #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
       xit[j]=p[j]-pt[j];  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
       pt[j]=p[j];  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
     }  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
     fptt=(*func)(ptt);  #define MAXN 20000
     if (fptt < fp) {  #define YEARM 12. /**< Number of months per year */
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  #define AGESUP 130
       if (t < 0.0) {  #define AGEBASE 40
         linmin(p,xit,n,fret,func);  #define AGEGOMP 10 /**< Minimal age for Gompertz adjustment */
         for (j=1;j<=n;j++) {  #ifdef _WIN32
           xi[j][ibig]=xi[j][n];  #define DIRSEPARATOR '\\'
           xi[j][n]=xit[j];  #define CHARSEPARATOR "\\"
         }  #define ODIRSEPARATOR '/'
 #ifdef DEBUG  #else
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  #define DIRSEPARATOR '/'
         for(j=1;j<=n;j++)  #define CHARSEPARATOR "/"
           printf(" %.12e",xit[j]);  #define ODIRSEPARATOR '\\'
         printf("\n");  #endif
 #endif  
       }  /* $Id$ */
     }  /* $State$ */
   }  
 }  char version[]="Imach version 0.98nY, December 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015";
   char fullversion[]="$Revision$ $Date$"; 
 /**** Prevalence limit ****************/  char strstart[80];
   char optionfilext[10], optionfilefiname[FILENAMELENGTH];
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
 {  int nvar=0, nforce=0; /* Number of variables, number of forces */
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
      matrix by transitions matrix until convergence is reached */  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
   int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
   int i, ii,j,k;  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
   double min, max, maxmin, maxmax,sumnew=0.;  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
   double **matprod2();  int cptcovprodnoage=0; /**< Number of covariate products without age */   
   double **out, cov[NCOVMAX], **pmij();  int cptcoveff=0; /* Total number of covariates to vary for printing results */
   double **newm;  int cptcov=0; /* Working variable */
   double agefin, delaymax=50 ; /* Max number of years to converge */  int npar=NPARMAX;
   int nlstate=2; /* Number of live states */
   for (ii=1;ii<=nlstate+ndeath;ii++)  int ndeath=1; /* Number of dead states */
     for (j=1;j<=nlstate+ndeath;j++){  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  int popbased=0;
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  int *wav; /* Number of waves for this individuual 0 is possible */
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  int maxwav=0; /* Maxim number of waves */
     newm=savm;  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
     /* Covariates have to be included here again */  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
     cov[1]=1.;  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
     cov[2]=agefin;                     to the likelihood and the sum of weights (done by funcone)*/
     if (cptcovn>0){  int mle=1, weightopt=0;
       for (k=1; k<=cptcovn;k++) {cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];/*printf("Tcode[ij]=%d nbcode=%d\n",Tcode[ij],nbcode[k][Tcode[ij]]);*/}  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
     }  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
              * wave mi and wave mi+1 is not an exact multiple of stepm. */
     savm=oldm;  int countcallfunc=0;  /* Count the number of calls to func */
     oldm=newm;  double jmean=1; /* Mean space between 2 waves */
     maxmax=0.;  double **matprod2(); /* test */
     for(j=1;j<=nlstate;j++){  double **oldm, **newm, **savm; /* Working pointers to matrices */
       min=1.;  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       max=0.;  /*FILE *fic ; */ /* Used in readdata only */
       for(i=1; i<=nlstate; i++) {  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
         sumnew=0;  FILE *ficlog, *ficrespow;
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  int globpr=0; /* Global variable for printing or not */
         prlim[i][j]= newm[i][j]/(1-sumnew);  double fretone; /* Only one call to likelihood */
         max=FMAX(max,prlim[i][j]);  long ipmx=0; /* Number of contributions */
         min=FMIN(min,prlim[i][j]);  double sw; /* Sum of weights */
       }  char filerespow[FILENAMELENGTH];
       maxmin=max-min;  char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
       maxmax=FMAX(maxmax,maxmin);  FILE *ficresilk;
     }  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
     if(maxmax < ftolpl){  FILE *ficresprobmorprev;
       return prlim;  FILE *fichtm, *fichtmcov; /* Html File */
     }  FILE *ficreseij;
   }  char filerese[FILENAMELENGTH];
 }  FILE *ficresstdeij;
   char fileresstde[FILENAMELENGTH];
 /*************** transition probabilities **********/  FILE *ficrescveij;
   char filerescve[FILENAMELENGTH];
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  FILE  *ficresvij;
 {  char fileresv[FILENAMELENGTH];
   double s1, s2;  FILE  *ficresvpl;
   /*double t34;*/  char fileresvpl[FILENAMELENGTH];
   int i,j,j1, nc, ii, jj;  char title[MAXLINE];
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
     for(i=1; i<= nlstate; i++){  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
     for(j=1; j<i;j++){  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  char command[FILENAMELENGTH];
         /*s2 += param[i][j][nc]*cov[nc];*/  int  outcmd=0;
         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);*/  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
       }  
       ps[i][j]=s2;  char filelog[FILENAMELENGTH]; /* Log file */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  char filerest[FILENAMELENGTH];
     }  char fileregp[FILENAMELENGTH];
     for(j=i+1; j<=nlstate+ndeath;j++){  char popfile[FILENAMELENGTH];
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/  
       }  /* struct timeval start_time, end_time, curr_time, last_time, forecast_time; */
       ps[i][j]=s2;  /* struct timezone tzp; */
     }  /* extern int gettimeofday(); */
   }  struct tm tml, *gmtime(), *localtime();
   for(i=1; i<= nlstate; i++){  
      s1=0;  extern time_t time();
     for(j=1; j<i; j++)  
       s1+=exp(ps[i][j]);  struct tm start_time, end_time, curr_time, last_time, forecast_time;
     for(j=i+1; j<=nlstate+ndeath; j++)  time_t  rstart_time, rend_time, rcurr_time, rlast_time, rforecast_time; /* raw time */
       s1+=exp(ps[i][j]);  struct tm tm;
     ps[i][i]=1./(s1+1.);  
     for(j=1; j<i; j++)  char strcurr[80], strfor[80];
       ps[i][j]= exp(ps[i][j])*ps[i][i];  
     for(j=i+1; j<=nlstate+ndeath; j++)  char *endptr;
       ps[i][j]= exp(ps[i][j])*ps[i][i];  long lval;
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */  double dval;
   } /* end i */  
   #define NR_END 1
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){  #define FREE_ARG char*
     for(jj=1; jj<= nlstate+ndeath; jj++){  #define FTOL 1.0e-10
       ps[ii][jj]=0;  
       ps[ii][ii]=1;  #define NRANSI 
     }  #define ITMAX 200 
   }  
   #define TOL 2.0e-4 
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){  
     for(jj=1; jj<= nlstate+ndeath; jj++){  #define CGOLD 0.3819660 
      printf("%lf ",ps[ii][jj]);  #define ZEPS 1.0e-10 
    }  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     printf("\n ");  
     }  #define GOLD 1.618034 
     printf("\n ");printf("%lf ",cov[2]);*/  #define GLIMIT 100.0 
 /*  #define TINY 1.0e-20 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);  
   goto end;*/  static double maxarg1,maxarg2;
     return ps;  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
 }  #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     
 /**************** Product of 2 matrices ******************/  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
   #define rint(a) floor(a+0.5)
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/myutils_8h-source.html */
 {  /* #define mytinydouble 1.0e-16 */
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times  /* #define DEQUAL(a,b) (fabs((a)-(b))<mytinydouble) */
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */  /* http://www.thphys.uni-heidelberg.de/~robbers/cmbeasy/doc/html/mynrutils_8h-source.html */
   /* in, b, out are matrice of pointers which should have been initialized  /* static double dsqrarg; */
      before: only the contents of out is modified. The function returns  /* #define DSQR(a) (DEQUAL((dsqrarg=(a)),0.0) ? 0.0 : dsqrarg*dsqrarg) */
      a pointer to pointers identical to out */  static double sqrarg;
   long i, j, k;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
   for(i=nrl; i<= nrh; i++)  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
     for(k=ncolol; k<=ncoloh; k++)  int agegomp= AGEGOMP;
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  
         out[i][k] +=in[i][j]*b[j][k];  int imx; 
   int stepm=1;
   return out;  /* Stepm, step in month: minimum step interpolation*/
 }  
   int estepm;
   /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
 /************* Higher Matrix Product ***************/  
   int m,nb;
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )  long *num;
 {  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
      duration (i.e. until  double **pmmij, ***probs;
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  double *ageexmed,*agecens;
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  double dateintmean=0;
      (typically every 2 years instead of every month which is too big).  
      Model is determined by parameters x and covariates have to be  double *weight;
      included manually here.  int **s; /* Status */
   double *agedc;
      */  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
                     * covar=matrix(0,NCOVMAX,1,n); 
   int i, j, d, h, k;                    * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
   double **out, cov[NCOVMAX];  double  idx; 
   double **newm;  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
   int *Ndum; /** Freq of modality (tricode */
   /* Hstepm could be zero and should return the unit matrix */  int **codtab; /**< codtab=imatrix(1,100,1,10); */
   for (i=1;i<=nlstate+ndeath;i++)  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
     for (j=1;j<=nlstate+ndeath;j++){  double *lsurv, *lpop, *tpop;
       oldm[i][j]=(i==j ? 1.0 : 0.0);  
       po[i][j][0]=(i==j ? 1.0 : 0.0);  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
     }  double ftolhess; /**< Tolerance for computing hessian */
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  
   for(h=1; h <=nhstepm; h++){  /**************** split *************************/
     for(d=1; d <=hstepm; d++){  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
       newm=savm;  {
       /* Covariates have to be included here again */    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       cov[1]=1.;       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;    */ 
       if (cptcovn>0){    char  *ss;                            /* pointer */
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];    int   l1, l2;                         /* length counters */
     }  
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/    l1 = strlen(path );                   /* length of path */
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       savm=oldm;      strcpy( name, path );               /* we got the fullname name because no directory */
       oldm=newm;      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     }        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
     for(i=1; i<=nlstate+ndeath; i++)      /* get current working directory */
       for(j=1;j<=nlstate+ndeath;j++) {      /*    extern  char* getcwd ( char *buf , int len);*/
         po[i][j][h]=newm[i][j];      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);        return( GLOCK_ERROR_GETCWD );
          */      }
       }      /* got dirc from getcwd*/
   } /* end h */      printf(" DIRC = %s \n",dirc);
   return po;    } else {                              /* strip direcotry from path */
 }      ss++;                               /* after this, the filename */
       l2 = strlen( ss );                  /* length of filename */
       if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
 /*************** log-likelihood *************/      strcpy( name, ss );         /* save file name */
 double func( double *x)      strncpy( dirc, path, l1 - l2 );     /* now the directory */
 {      dirc[l1-l2] = 0;                    /* add zero */
   int i, ii, j, k, mi, d;      printf(" DIRC2 = %s \n",dirc);
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    }
   double **out;    /* We add a separator at the end of dirc if not exists */
   double sw; /* Sum of weights */    l1 = strlen( dirc );                  /* length of directory */
   double lli; /* Individual log likelihood */    if( dirc[l1-1] != DIRSEPARATOR ){
   long ipmx;      dirc[l1] =  DIRSEPARATOR;
   /*extern weight */      dirc[l1+1] = 0; 
   /* We are differentiating ll according to initial status */      printf(" DIRC3 = %s \n",dirc);
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    }
   /*for(i=1;i<imx;i++)    ss = strrchr( name, '.' );            /* find last / */
 printf(" %d\n",s[4][i]);    if (ss >0){
   */      ss++;
       strcpy(ext,ss);                     /* save extension */
   for(k=1; k<=nlstate; k++) ll[k]=0.;      l1= strlen( name);
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){      l2= strlen(ss)+1;
        for(mi=1; mi<= wav[i]-1; mi++){      strncpy( finame, name, l1-l2);
       for (ii=1;ii<=nlstate+ndeath;ii++)      finame[l1-l2]= 0;
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);    }
             for(d=0; d<dh[mi][i]; d++){  
         newm=savm;    return( 0 );                          /* we're done */
           cov[1]=1.;  }
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  
           if (cptcovn>0){  
             for (k=1; k<=cptcovn;k++) cov[2+k]=covar[1+k-1][i];  /******************************************/
             }  
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,  void replace_back_to_slash(char *s, char*t)
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));  {
           savm=oldm;    int i;
           oldm=newm;    int lg=0;
     i=0;
     lg=strlen(t);
       } /* end mult */    for(i=0; i<= lg; i++) {
          (s[i] = t[i]);
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);      if (t[i]== '\\') s[i]='/';
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/    }
       ipmx +=1;  }
       sw += weight[i];  
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  char *trimbb(char *out, char *in)
     } /* end of wave */  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
   } /* end of individual */    char *s;
     s=out;
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];    while (*in != '\0'){
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */      while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */        in++;
   return -l;      }
 }      *out++ = *in++;
     }
     *out='\0';
 /*********** Maximum Likelihood Estimation ***************/    return s;
   }
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  
 {  char *cutl(char *blocc, char *alocc, char *in, char occ)
   int i,j, iter;  {
   double **xi,*delti;    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
   double fret;       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
   xi=matrix(1,npar,1,npar);       gives blocc="abcdef2ghi" and alocc="j".
   for (i=1;i<=npar;i++)       If occ is not found blocc is null and alocc is equal to in. Returns blocc
     for (j=1;j<=npar;j++)    */
       xi[i][j]=(i==j ? 1.0 : 0.0);    char *s, *t;
   printf("Powell\n");    t=in;s=in;
   powell(p,xi,npar,ftol,&iter,&fret,func);    while ((*in != occ) && (*in != '\0')){
       *alocc++ = *in++;
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));    }
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));    if( *in == occ){
       *(alocc)='\0';
 }      s=++in;
     }
 /**** Computes Hessian and covariance matrix ***/   
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    if (s == t) {/* occ not found */
 {      *(alocc-(in-s))='\0';
   double  **a,**y,*x,pd;      in=s;
   double **hess;    }
   int i, j,jk;    while ( *in != '\0'){
   int *indx;      *blocc++ = *in++;
     }
   double hessii(double p[], double delta, int theta, double delti[]);  
   double hessij(double p[], double delti[], int i, int j);    *blocc='\0';
   void lubksb(double **a, int npar, int *indx, double b[]) ;    return t;
   void ludcmp(double **a, int npar, int *indx, double *d) ;  }
   char *cutv(char *blocc, char *alocc, char *in, char occ)
   {
   hess=matrix(1,npar,1,npar);    /* cuts string in into blocc and alocc where blocc ends before last occurence of char 'occ' 
        and alocc starts after last occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
   printf("\nCalculation of the hessian matrix. Wait...\n");       gives blocc="abcdef2ghi" and alocc="j".
   for (i=1;i<=npar;i++){       If occ is not found blocc is null and alocc is equal to in. Returns alocc
     printf("%d",i);fflush(stdout);    */
     hess[i][i]=hessii(p,ftolhess,i,delti);    char *s, *t;
     /*printf(" %f ",p[i]);*/    t=in;s=in;
   }    while (*in != '\0'){
       while( *in == occ){
   for (i=1;i<=npar;i++) {        *blocc++ = *in++;
     for (j=1;j<=npar;j++)  {        s=in;
       if (j>i) {      }
         printf(".%d%d",i,j);fflush(stdout);      *blocc++ = *in++;
         hess[i][j]=hessij(p,delti,i,j);    }
         hess[j][i]=hess[i][j];    if (s == t) /* occ not found */
       }      *(blocc-(in-s))='\0';
     }    else
   }      *(blocc-(in-s)-1)='\0';
   printf("\n");    in=s;
     while ( *in != '\0'){
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");      *alocc++ = *in++;
      }
   a=matrix(1,npar,1,npar);  
   y=matrix(1,npar,1,npar);    *alocc='\0';
   x=vector(1,npar);    return s;
   indx=ivector(1,npar);  }
   for (i=1;i<=npar;i++)  
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  int nbocc(char *s, char occ)
   ludcmp(a,npar,indx,&pd);  {
     int i,j=0;
   for (j=1;j<=npar;j++) {    int lg=20;
     for (i=1;i<=npar;i++) x[i]=0;    i=0;
     x[j]=1;    lg=strlen(s);
     lubksb(a,npar,indx,x);    for(i=0; i<= lg; i++) {
     for (i=1;i<=npar;i++){    if  (s[i] == occ ) j++;
       matcov[i][j]=x[i];    }
     }    return j;
   }  }
   
   printf("\n#Hessian matrix#\n");  /* void cutv(char *u,char *v, char*t, char occ) */
   for (i=1;i<=npar;i++) {  /* { */
     for (j=1;j<=npar;j++) {  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       printf("%.3e ",hess[i][j]);  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
     }  /*      gives u="abcdef2ghi" and v="j" *\/ */
     printf("\n");  /*   int i,lg,j,p=0; */
   }  /*   i=0; */
   /*   lg=strlen(t); */
   /* Recompute Inverse */  /*   for(j=0; j<=lg-1; j++) { */
   for (i=1;i<=npar;i++)  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];  /*   } */
   ludcmp(a,npar,indx,&pd);  
   /*   for(j=0; j<p; j++) { */
   /*  printf("\n#Hessian matrix recomputed#\n");  /*     (u[j] = t[j]); */
   /*   } */
   for (j=1;j<=npar;j++) {  /*      u[p]='\0'; */
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;  /*    for(j=0; j<= lg; j++) { */
     lubksb(a,npar,indx,x);  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
     for (i=1;i<=npar;i++){  /*   } */
       y[i][j]=x[i];  /* } */
       printf("%.3e ",y[i][j]);  
     }  #ifdef _WIN32
     printf("\n");  char * strsep(char **pp, const char *delim)
   }  {
   */    char *p, *q;
            
   free_matrix(a,1,npar,1,npar);    if ((p = *pp) == NULL)
   free_matrix(y,1,npar,1,npar);      return 0;
   free_vector(x,1,npar);    if ((q = strpbrk (p, delim)) != NULL)
   free_ivector(indx,1,npar);    {
   free_matrix(hess,1,npar,1,npar);      *pp = q + 1;
       *q = '\0';
     }
 }    else
       *pp = 0;
 /*************** hessian matrix ****************/    return p;
 double hessii( double x[], double delta, int theta, double delti[])  }
 {  #endif
   int i;  
   int l=1, lmax=20;  /********************** nrerror ********************/
   double k1,k2;  
   double p2[NPARMAX+1];  void nrerror(char error_text[])
   double res;  {
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;    fprintf(stderr,"ERREUR ...\n");
   double fx;    fprintf(stderr,"%s\n",error_text);
   int k=0,kmax=10;    exit(EXIT_FAILURE);
   double l1;  }
   /*********************** vector *******************/
   fx=func(x);  double *vector(int nl, int nh)
   for (i=1;i<=npar;i++) p2[i]=x[i];  {
   for(l=0 ; l <=lmax; l++){    double *v;
     l1=pow(10,l);    v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
     delts=delt;    if (!v) nrerror("allocation failure in vector");
     for(k=1 ; k <kmax; k=k+1){    return v-nl+NR_END;
       delt = delta*(l1*k);  }
       p2[theta]=x[theta] +delt;  
       k1=func(p2)-fx;  /************************ free vector ******************/
       p2[theta]=x[theta]-delt;  void free_vector(double*v, int nl, int nh)
       k2=func(p2)-fx;  {
       /*res= (k1-2.0*fx+k2)/delt/delt; */    free((FREE_ARG)(v+nl-NR_END));
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */  }
        
 #ifdef DEBUG  /************************ivector *******************************/
       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);  int *ivector(long nl,long nh)
 #endif  {
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    int *v;
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
         k=kmax;    if (!v) nrerror("allocation failure in ivector");
       }    return v-nl+NR_END;
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */  }
         k=kmax; l=lmax*10.;  
       }  /******************free ivector **************************/
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  void free_ivector(int *v, long nl, long nh)
         delts=delt;  {
       }    free((FREE_ARG)(v+nl-NR_END));
     }  }
   }  
   delti[theta]=delts;  /************************lvector *******************************/
   return res;  long *lvector(long nl,long nh)
    {
 }    long *v;
     v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
 double hessij( double x[], double delti[], int thetai,int thetaj)    if (!v) nrerror("allocation failure in ivector");
 {    return v-nl+NR_END;
   int i;  }
   int l=1, l1, lmax=20;  
   double k1,k2,k3,k4,res,fx;  /******************free lvector **************************/
   double p2[NPARMAX+1];  void free_lvector(long *v, long nl, long nh)
   int k;  {
     free((FREE_ARG)(v+nl-NR_END));
   fx=func(x);  }
   for (k=1; k<=2; k++) {  
     for (i=1;i<=npar;i++) p2[i]=x[i];  /******************* imatrix *******************************/
     p2[thetai]=x[thetai]+delti[thetai]/k;  int **imatrix(long nrl, long nrh, long ncl, long nch) 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
     k1=func(p2)-fx;  { 
      long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     p2[thetai]=x[thetai]+delti[thetai]/k;    int **m; 
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    
     k2=func(p2)-fx;    /* allocate pointers to rows */ 
      m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
     p2[thetai]=x[thetai]-delti[thetai]/k;    if (!m) nrerror("allocation failure 1 in matrix()"); 
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    m += NR_END; 
     k3=func(p2)-fx;    m -= nrl; 
      
     p2[thetai]=x[thetai]-delti[thetai]/k;    
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;    /* allocate rows and set pointers to them */ 
     k4=func(p2)-fx;    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
 #ifdef DEBUG    m[nrl] += NR_END; 
     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);    m[nrl] -= ncl; 
 #endif    
   }    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   return res;    
 }    /* return pointer to array of pointers to rows */ 
     return m; 
 /************** Inverse of matrix **************/  } 
 void ludcmp(double **a, int n, int *indx, double *d)  
 {  /****************** free_imatrix *************************/
   int i,imax,j,k;  void free_imatrix(m,nrl,nrh,ncl,nch)
   double big,dum,sum,temp;        int **m;
   double *vv;        long nch,ncl,nrh,nrl; 
         /* free an int matrix allocated by imatrix() */ 
   vv=vector(1,n);  { 
   *d=1.0;    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
   for (i=1;i<=n;i++) {    free((FREE_ARG) (m+nrl-NR_END)); 
     big=0.0;  } 
     for (j=1;j<=n;j++)  
       if ((temp=fabs(a[i][j])) > big) big=temp;  /******************* matrix *******************************/
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");  double **matrix(long nrl, long nrh, long ncl, long nch)
     vv[i]=1.0/big;  {
   }    long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   for (j=1;j<=n;j++) {    double **m;
     for (i=1;i<j;i++) {  
       sum=a[i][j];    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];    if (!m) nrerror("allocation failure 1 in matrix()");
       a[i][j]=sum;    m += NR_END;
     }    m -= nrl;
     big=0.0;  
     for (i=j;i<=n;i++) {    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       sum=a[i][j];    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       for (k=1;k<j;k++)    m[nrl] += NR_END;
         sum -= a[i][k]*a[k][j];    m[nrl] -= ncl;
       a[i][j]=sum;  
       if ( (dum=vv[i]*fabs(sum)) >= big) {    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         big=dum;    return m;
         imax=i;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
       }  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
     }  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
     if (j != imax) {     */
       for (k=1;k<=n;k++) {  }
         dum=a[imax][k];  
         a[imax][k]=a[j][k];  /*************************free matrix ************************/
         a[j][k]=dum;  void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
       }  {
       *d = -(*d);    free((FREE_ARG)(m[nrl]+ncl-NR_END));
       vv[imax]=vv[j];    free((FREE_ARG)(m+nrl-NR_END));
     }  }
     indx[j]=imax;  
     if (a[j][j] == 0.0) a[j][j]=TINY;  /******************* ma3x *******************************/
     if (j != n) {  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       dum=1.0/(a[j][j]);  {
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
     }    double ***m;
   }  
   free_vector(vv,1,n);  /* Doesn't work */    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
 ;    if (!m) nrerror("allocation failure 1 in matrix()");
 }    m += NR_END;
     m -= nrl;
 void lubksb(double **a, int n, int *indx, double b[])  
 {    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
   int i,ii=0,ip,j;    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
   double sum;    m[nrl] += NR_END;
      m[nrl] -= ncl;
   for (i=1;i<=n;i++) {  
     ip=indx[i];    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
     sum=b[ip];  
     b[ip]=b[i];    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
     if (ii)    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];    m[nrl][ncl] += NR_END;
     else if (sum) ii=i;    m[nrl][ncl] -= nll;
     b[i]=sum;    for (j=ncl+1; j<=nch; j++) 
   }      m[nrl][j]=m[nrl][j-1]+nlay;
   for (i=n;i>=1;i--) {    
     sum=b[i];    for (i=nrl+1; i<=nrh; i++) {
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
     b[i]=sum/a[i][i];      for (j=ncl+1; j<=nch; j++) 
   }        m[i][j]=m[i][j-1]+nlay;
 }    }
     return m; 
 /************ Frequencies ********************/    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
 {  /* Some frequencies */    */
    }
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;  
   double ***freq; /* Frequencies */  /*************************free ma3x ************************/
   double *pp;  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
   double pos;  {
   FILE *ficresp;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
   char fileresp[FILENAMELENGTH];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     free((FREE_ARG)(m+nrl-NR_END));
   pp=vector(1,nlstate);  }
   
   strcpy(fileresp,"p");  /*************** function subdirf ***********/
   strcat(fileresp,fileres);  char *subdirf(char fileres[])
   if((ficresp=fopen(fileresp,"w"))==NULL) {  {
     printf("Problem with prevalence resultfile: %s\n", fileresp);    /* Caution optionfilefiname is hidden */
     exit(0);    strcpy(tmpout,optionfilefiname);
   }    strcat(tmpout,"/"); /* Add to the right */
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);    strcat(tmpout,fileres);
   j1=0;    return tmpout;
   }
   j=cptcovn;  
   if (cptcovn<1) {j=1;ncodemax[1]=1;}  /*************** function subdirf2 ***********/
   char *subdirf2(char fileres[], char *preop)
   for(k1=1; k1<=j;k1++){  {
    for(i1=1; i1<=ncodemax[k1];i1++){    
        j1++;    /* Caution optionfilefiname is hidden */
     strcpy(tmpout,optionfilefiname);
         for (i=-1; i<=nlstate+ndeath; i++)      strcat(tmpout,"/");
          for (jk=-1; jk<=nlstate+ndeath; jk++)      strcat(tmpout,preop);
            for(m=agemin; m <= agemax+3; m++)    strcat(tmpout,fileres);
              freq[i][jk][m]=0;    return tmpout;
          }
        for (i=1; i<=imx; i++) {  
          bool=1;  /*************** function subdirf3 ***********/
          if  (cptcovn>0) {  char *subdirf3(char fileres[], char *preop, char *preop2)
            for (z1=1; z1<=cptcovn; z1++)  {
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;    
          }    /* Caution optionfilefiname is hidden */
           if (bool==1) {    strcpy(tmpout,optionfilefiname);
            for(m=firstpass; m<=lastpass-1; m++){    strcat(tmpout,"/");
              if(agev[m][i]==0) agev[m][i]=agemax+1;    strcat(tmpout,preop);
              if(agev[m][i]==1) agev[m][i]=agemax+2;    strcat(tmpout,preop2);
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    strcat(tmpout,fileres);
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    return tmpout;
            }  }
          }  
        }  char *asc_diff_time(long time_sec, char ascdiff[])
         if  (cptcovn>0) {  {
          fprintf(ficresp, "\n#Variable");    long sec_left, days, hours, minutes;
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);    days = (time_sec) / (60*60*24);
        }    sec_left = (time_sec) % (60*60*24);
        fprintf(ficresp, "\n#");    hours = (sec_left) / (60*60) ;
        for(i=1; i<=nlstate;i++)    sec_left = (sec_left) %(60*60);
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);    minutes = (sec_left) /60;
        fprintf(ficresp, "\n");    sec_left = (sec_left) % (60);
            sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
   for(i=(int)agemin; i <= (int)agemax+3; i++){    return ascdiff;
     if(i==(int)agemax+3)  }
       printf("Total");  
     else  /***************** f1dim *************************/
       printf("Age %d", i);  extern int ncom; 
     for(jk=1; jk <=nlstate ; jk++){  extern double *pcom,*xicom;
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)  extern double (*nrfunc)(double []); 
         pp[jk] += freq[jk][m][i];   
     }  double f1dim(double x) 
     for(jk=1; jk <=nlstate ; jk++){  { 
       for(m=-1, pos=0; m <=0 ; m++)    int j; 
         pos += freq[jk][m][i];    double f;
       if(pp[jk]>=1.e-10)    double *xt; 
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);   
       else    xt=vector(1,ncom); 
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
     }    f=(*nrfunc)(xt); 
     for(jk=1; jk <=nlstate ; jk++){    free_vector(xt,1,ncom); 
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)    return f; 
         pp[jk] += freq[jk][m][i];  } 
     }  
     for(jk=1,pos=0; jk <=nlstate ; jk++)  /*****************brent *************************/
       pos += pp[jk];  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
     for(jk=1; jk <=nlstate ; jk++){  { 
       if(pos>=1.e-5)    int iter; 
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);    double a,b,d,etemp;
       else    double fu=0,fv,fw,fx;
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    double ftemp=0.;
       if( i <= (int) agemax){    double p,q,r,tol1,tol2,u,v,w,x,xm; 
         if(pos>=1.e-5)    double e=0.0; 
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);   
       else    a=(ax < cx ? ax : cx); 
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    b=(ax > cx ? ax : cx); 
       }    x=w=v=bx; 
     }    fw=fv=fx=(*f)(x); 
     for(jk=-1; jk <=nlstate+ndeath; jk++)    for (iter=1;iter<=ITMAX;iter++) { 
       for(m=-1; m <=nlstate+ndeath; m++)      xm=0.5*(a+b); 
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
     if(i <= (int) agemax)      /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
       fprintf(ficresp,"\n");      printf(".");fflush(stdout);
     printf("\n");      fprintf(ficlog,".");fflush(ficlog);
     }  #ifdef DEBUGBRENT
     }      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
  }      fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
        /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
   fclose(ficresp);  #endif
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
   free_vector(pp,1,nlstate);        *xmin=x; 
         return fx; 
 }  /* End of Freq */      } 
       ftemp=fu;
 /************* Waves Concatenation ***************/      if (fabs(e) > tol1) { 
         r=(x-w)*(fx-fv); 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)        q=(x-v)*(fx-fw); 
 {        p=(x-v)*q-(x-w)*r; 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.        q=2.0*(q-r); 
      Death is a valid wave (if date is known).        if (q > 0.0) p = -p; 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i        q=fabs(q); 
      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]        etemp=e; 
      and mw[mi+1][i]. dh depends on stepm.        e=d; 
      */        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
           d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
   int i, mi, m;        else { 
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;          d=p/q; 
 float sum=0.;          u=x+d; 
           if (u-a < tol2 || b-u < tol2) 
   for(i=1; i<=imx; i++){            d=SIGN(tol1,xm-x); 
     mi=0;        } 
     m=firstpass;      } else { 
     while(s[m][i] <= nlstate){        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       if(s[m][i]>=1)      } 
         mw[++mi][i]=m;      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       if(m >=lastpass)      fu=(*f)(u); 
         break;      if (fu <= fx) { 
       else        if (u >= x) a=x; else b=x; 
         m++;        SHFT(v,w,x,u) 
     }/* end while */          SHFT(fv,fw,fx,fu) 
     if (s[m][i] > nlstate){          } else { 
       mi++;     /* Death is another wave */            if (u < x) a=u; else b=u; 
       /* if(mi==0)  never been interviewed correctly before death */            if (fu <= fw || w == x) { 
          /* Only death is a correct wave */              v=w; 
       mw[mi][i]=m;              w=u; 
     }              fv=fw; 
               fw=fu; 
     wav[i]=mi;            } else if (fu <= fv || v == x || v == w) { 
     if(mi==0)              v=u; 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);              fv=fu; 
   }            } 
           } 
   for(i=1; i<=imx; i++){    } 
     for(mi=1; mi<wav[i];mi++){    nrerror("Too many iterations in brent"); 
       if (stepm <=0)    *xmin=x; 
         dh[mi][i]=1;    return fx; 
       else{  } 
         if (s[mw[mi+1][i]][i] > nlstate) {  
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);  /****************** mnbrak ***********************/
           if(j=0) j=1;  /* Survives at least one month after exam */  
         }  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
         else{              double (*func)(double)) 
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  { 
           k=k+1;    double ulim,u,r,q, dum;
           if (j >= jmax) jmax=j;    double fu; 
           else if (j <= jmin)jmin=j;   
           sum=sum+j;    *fa=(*func)(*ax); 
         }    *fb=(*func)(*bx); 
         jk= j/stepm;    if (*fb > *fa) { 
         jl= j -jk*stepm;      SHFT(dum,*ax,*bx,dum) 
         ju= j -(jk+1)*stepm;        SHFT(dum,*fb,*fa,dum) 
         if(jl <= -ju)        } 
           dh[mi][i]=jk;    *cx=(*bx)+GOLD*(*bx-*ax); 
         else    *fc=(*func)(*cx); 
           dh[mi][i]=jk+1;    while (*fb > *fc) { /* Declining fa, fb, fc */
         if(dh[mi][i]==0)      r=(*bx-*ax)*(*fb-*fc); 
           dh[mi][i]=1; /* At least one step */      q=(*bx-*cx)*(*fb-*fa); 
       }      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
     }        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); /* Minimum abscisse of a parabolic estimated from (a,fa), (b,fb) and (c,fc). */
   }      ulim=(*bx)+GLIMIT*(*cx-*bx); /* Maximum abscisse where function can be evaluated */
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);      if ((*bx-u)*(u-*cx) > 0.0) { /* if u between b and c */
 }        fu=(*func)(u); 
 /*********** Tricode ****************************/  #ifdef DEBUG
 void tricode(int *Tvar, int **nbcode, int imx)        /* f(x)=A(x-u)**2+f(u) */
 {        double A, fparabu; 
   int Ndum[80],ij, k, j, i;        A= (*fb - *fa)/(*bx-*ax)/(*bx+*ax-2*u);
   int cptcode=0;        fparabu= *fa - A*(*ax-u)*(*ax-u);
   for (k=0; k<79; k++) Ndum[k]=0;        printf("mnbrak (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf, fparabu=%.12f)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu, fparabu);
   for (k=1; k<=7; k++) ncodemax[k]=0;        fprintf(ficlog, "mnbrak (*ax=%.12f, *fa=%.12lf), (*bx=%.12f, *fb=%.12lf), (*cx=%.12f, *fc=%.12lf),  (*u=%.12f, fu=%.12lf, fparabu=%.12f)\n",*ax,*fa,*bx,*fb,*cx,*fc,u,fu, fparabu);
    #endif 
   for (j=1; j<=cptcovn; j++) {      } else if ((*cx-u)*(u-ulim) > 0.0) { /* u is after c but before ulim */
     for (i=1; i<=imx; i++) {        fu=(*func)(u); 
       ij=(int)(covar[Tvar[j]][i]);        if (fu < *fc) { 
       Ndum[ij]++;          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
       if (ij > cptcode) cptcode=ij;            SHFT(*fb,*fc,fu,(*func)(u)) 
     }            } 
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { /* u outside ulim (verifying that ulim is beyond c) */
     for (i=0; i<=cptcode; i++) {        u=ulim; 
       if(Ndum[i]!=0) ncodemax[j]++;        fu=(*func)(u); 
     }      } else { 
          u=(*cx)+GOLD*(*cx-*bx); 
     ij=1;        fu=(*func)(u); 
     for (i=1; i<=ncodemax[j]; i++) {      } 
       for (k=0; k<=79; k++) {      SHFT(*ax,*bx,*cx,u) 
         if (Ndum[k] != 0) {        SHFT(*fa,*fb,*fc,fu) 
           nbcode[Tvar[j]][ij]=k;        } 
           ij++;  } 
         }  
         if (ij > ncodemax[j]) break;  /*************** linmin ************************/
       }    /* Given an n -dimensional point p[1..n] and an n -dimensional direction xi[1..n] , moves and
     }  resets p to where the function func(p) takes on a minimum along the direction xi from p ,
   }    and replaces xi by the actual vector displacement that p was moved. Also returns as fret
   the value of func at the returned location p . This is actually all accomplished by calling the
   }  routines mnbrak and brent .*/
   int ncom; 
 /*********** Health Expectancies ****************/  double *pcom,*xicom;
   double (*nrfunc)(double []); 
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)   
 {  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
   /* Health expectancies */  { 
   int i, j, nhstepm, hstepm, h;    double brent(double ax, double bx, double cx, 
   double age, agelim,hf;                 double (*f)(double), double tol, double *xmin); 
   double ***p3mat;    double f1dim(double x); 
      void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
   fprintf(ficreseij,"# Health expectancies\n");                double *fc, double (*func)(double)); 
   fprintf(ficreseij,"# Age");    int j; 
   for(i=1; i<=nlstate;i++)    double xx,xmin,bx,ax; 
     for(j=1; j<=nlstate;j++)    double fx,fb,fa;
       fprintf(ficreseij," %1d-%1d",i,j);   
   fprintf(ficreseij,"\n");    ncom=n; 
     pcom=vector(1,n); 
   hstepm=1*YEARM; /*  Every j years of age (in month) */    xicom=vector(1,n); 
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    nrfunc=func; 
     for (j=1;j<=n;j++) { 
   agelim=AGESUP;      pcom[j]=p[j]; 
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */      xicom[j]=xi[j]; 
     /* nhstepm age range expressed in number of stepm */    } 
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);    ax=0.0; 
     /* Typically if 20 years = 20*12/6=40 stepm */    xx=1.0; 
     if (stepm >= YEARM) hstepm=1;    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); /* Find a bracket a,x,b in direction n=xi ie xicom */
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); /* Find a minimum P+lambda n in that direction (lambdamin), with TOL between abscisses */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  #ifdef DEBUG
     /* Computed by stepm unit matrices, product of hstepm matrices, stored    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */    fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);    #endif
     for (j=1;j<=n;j++) { 
       xi[j] *= xmin; 
     for(i=1; i<=nlstate;i++)      p[j] += xi[j]; 
       for(j=1; j<=nlstate;j++)    } 
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){    free_vector(xicom,1,n); 
           eij[i][j][(int)age] +=p3mat[i][j][h];    free_vector(pcom,1,n); 
         }  } 
      
     hf=1;  
     if (stepm >= YEARM) hf=stepm/YEARM;  /*************** powell ************************/
     fprintf(ficreseij,"%.0f",age );  /*
     for(i=1; i<=nlstate;i++)  Minimization of a function func of n variables. Input consists of an initial starting point
       for(j=1; j<=nlstate;j++){  p[1..n] ; an initial matrix xi[1..n][1..n] , whose columns contain the initial set of di-
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);  rections (usually the n unit vectors); and ftol , the fractional tolerance in the function value
       }  such that failure to decrease by more than this amount on one iteration signals doneness. On
     fprintf(ficreseij,"\n");  output, p is set to the best point found, xi is the then-current direction set, fret is the returned
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  function value at p , and iter is the number of iterations taken. The routine linmin is used.
   }   */
 }  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
               double (*func)(double [])) 
 /************ Variance ******************/  { 
 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)    void linmin(double p[], double xi[], int n, double *fret, 
 {                double (*func)(double [])); 
   /* Variance of health expectancies */    int i,ibig,j; 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    double del,t,*pt,*ptt,*xit;
   double **newm;    double fp,fptt;
   double **dnewm,**doldm;    double *xits;
   int i, j, nhstepm, hstepm, h;    int niterf, itmp;
   int k, cptcode;  
    double *xp;    pt=vector(1,n); 
   double **gp, **gm;    ptt=vector(1,n); 
   double ***gradg, ***trgradg;    xit=vector(1,n); 
   double ***p3mat;    xits=vector(1,n); 
   double age,agelim;    *fret=(*func)(p); 
   int theta;    for (j=1;j<=n;j++) pt[j]=p[j]; 
       rcurr_time = time(NULL);  
    fprintf(ficresvij,"# Covariances of life expectancies\n");    for (*iter=1;;++(*iter)) { 
   fprintf(ficresvij,"# Age");      fp=(*fret); 
   for(i=1; i<=nlstate;i++)      ibig=0; 
     for(j=1; j<=nlstate;j++)      del=0.0; 
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);      rlast_time=rcurr_time;
   fprintf(ficresvij,"\n");      /* (void) gettimeofday(&curr_time,&tzp); */
       rcurr_time = time(NULL);  
   xp=vector(1,npar);      curr_time = *localtime(&rcurr_time);
   dnewm=matrix(1,nlstate,1,npar);      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, rcurr_time-rlast_time, rcurr_time-rstart_time);fflush(stdout);
   doldm=matrix(1,nlstate,1,nlstate);      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret,rcurr_time-rlast_time, rcurr_time-rstart_time); fflush(ficlog);
    /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tm_sec-start_time.tm_sec); */
   hstepm=1*YEARM; /* Every year of age */     for (i=1;i<=n;i++) {
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        printf(" %d %.12f",i, p[i]);
   agelim = AGESUP;        fprintf(ficlog," %d %.12lf",i, p[i]);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        fprintf(ficrespow," %.12lf", p[i]);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */      }
     if (stepm >= YEARM) hstepm=1;      printf("\n");
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */      fprintf(ficlog,"\n");
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      fprintf(ficrespow,"\n");fflush(ficrespow);
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);      if(*iter <=3){
     gp=matrix(0,nhstepm,1,nlstate);        tml = *localtime(&rcurr_time);
     gm=matrix(0,nhstepm,1,nlstate);        strcpy(strcurr,asctime(&tml));
         rforecast_time=rcurr_time; 
     for(theta=1; theta <=npar; theta++){        itmp = strlen(strcurr);
       for(i=1; i<=npar; i++){ /* Computes gradient */        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          strcurr[itmp-1]='\0';
       }        printf("\nConsidering the time needed for the last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,rcurr_time-rlast_time);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        for(niterf=10;niterf<=30;niterf+=10){
       for(j=1; j<= nlstate; j++){          rforecast_time=rcurr_time+(niterf-*iter)*(rcurr_time-rlast_time);
         for(h=0; h<=nhstepm; h++){          forecast_time = *localtime(&rforecast_time);
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)          strcpy(strfor,asctime(&forecast_time));
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];          itmp = strlen(strfor);
         }          if(strfor[itmp-1]=='\n')
       }          strfor[itmp-1]='\0';
              printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
       for(i=1; i<=npar; i++) /* Computes gradient */          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(rforecast_time-rcurr_time,tmpout),strfor,strcurr);
         xp[i] = x[i] - (i==theta ?delti[theta]:0);        }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (i=1;i<=n;i++) { 
       for(j=1; j<= nlstate; j++){        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
         for(h=0; h<=nhstepm; h++){        fptt=(*fret); 
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)  #ifdef DEBUG
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];            printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
         }            fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
       }  #endif
       for(j=1; j<= nlstate; j++)        printf("%d",i);fflush(stdout);
         for(h=0; h<=nhstepm; h++){        fprintf(ficlog,"%d",i);fflush(ficlog);
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        linmin(p,xit,n,fret,func); 
         }        if (fabs(fptt-(*fret)) > del) { 
     } /* End theta */          del=fabs(fptt-(*fret)); 
           ibig=i; 
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);        } 
   #ifdef DEBUG
     for(h=0; h<=nhstepm; h++)        printf("%d %.12e",i,(*fret));
       for(j=1; j<=nlstate;j++)        fprintf(ficlog,"%d %.12e",i,(*fret));
         for(theta=1; theta <=npar; theta++)        for (j=1;j<=n;j++) {
           trgradg[h][j][theta]=gradg[h][theta][j];          xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
           printf(" x(%d)=%.12e",j,xit[j]);
     for(i=1;i<=nlstate;i++)          fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
       for(j=1;j<=nlstate;j++)        }
         vareij[i][j][(int)age] =0.;        for(j=1;j<=n;j++) {
     for(h=0;h<=nhstepm;h++){          printf(" p(%d)=%.12e",j,p[j]);
       for(k=0;k<=nhstepm;k++){          fprintf(ficlog," p(%d)=%.12e",j,p[j]);
         matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);        }
         matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);        printf("\n");
         for(i=1;i<=nlstate;i++)        fprintf(ficlog,"\n");
           for(j=1;j<=nlstate;j++)  #endif
             vareij[i][j][(int)age] += doldm[i][j];      } /* end i */
       }      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
     }  #ifdef DEBUG
     h=1;        int k[2],l;
     if (stepm >= YEARM) h=stepm/YEARM;        k[0]=1;
     fprintf(ficresvij,"%.0f ",age );        k[1]=-1;
     for(i=1; i<=nlstate;i++)        printf("Max: %.12e",(*func)(p));
       for(j=1; j<=nlstate;j++){        fprintf(ficlog,"Max: %.12e",(*func)(p));
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);        for (j=1;j<=n;j++) {
       }          printf(" %.12e",p[j]);
     fprintf(ficresvij,"\n");          fprintf(ficlog," %.12e",p[j]);
     free_matrix(gp,0,nhstepm,1,nlstate);        }
     free_matrix(gm,0,nhstepm,1,nlstate);        printf("\n");
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);        fprintf(ficlog,"\n");
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);        for(l=0;l<=1;l++) {
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          for (j=1;j<=n;j++) {
   } /* End age */            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
              printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   free_vector(xp,1,npar);            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
   free_matrix(doldm,1,nlstate,1,npar);          }
   free_matrix(dnewm,1,nlstate,1,nlstate);          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)));
 }        }
   #endif
 /************ Variance of prevlim ******************/  
 void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij)  
 {        free_vector(xit,1,n); 
   /* Variance of prevalence limit */        free_vector(xits,1,n); 
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        free_vector(ptt,1,n); 
   double **newm;        free_vector(pt,1,n); 
   double **dnewm,**doldm;        return; 
   int i, j, nhstepm, hstepm;      } 
   int k, cptcode;      if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
   double *xp;      for (j=1;j<=n;j++) { /* Computes an extrapolated point */
   double *gp, *gm;        ptt[j]=2.0*p[j]-pt[j]; 
   double **gradg, **trgradg;        xit[j]=p[j]-pt[j]; 
   double age,agelim;        pt[j]=p[j]; 
   int theta;      } 
          fptt=(*func)(ptt); 
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      if (fptt < fp) { /* If extrapolated point is better, decide if we keep that new direction or not */
   fprintf(ficresvpl,"# Age");        /* (x1 f1=fp), (x2 f2=*fret), (x3 f3=fptt), (xm fm) */
   for(i=1; i<=nlstate;i++)        /* From x1 (P0) distance of x2 is at h and x3 is 2h */
       fprintf(ficresvpl," %1d-%1d",i,i);        /* Let f"(x2) be the 2nd derivative equal everywhere.  */
   fprintf(ficresvpl,"\n");        /* Then the parabolic through (x1,f1), (x2,f2) and (x3,f3) */
         /* will reach at f3 = fm + h^2/2 f"m  ; f" = (f1 -2f2 +f3 ) / h**2 */
   xp=vector(1,npar);        /* f1-f3 = delta(2h) = 2 h**2 f'' = 2(f1- 2f2 +f3) */
   dnewm=matrix(1,nlstate,1,npar);        /* Thus we compare delta(2h) with observed f1-f3 */
   doldm=matrix(1,nlstate,1,nlstate);        /* or best gain on one ancient line 'del' with total  */
          /* gain f1-f2 = f1 - f2 - 'del' with del  */
   hstepm=1*YEARM; /* Every year of age */        /* t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */  
   agelim = AGESUP;        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del);
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        t= t- del*SQR(fp-fptt);
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */        printf("t1= %.12lf, t2= %.12lf, t=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t);
     if (stepm >= YEARM) hstepm=1;        fprintf(ficlog,"t1= %.12lf, t2= %.12lf, t=%.12lf\n", 2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del),del*SQR(fp-fptt),t);
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */  #ifdef DEBUG
     gradg=matrix(1,npar,1,nlstate);        printf("t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
     gp=vector(1,nlstate);               (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
     gm=vector(1,nlstate);        fprintf(ficlog,"t3= %.12lf, t4= %.12lf, t3*= %.12lf, t4*= %.12lf\n",SQR(fp-(*fret)-del),SQR(fp-fptt),
                (fp-(*fret)-del)*(fp-(*fret)-del),(fp-fptt)*(fp-fptt));
     for(theta=1; theta <=npar; theta++){        printf("tt= %.12lf, t=%.12lf\n",2.0*(fp-2.0*(*fret)+fptt)*(fp-(*fret)-del)*(fp-(*fret)-del)-del*(fp-fptt)*(fp-fptt),t);
       for(i=1; i<=npar; i++){ /* Computes gradient */        fprintf(ficlog, "tt= %.12lf, t=%.12lf\n",2.0*(fp-2.0*(*fret)+fptt)*(fp-(*fret)-del)*(fp-(*fret)-del)-del*(fp-fptt)*(fp-fptt),t);
         xp[i] = x[i] + (i==theta ?delti[theta]:0);  #endif
       }        if (t < 0.0) { /* Then we use it for last direction */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          linmin(p,xit,n,fret,func); /* computes mean on the extrapolated direction.*/
       for(i=1;i<=nlstate;i++)          for (j=1;j<=n;j++) { 
         gp[i] = prlim[i][i];            xi[j][ibig]=xi[j][n]; /* Replace the direction with biggest decrease by n */
                xi[j][n]=xit[j];      /* and nth direction by the extrapolated */
       for(i=1; i<=npar; i++) /* Computes gradient */          }
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          printf("Gaining to use average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);          fprintf(ficlog,"Gaining to use average direction of P0 P%d instead of biggest increase direction :\n",n,ibig);
       for(i=1;i<=nlstate;i++)  
         gm[i] = prlim[i][i];  #ifdef DEBUG
           printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
       for(i=1;i<=nlstate;i++)          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];          for(j=1;j<=n;j++){
     } /* End theta */            printf(" %.12e",xit[j]);
             fprintf(ficlog," %.12e",xit[j]);
     trgradg =matrix(1,nlstate,1,npar);          }
           printf("\n");
     for(j=1; j<=nlstate;j++)          fprintf(ficlog,"\n");
       for(theta=1; theta <=npar; theta++)  #endif
         trgradg[j][theta]=gradg[theta][j];        } /* end of t negative */
       } /* end if (fptt < fp)  */
     for(i=1;i<=nlstate;i++)    } 
       varpl[i][(int)age] =0.;  } 
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);  
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);  /**** Prevalence limit (stable or period prevalence)  ****************/
     for(i=1;i<=nlstate;i++)  
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
   {
     fprintf(ficresvpl,"%.0f ",age );    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
     for(i=1; i<=nlstate;i++)       matrix by transitions matrix until convergence is reached */
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));  
     fprintf(ficresvpl,"\n");    int i, ii,j,k;
     free_vector(gp,1,nlstate);    double min, max, maxmin, maxmax,sumnew=0.;
     free_vector(gm,1,nlstate);    /* double **matprod2(); */ /* test */
     free_matrix(gradg,1,npar,1,nlstate);    double **out, cov[NCOVMAX+1], **pmij();
     free_matrix(trgradg,1,nlstate,1,npar);    double **newm;
   } /* End age */    double agefin, delaymax=50 ; /* Max number of years to converge */
   
   free_vector(xp,1,npar);    for (ii=1;ii<=nlstate+ndeath;ii++)
   free_matrix(doldm,1,nlstate,1,npar);      for (j=1;j<=nlstate+ndeath;j++){
   free_matrix(dnewm,1,nlstate,1,nlstate);        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
       }
 }  
      cov[1]=1.;
    
    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
 /***********************************************/    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
 /**************** Main Program *****************/      newm=savm;
 /***********************************************/      /* Covariates have to be included here again */
       cov[2]=agefin;
 /*int main(int argc, char *argv[])*/      
 int main()      for (k=1; k<=cptcovn;k++) {
 {        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         /*printf("prevalim ij=%d k=%d Tvar[%d]=%d nbcode=%d cov=%lf codtab[%d][Tvar[%d]]=%d \n",ij,k, k, Tvar[k],nbcode[Tvar[k]][codtab[ij][Tvar[k]]],cov[2+k], ij, k, codtab[ij][Tvar[k]]);*/
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;      }
   double agedeb, agefin,hf;      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
   double agemin=1.e20, agemax=-1.e20;      /* for (k=1; k<=cptcovprod;k++) /\* Useless *\/ */
       /*   cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]] * nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]]; */
   double fret;      
   double **xi,tmp,delta;      /*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]);*/
   double dum; /* Dummy variable */      /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
   double ***p3mat;      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
   int *indx;      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
   char line[MAXLINE], linepar[MAXLINE];      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
   char title[MAXLINE];      
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];      savm=oldm;
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];      oldm=newm;
   char filerest[FILENAMELENGTH];      maxmax=0.;
   char fileregp[FILENAMELENGTH];      for(j=1;j<=nlstate;j++){
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        min=1.;
   int firstobs=1, lastobs=10;        max=0.;
   int sdeb, sfin; /* Status at beginning and end */        for(i=1; i<=nlstate; i++) {
   int c,  h , cpt,l;          sumnew=0;
   int ju,jl, mi;          for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
   int i1,j1, k1,jk,aa,bb, stepsize;          prlim[i][j]= newm[i][j]/(1-sumnew);
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;          /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
            max=FMAX(max,prlim[i][j]);
   int hstepm, nhstepm;          min=FMIN(min,prlim[i][j]);
   double bage, fage, age, agelim, agebase;        }
   double ftolpl=FTOL;        maxmin=max-min;
   double **prlim;        maxmax=FMAX(maxmax,maxmin);
   double *severity;      }
   double ***param; /* Matrix of parameters */      if(maxmax < ftolpl){
   double  *p;        return prlim;
   double **matcov; /* Matrix of covariance */      }
   double ***delti3; /* Scale */    }
   double *delti; /* Scale */  }
   double ***eij, ***vareij;  
   double **varpl; /* Variances of prevalence limits by age */  /*************** transition probabilities ***************/ 
   double *epj, vepp;  
   char version[80]="Imach version 0.64, May 2000, INED-EUROREVES ";  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
   char *alph[]={"a","a","b","c","d","e"}, str[4];  {
   char z[1]="c", occ;    /* According to parameters values stored in x and the covariate's values stored in cov,
 #include <sys/time.h>       computes the probability to be observed in state j being in state i by appying the
 #include <time.h>       model to the ncovmodel covariates (including constant and age).
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
   /* long total_usecs;       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
   struct timeval start_time, end_time;       ncth covariate in the global vector x is given by the formula:
         j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
        Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
        sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
   printf("\nIMACH, Version 0.64a");       Outputs ps[i][j] the probability to be observed in j being in j according to
   printf("\nEnter the parameter file name: ");       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     */
 #ifdef windows    double s1, lnpijopii;
   scanf("%s",pathtot);    /*double t34;*/
   cygwin_split_path(pathtot,path,optionfile);    int i,j, nc, ii, jj;
      printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);  
      chdir(path);      for(i=1; i<= nlstate; i++){
          for(j=1; j<i;j++){
   /*size=30;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   getcwd(pathcd, size);              /*lnpijopii += param[i][j][nc]*cov[nc];*/
   printf("pathcd=%s, path=%s, optionfile=%s\n",pathcd,path,optionfile);            lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
   cutv(path,optionfile,pathtot,'\\');  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   chdir(path);          }
   replace(pathc,path);          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   */        }
 #endif        for(j=i+1; j<=nlstate+ndeath;j++){
 #ifdef unix          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   scanf("%s",optionfile);            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
 #endif            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
   /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
 /*-------- arguments in the command line --------*/          }
           ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   strcpy(fileres,"r");        }
   strcat(fileres, optionfile);      }
       
   /*---------arguments file --------*/      for(i=1; i<= nlstate; i++){
         s1=0;
   if((ficpar=fopen(optionfile,"r"))==NULL)    {        for(j=1; j<i; j++){
     printf("Problem with optionfile %s\n",optionfile);          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
     goto end;          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
   }        }
         for(j=i+1; j<=nlstate+ndeath; j++){
   strcpy(filereso,"o");          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   strcat(filereso,fileres);          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
   if((ficparo=fopen(filereso,"w"))==NULL) {        }
     printf("Problem with Output resultfile: %s\n", filereso);goto end;        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
   }        ps[i][i]=1./(s1+1.);
         /* Computing other pijs */
   /* Reads comments: lines beginning with '#' */        for(j=1; j<i; j++)
   while((c=getc(ficpar))=='#' && c!= EOF){          ps[i][j]= exp(ps[i][j])*ps[i][i];
     ungetc(c,ficpar);        for(j=i+1; j<=nlstate+ndeath; j++)
     fgets(line, MAXLINE, ficpar);          ps[i][j]= exp(ps[i][j])*ps[i][i];
     puts(line);        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     fputs(line,ficparo);      } /* end i */
   }      
   ungetc(c,ficpar);      for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
         for(jj=1; jj<= nlstate+ndeath; jj++){
   fscanf(ficpar,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%lf stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model);          ps[ii][jj]=0;
   printf("title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt,model);          ps[ii][ii]=1;
   fprintf(ficparo,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt,model);        }
       }
   covar=matrix(1,NCOVMAX,1,n);          
   if (strlen(model)<=1) cptcovn=0;      
   else {      /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
     j=0;      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
     j=nbocc(model,'+');      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
     cptcovn=j+1;      /*   } */
   }      /*   printf("\n "); */
       /* } */
   ncovmodel=2+cptcovn;      /* printf("\n ");printf("%lf ",cov[2]);*/
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */      /*
          for(i=1; i<= npar; i++) printf("%f ",x[i]);
   /* Read guess parameters */        goto end;*/
   /* Reads comments: lines beginning with '#' */      return ps;
   while((c=getc(ficpar))=='#' && c!= EOF){  }
     ungetc(c,ficpar);  
     fgets(line, MAXLINE, ficpar);  /**************** Product of 2 matrices ******************/
     puts(line);  
     fputs(line,ficparo);  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
   }  {
   ungetc(c,ficpar);    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
         b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);    /* in, b, out are matrice of pointers which should have been initialized 
     for(i=1; i <=nlstate; i++)       before: only the contents of out is modified. The function returns
     for(j=1; j <=nlstate+ndeath-1; j++){       a pointer to pointers identical to out */
       fscanf(ficpar,"%1d%1d",&i1,&j1);    int i, j, k;
       fprintf(ficparo,"%1d%1d",i1,j1);    for(i=nrl; i<= nrh; i++)
       printf("%1d%1d",i,j);      for(k=ncolol; k<=ncoloh; k++){
       for(k=1; k<=ncovmodel;k++){        out[i][k]=0.;
         fscanf(ficpar," %lf",&param[i][j][k]);        for(j=ncl; j<=nch; j++)
         printf(" %lf",param[i][j][k]);          out[i][k] +=in[i][j]*b[j][k];
         fprintf(ficparo," %lf",param[i][j][k]);      }
       }    return out;
       fscanf(ficpar,"\n");  }
       printf("\n");  
       fprintf(ficparo,"\n");  
     }  /************* Higher Matrix Product ***************/
    
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   p=param[1][1];  {
      /* Computes the transition matrix starting at age 'age' over 
   /* Reads comments: lines beginning with '#' */       'nhstepm*hstepm*stepm' months (i.e. until
   while((c=getc(ficpar))=='#' && c!= EOF){       age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
     ungetc(c,ficpar);       nhstepm*hstepm matrices. 
     fgets(line, MAXLINE, ficpar);       Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
     puts(line);       (typically every 2 years instead of every month which is too big 
     fputs(line,ficparo);       for the memory).
   }       Model is determined by parameters x and covariates have to be 
   ungetc(c,ficpar);       included manually here. 
   
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);       */
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */  
   for(i=1; i <=nlstate; i++){    int i, j, d, h, k;
     for(j=1; j <=nlstate+ndeath-1; j++){    double **out, cov[NCOVMAX+1];
       fscanf(ficpar,"%1d%1d",&i1,&j1);    double **newm;
       printf("%1d%1d",i,j);  
       fprintf(ficparo,"%1d%1d",i1,j1);    /* Hstepm could be zero and should return the unit matrix */
       for(k=1; k<=ncovmodel;k++){    for (i=1;i<=nlstate+ndeath;i++)
         fscanf(ficpar,"%le",&delti3[i][j][k]);      for (j=1;j<=nlstate+ndeath;j++){
         printf(" %le",delti3[i][j][k]);        oldm[i][j]=(i==j ? 1.0 : 0.0);
         fprintf(ficparo," %le",delti3[i][j][k]);        po[i][j][0]=(i==j ? 1.0 : 0.0);
       }      }
       fscanf(ficpar,"\n");    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
       printf("\n");    for(h=1; h <=nhstepm; h++){
       fprintf(ficparo,"\n");      for(d=1; d <=hstepm; d++){
     }        newm=savm;
   }        /* Covariates have to be included here again */
   delti=delti3[1][1];        cov[1]=1.;
          cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   /* Reads comments: lines beginning with '#' */        for (k=1; k<=cptcovn;k++) 
   while((c=getc(ficpar))=='#' && c!= EOF){          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
     ungetc(c,ficpar);        for (k=1; k<=cptcovage;k++)
     fgets(line, MAXLINE, ficpar);          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
     puts(line);        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
     fputs(line,ficparo);          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   }  
   ungetc(c,ficpar);  
          /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   matcov=matrix(1,npar,1,npar);        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   for(i=1; i <=npar; i++){        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
     fscanf(ficpar,"%s",&str);                     pmij(pmmij,cov,ncovmodel,x,nlstate));
     printf("%s",str);        savm=oldm;
     fprintf(ficparo,"%s",str);        oldm=newm;
     for(j=1; j <=i; j++){      }
       fscanf(ficpar," %le",&matcov[i][j]);      for(i=1; i<=nlstate+ndeath; i++)
       printf(" %.5le",matcov[i][j]);        for(j=1;j<=nlstate+ndeath;j++) {
       fprintf(ficparo," %.5le",matcov[i][j]);          po[i][j][h]=newm[i][j];
     }          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
     fscanf(ficpar,"\n");        }
     printf("\n");      /*printf("h=%d ",h);*/
     fprintf(ficparo,"\n");    } /* end h */
   }  /*     printf("\n H=%d \n",h); */
   for(i=1; i <=npar; i++)    return po;
     for(j=i+1;j<=npar;j++)  }
       matcov[i][j]=matcov[j][i];  
      #ifdef NLOPT
   printf("\n");    double  myfunc(unsigned n, const double *p1, double *grad, void *pd){
     double fret;
     double *xt;
    if(mle==1){    int j;
     /*-------- data file ----------*/    myfunc_data *d2 = (myfunc_data *) pd;
     if((ficres =fopen(fileres,"w"))==NULL) {  /* xt = (p1-1); */
       printf("Problem with resultfile: %s\n", fileres);goto end;    xt=vector(1,n); 
     }    for (j=1;j<=n;j++)   xt[j]=p1[j-1]; /* xt[1]=p1[0] */
     fprintf(ficres,"#%s\n",version);  
        fret=(d2->function)(xt); /*  p xt[1]@8 is fine */
     if((fic=fopen(datafile,"r"))==NULL)    {    /* fret=(*func)(xt); /\*  p xt[1]@8 is fine *\/ */
       printf("Problem with datafile: %s\n", datafile);goto end;    printf("Function = %.12lf ",fret);
     }    for (j=1;j<=n;j++) printf(" %d %.8lf", j, xt[j]); 
     printf("\n");
     n= lastobs;   free_vector(xt,1,n);
     severity = vector(1,maxwav);    return fret;
     outcome=imatrix(1,maxwav+1,1,n);  }
     num=ivector(1,n);  #endif
     moisnais=vector(1,n);  
     annais=vector(1,n);  /*************** log-likelihood *************/
     moisdc=vector(1,n);  double func( double *x)
     andc=vector(1,n);  {
     agedc=vector(1,n);    int i, ii, j, k, mi, d, kk;
     cod=ivector(1,n);    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     weight=vector(1,n);    double **out;
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */    double sw; /* Sum of weights */
     mint=matrix(1,maxwav,1,n);    double lli; /* Individual log likelihood */
     anint=matrix(1,maxwav,1,n);    int s1, s2;
     s=imatrix(1,maxwav+1,1,n);    double bbh, survp;
     adl=imatrix(1,maxwav+1,1,n);        long ipmx;
     tab=ivector(1,NCOVMAX);    /*extern weight */
     ncodemax=ivector(1,8);    /* We are differentiating ll according to initial status */
     /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     i=1;    /*for(i=1;i<imx;i++) 
     while (fgets(line, MAXLINE, fic) != NULL)    {      printf(" %d\n",s[4][i]);
       if ((i >= firstobs) && (i <=lastobs)) {    */
          
         for (j=maxwav;j>=1;j--){    ++countcallfunc;
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);  
           strcpy(line,stra);    cov[1]=1.;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);  
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);    for(k=1; k<=nlstate; k++) ll[k]=0.;
         }  
            if(mle==1){
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);        /* Computes the values of the ncovmodel covariates of the model
            depending if the covariates are fixed or variying (age dependent) and stores them in cov[]
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);           to be observed in j being in i according to the model.
          */
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
         for (j=ncov;j>=1;j--){          cov[2+k]=covar[Tvar[k]][i];
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);        }
         }        /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
         num[i]=atol(stra);           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
            has been calculated etc */
         /*printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.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]),  (mint[5][i]), (anint[5][i]), (s[5][i]),  (mint[6][i]), (anint[6][i]), (s[6][i]));*/        for(mi=1; mi<= wav[i]-1; mi++){
           for (ii=1;ii<=nlstate+ndeath;ii++)
         i=i+1;            for (j=1;j<=nlstate+ndeath;j++){
       }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
     /*scanf("%d",i);*/          for(d=0; d<dh[mi][i]; d++){
   imx=i-1; /* Number of individuals */            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   /* Calculation of the number of parameter from char model*/            for (kk=1; kk<=cptcovage;kk++) {
   Tvar=ivector(1,8);                  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
                }
   if (strlen(model) >1){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     j=0;                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     j=nbocc(model,'+');            savm=oldm;
     cptcovn=j+1;            oldm=newm;
              } /* end mult */
     strcpy(modelsav,model);        
     if (j==0) {          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);          /* But now since version 0.9 we anticipate for bias at large stepm.
     }           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     else {           * (in months) between two waves is not a multiple of stepm, we rounded to 
       for(i=j; i>=1;i--){           * the nearest (and in case of equal distance, to the lowest) interval but now
         cutv(stra,strb,modelsav,'+');           * we keep into memory the bias bh[mi][i] and also the previous matrix product
         if (strchr(strb,'*')) {           * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
           cutv(strd,strc,strb,'*');           * probability in order to take into account the bias as a fraction of the way
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
           cutv(strb,strc,strd,'V');           * -stepm/2 to stepm/2 .
           for (k=1; k<=lastobs;k++)           * For stepm=1 the results are the same as for previous versions of Imach.
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];           * For stepm > 1 the results are less biased than in previous versions. 
         }           */
         else {cutv(strd,strc,strb,'V');          s1=s[mw[mi][i]][i];
         Tvar[i+1]=atoi(strc);          s2=s[mw[mi+1][i]][i];
         }          bbh=(double)bh[mi][i]/(double)stepm; 
         strcpy(modelsav,stra);            /* bias bh is positive if real duration
       }           * is higher than the multiple of stepm and negative otherwise.
       cutv(strd,strc,stra,'V');           */
       Tvar[1]=atoi(strc);          /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
     }          if( s2 > nlstate){ 
   }            /* i.e. if s2 is a death state and if the date of death is known 
   /*printf("tvar=%d ",Tvar[1]);               then the contribution to the likelihood is the probability to 
   scanf("%d ",i);*/               die between last step unit time and current  step unit time, 
     fclose(fic);               which is also equal to probability to die before dh 
                minus probability to die before dh-stepm . 
     if (weightopt != 1) { /* Maximisation without weights*/               In version up to 0.92 likelihood was computed
       for(i=1;i<=n;i++) weight[i]=1.0;          as if date of death was unknown. Death was treated as any other
     }          health state: the date of the interview describes the actual state
     /*-calculation of age at interview from date of interview and age at death -*/          and not the date of a change in health state. The former idea was
     agev=matrix(1,maxwav,1,imx);          to consider that at each interview the state was recorded
              (healthy, disable or death) and IMaCh was corrected; but when we
     for (i=1; i<=imx; i++)  {          introduced the exact date of death then we should have modified
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);          the contribution of an exact death to the likelihood. This new
       for(m=1; (m<= maxwav); m++){          contribution is smaller and very dependent of the step unit
         if(s[m][i] >0){          stepm. It is no more the probability to die between last interview
           if (s[m][i] == nlstate+1) {          and month of death but the probability to survive from last
             if(agedc[i]>0)          interview up to one month before death multiplied by the
               if(moisdc[i]!=99 && andc[i]!=9999)          probability to die within a month. Thanks to Chris
               agev[m][i]=agedc[i];          Jackson for correcting this bug.  Former versions increased
             else{          mortality artificially. The bad side is that we add another loop
               printf("Warning negative age at death: %d line:%d\n",num[i],i);          which slows down the processing. The difference can be up to 10%
               agev[m][i]=-1;          lower mortality.
             }            */
           }            lli=log(out[s1][s2] - savm[s1][s2]);
           else if(s[m][i] !=9){ /* Should no more exist */  
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);  
             if(mint[m][i]==99 || anint[m][i]==9999)          } else if  (s2==-2) {
               agev[m][i]=1;            for (j=1,survp=0. ; j<=nlstate; j++) 
             else if(agev[m][i] <agemin){              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
               agemin=agev[m][i];            /*survp += out[s1][j]; */
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/            lli= log(survp);
             }          }
             else if(agev[m][i] >agemax){          
               agemax=agev[m][i];          else if  (s2==-4) { 
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/            for (j=3,survp=0. ; j<=nlstate; j++)  
             }              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
             /*agev[m][i]=anint[m][i]-annais[i];*/            lli= log(survp); 
             /*   agev[m][i] = age[i]+2*m;*/          } 
           }  
           else { /* =9 */          else if  (s2==-5) { 
             agev[m][i]=1;            for (j=1,survp=0. ; j<=2; j++)  
             s[m][i]=-1;              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
           }            lli= log(survp); 
         }          } 
         else /*= 0 Unknown */          
           agev[m][i]=1;          else{
       }            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
                /*  lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2]));*/ /* linear interpolation */
     }          } 
     for (i=1; i<=imx; i++)  {          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
       for(m=1; (m<= maxwav); m++){          /*if(lli ==000.0)*/
         if (s[m][i] > (nlstate+ndeath)) {          /*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); */
           printf("Error: Wrong value in nlstate or ndeath\n");            ipmx +=1;
           goto end;          sw += weight[i];
         }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       }        } /* end of wave */
     }      } /* end of individual */
     }  else if(mle==2){
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     free_vector(severity,1,maxwav);        for(mi=1; mi<= wav[i]-1; mi++){
     free_imatrix(outcome,1,maxwav+1,1,n);          for (ii=1;ii<=nlstate+ndeath;ii++)
     free_vector(moisnais,1,n);            for (j=1;j<=nlstate+ndeath;j++){
     free_vector(annais,1,n);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(mint,1,maxwav,1,n);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     free_matrix(anint,1,maxwav,1,n);            }
     free_vector(moisdc,1,n);          for(d=0; d<=dh[mi][i]; d++){
     free_vector(andc,1,n);            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                for (kk=1; kk<=cptcovage;kk++) {
     wav=ivector(1,imx);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     dh=imatrix(1,lastpass-firstpass+1,1,imx);            }
     mw=imatrix(1,lastpass-firstpass+1,1,imx);            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                             1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     /* Concatenates waves */            savm=oldm;
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);            oldm=newm;
           } /* end mult */
         
 Tcode=ivector(1,100);          s1=s[mw[mi][i]][i];
    nbcode=imatrix(1,nvar,1,8);            s2=s[mw[mi+1][i]][i];
    ncodemax[1]=1;          bbh=(double)bh[mi][i]/(double)stepm; 
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
            ipmx +=1;
    codtab=imatrix(1,100,1,10);          sw += weight[i];
    h=0;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    m=pow(2,cptcovn);        } /* end of wave */
        } /* end of individual */
    for(k=1;k<=cptcovn; k++){    }  else if(mle==3){  /* exponential inter-extrapolation */
      for(i=1; i <=(m/pow(2,k));i++){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
        for(j=1; j <= ncodemax[k]; j++){        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){        for(mi=1; mi<= wav[i]-1; mi++){
            h++;          for (ii=1;ii<=nlstate+ndeath;ii++)
            if (h>m) h=1;codtab[h][k]=j;            for (j=1;j<=nlstate+ndeath;j++){
          }              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
        }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
      }            }
    }          for(d=0; d<dh[mi][i]; d++){
             newm=savm;
    /*for(i=1; i <=m ;i++){            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
      for(k=1; k <=cptcovn; k++){            for (kk=1; kk<=cptcovage;kk++) {
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
      }            }
      printf("\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
    }*/                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
    /*scanf("%d",i);*/            savm=oldm;
                oldm=newm;
    /* Calculates basic frequencies. Computes observed prevalence at single age          } /* end mult */
        and prints on file fileres'p'. */        
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
           bbh=(double)bh[mi][i]/(double)stepm; 
   /*scanf("%d ",i);*/          lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
           ipmx +=1;
           sw += weight[i];
     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */        } /* end of wave */
     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */      } /* end of individual */
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    }else if (mle==4){  /* ml=4 no inter-extrapolation */
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
            for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     /* For Powell, parameters are in a vector p[] starting at p[1]        for(mi=1; mi<= wav[i]-1; mi++){
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */          for (ii=1;ii<=nlstate+ndeath;ii++)
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */            for (j=1;j<=nlstate+ndeath;j++){
                  oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             }
              for(d=0; d<dh[mi][i]; d++){
     /*--------- results files --------------*/            newm=savm;
     fprintf(ficres,"\ntitle=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncov=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt,model);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                for (kk=1; kk<=cptcovage;kk++) {
    jk=1;              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
    fprintf(ficres,"# Parameters\n");            }
    printf("# Parameters\n");          
    for(i=1,jk=1; i <=nlstate; i++){            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
      for(k=1; k <=(nlstate+ndeath); k++){                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
        if (k != i)            savm=oldm;
          {            oldm=newm;
            printf("%d%d ",i,k);          } /* end mult */
            fprintf(ficres,"%1d%1d ",i,k);        
            for(j=1; j <=ncovmodel; j++){          s1=s[mw[mi][i]][i];
              printf("%f ",p[jk]);          s2=s[mw[mi+1][i]][i];
              fprintf(ficres,"%f ",p[jk]);          if( s2 > nlstate){ 
              jk++;            lli=log(out[s1][s2] - savm[s1][s2]);
            }          }else{
            printf("\n");            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
            fprintf(ficres,"\n");          }
          }          ipmx +=1;
      }          sw += weight[i];
    }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   /*      printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]); */
     /* Computing hessian and covariance matrix */        } /* end of wave */
     ftolhess=ftol; /* Usually correct */      } /* end of individual */
     hesscov(matcov, p, npar, delti, ftolhess, func);    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
     fprintf(ficres,"# Scales\n");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     printf("# Scales\n");        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
      for(i=1,jk=1; i <=nlstate; i++){        for(mi=1; mi<= wav[i]-1; mi++){
       for(j=1; j <=nlstate+ndeath; j++){          for (ii=1;ii<=nlstate+ndeath;ii++)
         if (j!=i) {            for (j=1;j<=nlstate+ndeath;j++){
           fprintf(ficres,"%1d%1d",i,j);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           printf("%1d%1d",i,j);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           for(k=1; k<=ncovmodel;k++){            }
             printf(" %.5e",delti[jk]);          for(d=0; d<dh[mi][i]; d++){
             fprintf(ficres," %.5e",delti[jk]);            newm=savm;
             jk++;            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           }            for (kk=1; kk<=cptcovage;kk++) {
           printf("\n");              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
           fprintf(ficres,"\n");            }
         }          
       }            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
                savm=oldm;
     k=1;            oldm=newm;
     fprintf(ficres,"# Covariance\n");          } /* end mult */
     printf("# Covariance\n");        
     for(i=1;i<=npar;i++){          s1=s[mw[mi][i]][i];
       /*  if (k>nlstate) k=1;          s2=s[mw[mi+1][i]][i];
       i1=(i-1)/(ncovmodel*nlstate)+1;          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);          ipmx +=1;
       printf("%s%d%d",alph[k],i1,tab[i]);*/          sw += weight[i];
       fprintf(ficres,"%3d",i);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       printf("%3d",i);          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
       for(j=1; j<=i;j++){        } /* end of wave */
         fprintf(ficres," %.5e",matcov[i][j]);      } /* end of individual */
         printf(" %.5e",matcov[i][j]);    } /* End of if */
       }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
       fprintf(ficres,"\n");    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
       printf("\n");    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
       k++;    return -l;
     }  }
      
     while((c=getc(ficpar))=='#' && c!= EOF){  /*************** log-likelihood *************/
       ungetc(c,ficpar);  double funcone( double *x)
       fgets(line, MAXLINE, ficpar);  {
       puts(line);    /* Same as likeli but slower because of a lot of printf and if */
       fputs(line,ficparo);    int i, ii, j, k, mi, d, kk;
     }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     ungetc(c,ficpar);    double **out;
      double lli; /* Individual log likelihood */
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    double llt;
        int s1, s2;
     if (fage <= 2) {    double bbh, survp;
       bage = agemin;    /*extern weight */
       fage = agemax;    /* We are differentiating ll according to initial status */
     }    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
     /*for(i=1;i<imx;i++) 
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");      printf(" %d\n",s[4][i]);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    */
 /*------------ gnuplot -------------*/    cov[1]=1.;
 chdir(pathcd);  
   if((ficgp=fopen("graph.plt","w"))==NULL) {    for(k=1; k<=nlstate; k++) ll[k]=0.;
     printf("Problem with file graph.plt");goto end;  
   }    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
 #ifdef windows      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
   fprintf(ficgp,"cd \"%s\" \n",pathc);      for(mi=1; mi<= wav[i]-1; mi++){
 #endif        for (ii=1;ii<=nlstate+ndeath;ii++)
 m=pow(2,cptcovn);          for (j=1;j<=nlstate+ndeath;j++){
              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
  /* 1eme*/            savm[ii][j]=(ii==j ? 1.0 : 0.0);
   for (cpt=1; cpt<= nlstate ; cpt ++) {          }
    for (k1=1; k1<= m ; k1 ++) {        for(d=0; d<dh[mi][i]; d++){
           newm=savm;
 #ifdef windows          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" every :::%d::%d u 1:2 \"\%%lf",agemin,fage,fileres,k1-1,k1-1);          for (kk=1; kk<=cptcovage;kk++) {
 #endif            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
 #ifdef unix          }
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
 #endif          out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
 for (i=1; i<= nlstate ; i ++) {          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
   else fprintf(ficgp," \%%*lf (\%%*lf)");          savm=oldm;
 }          oldm=newm;
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);        } /* end mult */
     for (i=1; i<= nlstate ; i ++) {        
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");        s1=s[mw[mi][i]][i];
   else fprintf(ficgp," \%%*lf (\%%*lf)");        s2=s[mw[mi+1][i]][i];
 }        bbh=(double)bh[mi][i]/(double)stepm; 
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);        /* bias is positive if real duration
      for (i=1; i<= nlstate ; i ++) {         * is higher than the multiple of stepm and negative otherwise.
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");         */
   else fprintf(ficgp," \%%*lf (\%%*lf)");        if( s2 > nlstate && (mle <5) ){  /* Jackson */
 }            lli=log(out[s1][s2] - savm[s1][s2]);
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));        } else if  (s2==-2) {
 #ifdef unix          for (j=1,survp=0. ; j<=nlstate; j++) 
 fprintf(ficgp,"\nset ter gif small size 400,300");            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
 #endif          lli= log(survp);
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        }else if (mle==1){
    }          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   }        } else if(mle==2){
   /*2 eme*/          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         } else if(mle==3){  /* exponential inter-extrapolation */
   for (k1=1; k1<= m ; k1 ++) {          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 */
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);        } else if (mle==4){  /* mle=4 no inter-extrapolation */
              lli=log(out[s1][s2]); /* Original formula */
     for (i=1; i<= nlstate+1 ; i ++) {        } else{  /* mle=0 back to 1 */
       k=2*i;          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);          /*lli=log(out[s1][s2]); */ /* Original formula */
       for (j=1; j<= nlstate+1 ; j ++) {        } /* End of if */
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");        ipmx +=1;
   else fprintf(ficgp," \%%*lf (\%%*lf)");        sw += weight[i];
 }          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");        /*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]); */
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);        if(globpr){
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
       for (j=1; j<= nlstate+1 ; j ++) {   %11.6f %11.6f %11.6f ", \
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
         else fprintf(ficgp," \%%*lf (\%%*lf)");                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
 }            for(k=1,llt=0.,l=0.; k<=nlstate; k++){
       fprintf(ficgp,"\" t\"\" w l 0,");            llt +=ll[k]*gipmx/gsw;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
       for (j=1; j<= nlstate+1 ; j ++) {          }
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");          fprintf(ficresilk," %10.6f\n", -llt);
   else fprintf(ficgp," \%%*lf (\%%*lf)");        }
 }        } /* end of wave */
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");    } /* end of individual */
       else fprintf(ficgp,"\" t\"\" w l 0,");    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
     }    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   }    if(globpr==0){ /* First time we count the contributions and weights */
        gipmx=ipmx;
   /*3eme*/      gsw=sw;
     }
    for (k1=1; k1<= m ; k1 ++) {    return -l;
     for (cpt=1; cpt<= nlstate ; cpt ++) {  }
       k=2+nlstate*(cpt-1);  
       fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" every :::%d::%d u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k1-1,k1-1,k,cpt);  
       for (i=1; i< nlstate ; i ++) {  /*************** function likelione ***********/
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
       }  {
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    /* This routine should help understanding what is done with 
     }       the selection of individuals/waves and
    }       to check the exact contribution to the likelihood.
         Plotting could be done.
   /* CV preval stat */     */
     for (k1=1; k1<= m ; k1 ++) {    int k;
     for (cpt=1; cpt<nlstate ; cpt ++) {  
       k=3;    if(*globpri !=0){ /* Just counts and sums, no printings */
       fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);      strcpy(fileresilk,"ilk"); 
       for (i=1; i< nlstate ; i ++)      strcat(fileresilk,fileres);
         fprintf(ficgp,"+$%d",k+i+1);      if((ficresilk=fopen(fileresilk,"w"))==NULL) {
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);        printf("Problem with resultfile: %s\n", fileresilk);
              fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
       l=3+(nlstate+ndeath)*cpt;      }
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);      fprintf(ficresilk, "#individual(line's_record) s1 s2 wave# effective_wave# number_of_matrices_product pij weight -2ln(pij)*weight 0pij_x 0pij_(x-stepm) cumulating_loglikeli_by_health_state(reweighted=-2ll*weightXnumber_of_contribs/sum_of_weights) and_total\n");
       for (i=1; i< nlstate ; i ++) {      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
         l=3+(nlstate+ndeath)*cpt;      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
         fprintf(ficgp,"+$%d",l+i+1);      for(k=1; k<=nlstate; k++) 
       }        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);        fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);    }
     }  
   }    *fretone=(*funcone)(p);
      if(*globpri !=0){
   /* proba elementaires */      fclose(ficresilk);
   for(i=1,jk=1; i <=nlstate; i++){      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
     for(k=1; k <=(nlstate+ndeath); k++){      fflush(fichtm); 
       if (k != i) {    } 
         /*  fprintf(ficgp,"%1d%1d ",i,k);*/    return;
         for(j=1; j <=ncovmodel; j++){  }
           fprintf(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);  
           jk++;  
           fprintf(ficgp,"\n");  /*********** Maximum Likelihood Estimation ***************/
         }  
       }  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     }  {
   }    int i,j, iter=0;
   for(jk=1; jk <=m; jk++) {    double **xi;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);    double fret;
   for(i=1; i <=nlstate; i++) {    double fretone; /* Only one call to likelihood */
     for(k=1; k <=(nlstate+ndeath); k++){    /*  char filerespow[FILENAMELENGTH];*/
       if (k != i) {  
         fprintf(ficgp," exp(a%d%d+b%d%d*x",i,k,i,k);  #ifdef NLOPT
         for(j=3; j <=ncovmodel; j++)    int creturn;
           fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    nlopt_opt opt;
         fprintf(ficgp,")/(1");    /* double lb[9] = { -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL, -HUGE_VAL }; /\* lower bounds *\/ */
         for(k1=1; k1 <=(nlstate+ndeath); k1++)    double *lb;
           if (k1 != i) {    double minf; /* the minimum objective value, upon return */
             fprintf(ficgp,"+exp(a%d%d+b%d%d*x",i,k1,i,k1);    double * p1; /* Shifted parameters from 0 instead of 1 */
             for(j=3; j <=ncovmodel; j++)    myfunc_data dinst, *d = &dinst;
               fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  #endif
             fprintf(ficgp,")");  
           }  
         fprintf(ficgp,") t \"p%d%d\" ", i,k);    xi=matrix(1,npar,1,npar);
       if ((i+k)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    for (i=1;i<=npar;i++)
       }      for (j=1;j<=npar;j++)
     }        xi[i][j]=(i==j ? 1.0 : 0.0);
   }    printf("Powell\n");  fprintf(ficlog,"Powell\n");
 fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      strcpy(filerespow,"pow"); 
   }    strcat(filerespow,fileres);
      if((ficrespow=fopen(filerespow,"w"))==NULL) {
  fclose(ficgp);      printf("Problem with resultfile: %s\n", filerespow);
       fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
     chdir(path);    }
     free_matrix(agev,1,maxwav,1,imx);    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     free_ivector(wav,1,imx);    for (i=1;i<=nlstate;i++)
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      for(j=1;j<=nlstate+ndeath;j++)
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
        fprintf(ficrespow,"\n");
     free_imatrix(s,1,maxwav+1,1,n);  #ifdef POWELL
        powell(p,xi,npar,ftol,&iter,&fret,func);
      #endif
     free_ivector(num,1,n);  
     free_vector(agedc,1,n);  #ifdef NLOPT
     free_vector(weight,1,n);  #ifdef NEWUOA
     /*free_matrix(covar,1,NCOVMAX,1,n);*/    opt = nlopt_create(NLOPT_LN_NEWUOA,npar);
     fclose(ficparo);  #else
     fclose(ficres);    opt = nlopt_create(NLOPT_LN_BOBYQA,npar);
    }  #endif
        lb=vector(0,npar-1);
    /*________fin mle=1_________*/    for (i=0;i<npar;i++) lb[i]= -HUGE_VAL;
        nlopt_set_lower_bounds(opt, lb);
     nlopt_set_initial_step1(opt, 0.1);
      
     /* No more information from the sample is required now */    p1= (p+1); /*  p *(p+1)@8 and p *(p1)@8 are equal p1[0]=p[1] */
   /* Reads comments: lines beginning with '#' */    d->function = func;
   while((c=getc(ficpar))=='#' && c!= EOF){    printf(" Func %.12lf \n",myfunc(npar,p1,NULL,d));
     ungetc(c,ficpar);    nlopt_set_min_objective(opt, myfunc, d);
     fgets(line, MAXLINE, ficpar);    nlopt_set_xtol_rel(opt, ftol);
     puts(line);    if ((creturn=nlopt_optimize(opt, p1, &minf)) < 0) {
     fputs(line,ficparo);      printf("nlopt failed! %d\n",creturn); 
   }    }
   ungetc(c,ficpar);    else {
        printf("found minimum after %d evaluations (NLOPT=%d)\n", countcallfunc ,NLOPT);
       printf("found minimum at f(%g,%g) = %0.10g\n", p[0], p[1], minf);
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);      iter=1; /* not equal */
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);    }
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);    nlopt_destroy(opt);
 /*--------- index.htm --------*/  #endif
     free_matrix(xi,1,npar,1,npar);
   if((fichtm=fopen("index.htm","w"))==NULL)    {    fclose(ficrespow);
     printf("Problem with index.htm \n");goto end;    printf("\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   }    fprintf(ficlog,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
     fprintf(ficres,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
  fprintf(fichtm,"<body><ul> Imach, Version 0.63<hr> <li>Outputs files<br><br>\n  
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n  }
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>  
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>  /**** Computes Hessian and covariance matrix ***/
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>  {
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>    double  **a,**y,*x,pd;
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>    double **hess;
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>    int i, j;
         - Standard deviation of stationary prevalences: <a href=\"vpl%s\">vpl%s</a> <br><br>",fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres,fileres);    int *indx;
   
  fprintf(fichtm," <li>Graphs</li>\n<p>");    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
  m=cptcovn;    void lubksb(double **a, int npar, int *indx, double b[]) ;
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}    void ludcmp(double **a, int npar, int *indx, double *d) ;
     double gompertz(double p[]);
  j1=0;    hess=matrix(1,npar,1,npar);
  for(k1=1; k1<=m;k1++){  
    for(i1=1; i1<=ncodemax[k1];i1++){    printf("\nCalculation of the hessian matrix. Wait...\n");
        j1++;    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
        if (cptcovn > 0) {    for (i=1;i<=npar;i++){
          fprintf(fichtm,"<hr>************ Results for covariates");      printf("%d",i);fflush(stdout);
          for (cpt=1; cpt<=cptcovn;cpt++)      fprintf(ficlog,"%d",i);fflush(ficlog);
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);     
          fprintf(fichtm," ************\n<hr>");       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
        }      
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      /*  printf(" %f ",p[i]);
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);              printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
        for(cpt=1; cpt<nlstate;cpt++){    }
          fprintf(fichtm,"<br>- Prevalence of disability : p%s%d%d.gif<br>    
 <img src=\"p%s%d%d.gif\">",strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    for (i=1;i<=npar;i++) {
        }      for (j=1;j<=npar;j++)  {
     for(cpt=1; cpt<=nlstate;cpt++) {        if (j>i) { 
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident          printf(".%d%d",i,j);fflush(stdout);
 interval) in state (%d): v%s%d%d.gif <br>          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);            hess[i][j]=hessij(p,delti,i,j,func,npar);
      }          
      for(cpt=1; cpt<=nlstate;cpt++) {          hess[j][i]=hess[i][j];    
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>          /*printf(" %lf ",hess[i][j]);*/
 <img src=\"ex%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);        }
      }      }
      fprintf(fichtm,"\n<br>- Total life expectancy by age and    }
 health expectancies in states (1) and (2): e%s%d.gif<br>    printf("\n");
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);    fprintf(ficlog,"\n");
 fprintf(fichtm,"\n</body>");  
    }    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
  }    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 fclose(fichtm);    
     a=matrix(1,npar,1,npar);
   /*--------------- Prevalence limit --------------*/    y=matrix(1,npar,1,npar);
      x=vector(1,npar);
   strcpy(filerespl,"pl");    indx=ivector(1,npar);
   strcat(filerespl,fileres);    for (i=1;i<=npar;i++)
   if((ficrespl=fopen(filerespl,"w"))==NULL) {      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;    ludcmp(a,npar,indx,&pd);
   }  
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);    for (j=1;j<=npar;j++) {
   fprintf(ficrespl,"#Prevalence limit\n");      for (i=1;i<=npar;i++) x[i]=0;
   fprintf(ficrespl,"#Age ");      x[j]=1;
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);      lubksb(a,npar,indx,x);
   fprintf(ficrespl,"\n");      for (i=1;i<=npar;i++){ 
          matcov[i][j]=x[i];
   prlim=matrix(1,nlstate,1,nlstate);      }
   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 */    printf("\n#Hessian matrix#\n");
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    fprintf(ficlog,"\n#Hessian matrix#\n");
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    for (i=1;i<=npar;i++) { 
   k=0;      for (j=1;j<=npar;j++) { 
   agebase=agemin;        printf("%.3e ",hess[i][j]);
   agelim=agemax;        fprintf(ficlog,"%.3e ",hess[i][j]);
   ftolpl=1.e-10;      }
   i1=cptcovn;      printf("\n");
   if (cptcovn < 1){i1=1;}      fprintf(ficlog,"\n");
     }
   for(cptcov=1;cptcov<=i1;cptcov++){  
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    /* Recompute Inverse */
         k=k+1;    for (i=1;i<=npar;i++)
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
         fprintf(ficrespl,"\n#****** ");    ludcmp(a,npar,indx,&pd);
         for(j=1;j<=cptcovn;j++)  
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    /*  printf("\n#Hessian matrix recomputed#\n");
         fprintf(ficrespl,"******\n");  
            for (j=1;j<=npar;j++) {
         for (age=agebase; age<=agelim; age++){      for (i=1;i<=npar;i++) x[i]=0;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      x[j]=1;
           fprintf(ficrespl,"%.0f",age );      lubksb(a,npar,indx,x);
           for(i=1; i<=nlstate;i++)      for (i=1;i<=npar;i++){ 
           fprintf(ficrespl," %.5f", prlim[i][i]);        y[i][j]=x[i];
           fprintf(ficrespl,"\n");        printf("%.3e ",y[i][j]);
         }        fprintf(ficlog,"%.3e ",y[i][j]);
       }      }
     }      printf("\n");
   fclose(ficrespl);      fprintf(ficlog,"\n");
   /*------------- h Pij x at various ages ------------*/    }
      */
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);  
   if((ficrespij=fopen(filerespij,"w"))==NULL) {    free_matrix(a,1,npar,1,npar);
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;    free_matrix(y,1,npar,1,npar);
   }    free_vector(x,1,npar);
   printf("Computing pij: result on file '%s' \n", filerespij);    free_ivector(indx,1,npar);
      free_matrix(hess,1,npar,1,npar);
   stepsize=(int) (stepm+YEARM-1)/YEARM;  
   if (stepm<=24) stepsize=2;  
   }
   agelim=AGESUP;  
   hstepm=stepsize*YEARM; /* Every year of age */  /*************** hessian matrix ****************/
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
    {
   k=0;    int i;
   for(cptcov=1;cptcov<=i1;cptcov++){    int l=1, lmax=20;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    double k1,k2;
       k=k+1;    double p2[MAXPARM+1]; /* identical to x */
         fprintf(ficrespij,"\n#****** ");    double res;
         for(j=1;j<=cptcovn;j++)    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    double fx;
         fprintf(ficrespij,"******\n");    int k=0,kmax=10;
            double l1;
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */  
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    fx=func(x);
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */    for (i=1;i<=npar;i++) p2[i]=x[i];
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
           oldm=oldms;savm=savms;      l1=pow(10,l);
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);        delts=delt;
           fprintf(ficrespij,"# 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(ficrespij," %1d-%1d",i,j);        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
           fprintf(ficrespij,"\n");        p2[theta]=x[theta]-delt;
           for (h=0; h<=nhstepm; h++){        k2=func(p2)-fx;
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );        /*res= (k1-2.0*fx+k2)/delt/delt; */
             for(i=1; i<=nlstate;i++)        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
               for(j=1; j<=nlstate+ndeath;j++)        
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);  #ifdef DEBUGHESS
             fprintf(ficrespij,"\n");        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
           }        fprintf(ficlog,"%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);
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);  #endif
           fprintf(ficrespij,"\n");        /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
         }        if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
     }          k=kmax;
   }        }
         else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
   fclose(ficrespij);          k=kmax; l=lmax*10;
         }
   /*---------- Health expectancies and variances ------------*/        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
           delts=delt;
   strcpy(filerest,"t");        }
   strcat(filerest,fileres);      }
   if((ficrest=fopen(filerest,"w"))==NULL) {    }
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;    delti[theta]=delts;
   }    return res; 
   printf("Computing Total LEs with variances: file '%s' \n", filerest);    
   }
   
   strcpy(filerese,"e");  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
   strcat(filerese,fileres);  {
   if((ficreseij=fopen(filerese,"w"))==NULL) {    int i;
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);    int l=1, lmax=20;
   }    double k1,k2,k3,k4,res,fx;
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);    double p2[MAXPARM+1];
     int k;
  strcpy(fileresv,"v");  
   strcat(fileresv,fileres);    fx=func(x);
   if((ficresvij=fopen(fileresv,"w"))==NULL) {    for (k=1; k<=2; k++) {
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);      for (i=1;i<=npar;i++) p2[i]=x[i];
   }      p2[thetai]=x[thetai]+delti[thetai]/k;
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       k1=func(p2)-fx;
   k=0;    
   for(cptcov=1;cptcov<=i1;cptcov++){      p2[thetai]=x[thetai]+delti[thetai]/k;
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
       k=k+1;      k2=func(p2)-fx;
       fprintf(ficrest,"\n#****** ");    
       for(j=1;j<=cptcovn;j++)      p2[thetai]=x[thetai]-delti[thetai]/k;
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);      p2[thetaj]=x[thetaj]+delti[thetaj]/k;
       fprintf(ficrest,"******\n");      k3=func(p2)-fx;
     
       fprintf(ficreseij,"\n#****** ");      p2[thetai]=x[thetai]-delti[thetai]/k;
       for(j=1;j<=cptcovn;j++)      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);      k4=func(p2)-fx;
       fprintf(ficreseij,"******\n");      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
   #ifdef DEBUG
       fprintf(ficresvij,"\n#****** ");      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
       for(j=1;j<=cptcovn;j++)      fprintf(ficlog,"%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  #endif
       fprintf(ficresvij,"******\n");    }
     return res;
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  }
       oldm=oldms;savm=savms;  
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);    /************** Inverse of matrix **************/
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);  void ludcmp(double **a, int n, int *indx, double *d) 
       oldm=oldms;savm=savms;  { 
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    int i,imax,j,k; 
          double big,dum,sum,temp; 
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");    double *vv; 
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);   
       fprintf(ficrest,"\n");    vv=vector(1,n); 
            *d=1.0; 
       hf=1;    for (i=1;i<=n;i++) { 
       if (stepm >= YEARM) hf=stepm/YEARM;      big=0.0; 
       epj=vector(1,nlstate+1);      for (j=1;j<=n;j++) 
       for(age=bage; age <=fage ;age++){        if ((temp=fabs(a[i][j])) > big) big=temp; 
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);      if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
         fprintf(ficrest," %.0f",age);      vv[i]=1.0/big; 
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){    } 
           for(i=1, epj[j]=0.;i <=nlstate;i++) {    for (j=1;j<=n;j++) { 
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];      for (i=1;i<j;i++) { 
           }        sum=a[i][j]; 
           epj[nlstate+1] +=epj[j];        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
         }        a[i][j]=sum; 
         for(i=1, vepp=0.;i <=nlstate;i++)      } 
           for(j=1;j <=nlstate;j++)      big=0.0; 
             vepp += vareij[i][j][(int)age];      for (i=j;i<=n;i++) { 
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));        sum=a[i][j]; 
         for(j=1;j <=nlstate;j++){        for (k=1;k<j;k++) 
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));          sum -= a[i][k]*a[k][j]; 
         }        a[i][j]=sum; 
         fprintf(ficrest,"\n");        if ( (dum=vv[i]*fabs(sum)) >= big) { 
       }          big=dum; 
     }          imax=i; 
   }        } 
              } 
  fclose(ficreseij);      if (j != imax) { 
  fclose(ficresvij);        for (k=1;k<=n;k++) { 
   fclose(ficrest);          dum=a[imax][k]; 
   fclose(ficpar);          a[imax][k]=a[j][k]; 
   free_vector(epj,1,nlstate+1);          a[j][k]=dum; 
   /*scanf("%d ",i); */        } 
         *d = -(*d); 
   /*------- Variance limit prevalence------*/          vv[imax]=vv[j]; 
       } 
 strcpy(fileresvpl,"vpl");      indx[j]=imax; 
   strcat(fileresvpl,fileres);      if (a[j][j] == 0.0) a[j][j]=TINY; 
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {      if (j != n) { 
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);        dum=1.0/(a[j][j]); 
     exit(0);        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
   }      } 
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);    } 
     free_vector(vv,1,n);  /* Doesn't work */
  k=0;  ;
  for(cptcov=1;cptcov<=i1;cptcov++){  } 
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){  
      k=k+1;  void lubksb(double **a, int n, int *indx, double b[]) 
      fprintf(ficresvpl,"\n#****** ");  { 
      for(j=1;j<=cptcovn;j++)    int i,ii=0,ip,j; 
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    double sum; 
      fprintf(ficresvpl,"******\n");   
          for (i=1;i<=n;i++) { 
      varpl=matrix(1,nlstate,(int) bage, (int) fage);      ip=indx[i]; 
      oldm=oldms;savm=savms;      sum=b[ip]; 
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);      b[ip]=b[i]; 
    }      if (ii) 
  }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
       else if (sum) ii=i; 
   fclose(ficresvpl);      b[i]=sum; 
     } 
   /*---------- End : free ----------------*/    for (i=n;i>=1;i--) { 
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);      sum=b[i]; 
        for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);      b[i]=sum/a[i][i]; 
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    } 
    } 
    
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);  void pstamp(FILE *fichier)
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);  {
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);  }
    
   free_matrix(matcov,1,npar,1,npar);  /************ Frequencies ********************/
   free_vector(delti,1,npar);  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 */
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);    
     int i, m, jk, j1, bool, z1,j;
   printf("End of Imach\n");    int first;
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */    double ***freq; /* Frequencies */
      double *pp, **prop;
   /* 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);*/    double pos,posprop, k2, dateintsum=0,k2cpt=0;
   /*printf("Total time was %d uSec.\n", total_usecs);*/    char fileresp[FILENAMELENGTH];
   /*------ End -----------*/    
     pp=vector(1,nlstate);
  end:    prop=matrix(1,nlstate,iagemin,iagemax+3);
 #ifdef windows    strcpy(fileresp,"p");
  chdir(pathcd);    strcat(fileresp,fileres);
 #endif    if((ficresp=fopen(fileresp,"w"))==NULL) {
  system("wgnuplot graph.plt");      printf("Problem with prevalence resultfile: %s\n", fileresp);
       fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
 #ifdef windows      exit(0);
   while (z[0] != 'q') {    }
     chdir(pathcd);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
     printf("\nType e to edit output files, c to start again, and q for exiting: ");    j1=0;
     scanf("%s",z);    
     if (z[0] == 'c') system("./imach");    j=cptcoveff;
     else if (z[0] == 'e') {    if (cptcovn<1) {j=1;ncodemax[1]=1;}
       chdir(path);  
       system("index.htm");    first=1;
     }  
     else if (z[0] == 'q') exit(0);    /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
   }    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
 #endif    /*    j1++;
 }  */
     for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
         /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
           scanf("%d", i);*/
         for (i=-5; i<=nlstate+ndeath; i++)  
           for (jk=-5; jk<=nlstate+ndeath; jk++)  
             for(m=iagemin; m <= iagemax+3; m++)
               freq[i][jk][m]=0;
         
         for (i=1; i<=nlstate; i++)  
           for(m=iagemin; m <= iagemax+3; m++)
             prop[i][m]=0;
         
         dateintsum=0;
         k2cpt=0;
         for (i=1; i<=imx; i++) {
           bool=1;
           if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
             for (z1=1; z1<=cptcoveff; z1++)       
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
                   /* Tests if the value of each of the covariates of i is equal to filter j1 */
                 bool=0;
                 /* printf("bool=%d i=%d, z1=%d, Tvaraff[%d]=%d, covar[Tvarff][%d]=%2f, codtab[%d][%d]=%d, nbcode[Tvaraff][codtab[%d][%d]=%d, j1=%d\n", 
                   bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
                   j1,z1,nbcode[Tvaraff[z1]][codtab[j1][z1]],j1);*/
                 /* For j1=7 in V1+V2+V3+V4 = 0 1 1 0 and codtab[7][3]=1 and nbcde[3][?]=1*/
               } 
           }
    
           if (bool==1){
             for(m=firstpass; m<=lastpass; m++){
               k2=anint[m][i]+(mint[m][i]/12.);
               /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
                 if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
                 if (m<lastpass) {
                   freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
                 }
                 
                 if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
                   dateintsum=dateintsum+k2;
                   k2cpt++;
                 }
                 /*}*/
             }
           }
         } /* end i */
          
         /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
         pstamp(ficresp);
         if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresp, "**********\n#");
           fprintf(ficlog, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficlog, "**********\n#");
         }
         for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
         fprintf(ficresp, "\n");
         
         for(i=iagemin; i <= iagemax+3; i++){
           if(i==iagemax+3){
             fprintf(ficlog,"Total");
           }else{
             if(first==1){
               first=0;
               printf("See log file for details...\n");
             }
             fprintf(ficlog,"Age %d", i);
           }
           for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
               pp[jk] += freq[jk][m][i]; 
           }
           for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pos=0; m <=0 ; m++)
               pos += freq[jk][m][i];
             if(pp[jk]>=1.e-10){
               if(first==1){
                 printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               }
               fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
             }else{
               if(first==1)
                 printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
             }
           }
   
           for(jk=1; jk <=nlstate ; jk++){
             for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
               pp[jk] += freq[jk][m][i];
           }       
           for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
             pos += pp[jk];
             posprop += prop[jk][i];
           }
           for(jk=1; jk <=nlstate ; jk++){
             if(pos>=1.e-5){
               if(first==1)
                 printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
               fprintf(ficlog," %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
             }else{
               if(first==1)
                 printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
             }
             if( i <= iagemax){
               if(pos>=1.e-5){
                 fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
                 /*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]);*/
               }
               else
                 fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
             }
           }
           
           for(jk=-1; jk <=nlstate+ndeath; jk++)
             for(m=-1; m <=nlstate+ndeath; m++)
               if(freq[jk][m][i] !=0 ) {
               if(first==1)
                 printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                 fprintf(ficlog," %d%d=%.0f",jk,m,freq[jk][m][i]);
               }
           if(i <= iagemax)
             fprintf(ficresp,"\n");
           if(first==1)
             printf("Others in log...\n");
           fprintf(ficlog,"\n");
         }
         /*}*/
     }
     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);
     /* End of Freq */
   }
   
   /************ Prevalence ********************/
   void prevalence(double ***probs, double agemin, double agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax,double **mint,double **anint, double dateprev1,double dateprev2, int firstpass, int lastpass)
   {  
     /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
        in each health status at the date of interview (if between dateprev1 and dateprev2).
        We still use firstpass and lastpass as another selection.
     */
    
     int i, m, jk, j1, bool, z1,j;
   
     double **prop;
     double posprop; 
     double  y2; /* in fractional years */
     int iagemin, iagemax;
     int first; /** to stop verbosity which is redirected to log file */
   
     iagemin= (int) agemin;
     iagemax= (int) agemax;
     /*pp=vector(1,nlstate);*/
     prop=matrix(1,nlstate,iagemin,iagemax+3); 
     /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
     j1=0;
     
     /*j=cptcoveff;*/
     if (cptcovn<1) {j=1;ncodemax[1]=1;}
     
     first=1;
     for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
       /*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 (i=1; i<=imx; i++) { /* Each individual */
           bool=1;
           if  (cptcovn>0) {
             for (z1=1; z1<=cptcoveff; z1++) 
               if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
                 bool=0;
           } 
           if (bool==1) { 
             for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
               y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
               if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
                 if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
                 if((int)agev[m][i] <iagemin || (int)agev[m][i] >iagemax+3) printf("Error on individual =%d agev[m][i]=%f m=%d\n",i, agev[m][i],m); 
                 if (s[m][i]>0 && s[m][i]<=nlstate) { 
                   /*if(i>4620) printf(" i=%d m=%d s[m][i]=%d (int)agev[m][i]=%d weight[i]=%f prop=%f\n",i,m,s[m][i],(int)agev[m][m],weight[i],prop[s[m][i]][(int)agev[m][i]]);*/
                   prop[s[m][i]][(int)agev[m][i]] += weight[i];
                   prop[s[m][i]][iagemax+3] += weight[i]; 
                 } 
               }
             } /* end selection of waves */
           }
         }
         for(i=iagemin; i <= iagemax+3; i++){  
           for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
             posprop += prop[jk][i]; 
           } 
           
           for(jk=1; jk <=nlstate ; jk++){     
             if( i <=  iagemax){ 
               if(posprop>=1.e-5){ 
                 probs[i][jk][j1]= prop[jk][i]/posprop;
               } else{
                 if(first==1){
                   first=0;
                   printf("Warning Observed prevalence probs[%d][%d][%d]=%lf because of lack of cases\nSee others on log file...\n",jk,i,j1,probs[i][jk][j1]);
                 }
               }
             } 
           }/* end jk */ 
         }/* end i */ 
       /*} *//* end i1 */
     } /* end j1 */
     
     /*  free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath, iagemin, iagemax+3);*/
     /*free_vector(pp,1,nlstate);*/
     free_matrix(prop,1,nlstate, iagemin,iagemax+3);
   }  /* End of prevalence */
   
   /************* Waves Concatenation ***************/
   
   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)
   {
     /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
        Death is a valid wave (if date is known).
        mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
        dh[m][i] 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, mi, m;
     /* int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
        double sum=0., jmean=0.;*/
     int first;
     int j, k=0,jk, ju, jl;
     double sum=0.;
     first=0;
     jmin=100000;
     jmax=-1;
     jmean=0.;
     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;
         else
           m++;
       }/* end while */
       if (s[m][i] > nlstate){
         mi++;     /* Death is another wave */
         /* if(mi==0)  never been interviewed correctly before death */
            /* Only death is a correct wave */
         mw[mi][i]=m;
       }
   
       wav[i]=mi;
       if(mi==0){
         nbwarn++;
         if(first==0){
           printf("Warning! No valid information for individual %ld line=%d (skipped) and may be others, see log file\n",num[i],i);
           first=1;
         }
         if(first==1){
           fprintf(ficlog,"Warning! No valid information for individual %ld line=%d (skipped)\n",num[i],i);
         }
       } /* end mi==0 */
     } /* End individuals */
   
     for(i=1; i<=imx; i++){
       for(mi=1; mi<wav[i];mi++){
         if (stepm <=0)
           dh[mi][i]=1;
         else{
           if (s[mw[mi+1][i]][i] > nlstate) { /* A death */
             if (agedc[i] < 2*AGESUP) {
               j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
               if(j==0) j=1;  /* Survives at least one month after exam */
               else if(j<0){
                 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]);
                 j=1; /* Temporary Dangerous patch */
                 printf("   We assumed that the date of interview was correct (and not the date of death) and postponed the death %d month(s) (one stepm) after the interview. You MUST fix the contradiction between dates.\n",stepm);
                 fprintf(ficlog,"Error! Negative delay (%d to death) between waves %d and %d of individual %ld at line %d who is aged %.1f with statuses from %d to %d\n ",j,mw[mi][i],mw[mi+1][i],num[i], i,agev[mw[mi][i]][i],s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);
                 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);
               }
               k=k+1;
               if (j >= jmax){
                 jmax=j;
                 ijmax=i;
               }
               if (j <= jmin){
                 jmin=j;
                 ijmin=i;
               }
               sum=sum+j;
               /*if (j<0) printf("j=%d num=%d \n",j,i);*/
               /*    printf("%d %d %d %d\n", s[mw[mi][i]][i] ,s[mw[mi+1][i]][i],j,i);*/
             }
           }
           else{
             j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
   /*        if (j<0) printf("%d %lf %lf %d %d %d\n", i,agev[mw[mi+1][i]][i], agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]); */
   
             k=k+1;
             if (j >= jmax) {
               jmax=j;
               ijmax=i;
             }
             else if (j <= jmin){
               jmin=j;
               ijmin=i;
             }
             /*        if (j<10) printf("j=%d jmin=%d num=%d ",j,jmin,i); */
             /*printf("%d %lf %d %d %d\n", i,agev[mw[mi][i]][i],j,s[mw[mi][i]][i] ,s[mw[mi+1][i]][i]);*/
             if(j<0){
               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]);
               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]);
             }
             sum=sum+j;
           }
           jk= j/stepm;
           jl= j -jk*stepm;
           ju= j -(jk+1)*stepm;
           if(mle <=1){ /* only if we use a the linear-interpoloation pseudo-likelihood */
             if(jl==0){
               dh[mi][i]=jk;
               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;
               bh[mi][i]=ju;
             }
           }else{
             if(jl <= -ju){
               dh[mi][i]=jk;
               bh[mi][i]=jl;       /* bias is positive if real duration
                                    * is higher than the multiple of stepm and negative otherwise.
                                    */
             }
             else{
               dh[mi][i]=jk+1;
               bh[mi][i]=ju;
             }
             if(dh[mi][i]==0){
               dh[mi][i]=1; /* At least one step */
               bh[mi][i]=ju; /* At least one step */
               /*  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);*/
             }
           } /* end if mle */
         }
       } /* end wave */
     }
     jmean=sum/k;
     printf("Delay (in months) between two waves Min=%d (for indiviudal %ld) Max=%d (%ld) Mean=%f\n\n ",jmin, num[ijmin], jmax, num[ijmax], jmean);
     fprintf(ficlog,"Delay (in months) between two waves Min=%d (for indiviudal %d) Max=%d (%d) Mean=%f\n\n ",jmin, ijmin, jmax, ijmax, jmean);
    }
   
   /*********** Tricode ****************************/
   void tricode(int *Tvar, int **nbcode, int imx, int *Ndum)
   {
     /**< Uses cptcovn+2*cptcovprod as the number of covariates */
     /*      Tvar[i]=atoi(stre);  find 'n' in Vn and stores in Tvar. If model=V2+V1 Tvar[1]=2 and Tvar[2]=1 
     /* Boring subroutine which should only output nbcode[Tvar[j]][k]
      * Tvar[5] in V2+V1+V3*age+V2*V4 is 2 (V2)
     /* nbcode[Tvar[j]][1]= 
     */
   
     int ij=1, k=0, j=0, i=0, maxncov=NCOVMAX;
     int modmaxcovj=0; /* Modality max of covariates j */
     int cptcode=0; /* Modality max of covariates j */
     int modmincovj=0; /* Modality min of covariates j */
   
   
     cptcoveff=0; 
    
     for (k=-1; k < maxncov; k++) Ndum[k]=0;
     for (k=1; k <= maxncov; k++) ncodemax[k]=0; /* Horrible constant again replaced by NCOVMAX */
   
     /* Loop on covariates without age and products */
     for (j=1; j<=(cptcovs); j++) { /* model V1 + V2*age+ V3 + V3*V4 : V1 + V3 = 2 only */
       for (i=1; i<=imx; i++) { /* Lopp on individuals: reads the data file to get the maximum value of the 
                                  modality of this covariate Vj*/ 
         ij=(int)(covar[Tvar[j]][i]); /* ij=0 or 1 or -1. Value of the covariate Tvar[j] for individual i
                                       * If product of Vn*Vm, still boolean *:
                                       * If it was coded 1, 2, 3, 4 should be splitted into 3 boolean variables
                                       * 1 => 0 0 0, 2 => 0 0 1, 3 => 0 1 1, 4=1 0 0   */
         /* Finds for covariate j, n=Tvar[j] of Vn . ij is the
                                         modality of the nth covariate of individual i. */
         if (ij > modmaxcovj)
           modmaxcovj=ij; 
         else if (ij < modmincovj) 
           modmincovj=ij; 
         if ((ij < -1) && (ij > NCOVMAX)){
           printf( "Error: minimal is less than -1 or maximal is bigger than %d. Exiting. \n", NCOVMAX );
           exit(1);
         }else
         Ndum[ij]++; /*counts and stores the occurence of this modality 0, 1, -1*/
         /*  If coded 1, 2, 3 , counts the number of 1 Ndum[1], number of 2, Ndum[2], etc */
         /*printf("i=%d ij=%d Ndum[ij]=%d imx=%d",i,ij,Ndum[ij],imx);*/
         /* getting the maximum value of the modality of the covariate
            (should be 0 or 1 now) Tvar[j]. If V=sex and male is coded 0 and
            female is 1, then modmaxcovj=1.*/
       }
       printf(" Minimal and maximal values of %d th covariate V%d: min=%d max=%d \n", j, Tvar[j], modmincovj, modmaxcovj);
       cptcode=modmaxcovj;
       /* Ndum[0] = frequency of 0 for model-covariate j, Ndum[1] frequency of 1 etc. */
      /*for (i=0; i<=cptcode; i++) {*/
       for (i=modmincovj;  i<=modmaxcovj; i++) { /* i=-1 ? 0 and 1*//* For each value of the modality of model-cov j */
         printf("Frequencies of covariates %d V%d %d\n", j, Tvar[j], Ndum[i]);
         if( Ndum[i] != 0 ){ /* Counts if nobody answered, empty modality */
           ncodemax[j]++;  /* ncodemax[j]= Number of non-null modalities of the j th covariate. */
         }
         /* In fact  ncodemax[j]=2 (dichotom. variables only) but it could be more for
            historical reasons: 3 if coded 1, 2, 3 and 4 and Ndum[2]=0 */
       } /* Ndum[-1] number of undefined modalities */
   
       /* j is a covariate, n=Tvar[j] of Vn; Fills nbcode */
       /* For covariate j, modalities could be 1, 2, 3, 4. If Ndum[2]=0 ncodemax[j] is not 4 but 3 */
       /* If Ndum[3}= 635; Ndum[4]=0; Ndum[5]=0; Ndum[6]=27; Ndum[7]=125;
          modmincovj=3; modmaxcovj = 7;
          There are only 3 modalities non empty (or 2 if 27 is too few) : ncodemax[j]=3;
          which will be coded 0, 1, 2 which in binary on 3-1 digits are 0=00 1=01, 2=10; defining two dummy 
          variables V1_1 and V1_2.
          nbcode[Tvar[j]][ij]=k;
          nbcode[Tvar[j]][1]=0;
          nbcode[Tvar[j]][2]=1;
          nbcode[Tvar[j]][3]=2;
       */
       ij=1; /* ij is similar to i but can jumps over null modalities */
       for (i=modmincovj; i<=modmaxcovj; i++) { /* i= 1 to 2 for dichotomous, or from 1 to 3 */
         for (k=0; k<= cptcode; k++) { /* k=-1 ? k=0 to 1 *//* Could be 1 to 4 */
           /*recode from 0 */
           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. 
                                        k is a modality. If we have model=V1+V1*sex 
                                        then: nbcode[1][1]=0 ; nbcode[1][2]=1; nbcode[2][1]=0 ; nbcode[2][2]=1; */
             ij++;
           }
           if (ij > ncodemax[j]) break; 
         }  /* end of loop on */
       } /* end of loop on modality */ 
     } /* end of loop on model-covariate j. nbcode[Tvarj][1]=0 and nbcode[Tvarj][2]=1 sets the value of covariate j*/  
     
    for (k=-1; k< maxncov; k++) Ndum[k]=0; 
     
     for (i=1; i<=ncovmodel-2; i++) { /* -2, cste and age */ 
      /* Listing of all covariables in statement model to see if some covariates appear twice. For example, V1 appears twice in V1+V1*V2.*/ 
      ij=Tvar[i]; /* Tvar might be -1 if status was unknown */ 
      Ndum[ij]++; 
    } 
   
    ij=1;
    for (i=0; i<=  maxncov-1; i++) { /* modmaxcovj is unknown here. Only Ndum[2(V2),3(age*V3), 5(V3*V2) 6(V1*V4) */
      /*printf("Ndum[%d]=%d\n",i, Ndum[i]);*/
      if((Ndum[i]!=0) && (i<=ncovcol)){
        /*printf("diff Ndum[%d]=%d\n",i, Ndum[i]);*/
        Tvaraff[ij]=i; /*For printing (unclear) */
        ij++;
      }else
          Tvaraff[ij]=0;
    }
    ij--;
    cptcoveff=ij; /*Number of total covariates*/
   
   }
   
   
   /*********** Health Expectancies ****************/
   
   void evsij(double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int cij, int estepm,char strstart[] )
   
   {
     /* Health expectancies, no variances */
     int i, j, nhstepm, hstepm, h, nstepm;
     int nhstepma, nstepma; /* Decreasing with age */
     double age, agelim, hf;
     double ***p3mat;
     double eip;
   
     pstamp(ficreseij);
     fprintf(ficreseij,"# (a) Life expectancies by health status at initial age and (b) health expectancies by health status at initial age\n");
     fprintf(ficreseij,"# Age");
     for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++){
         fprintf(ficreseij," e%1d%1d ",i,j);
       }
       fprintf(ficreseij," e%1d. ",i);
     }
     fprintf(ficreseij,"\n");
   
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
      * if stepm=24 months pijx are given only every 2 years and by summing them
      * 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
      * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
      * curvature will be obtained if estepm is as small as stepm. */
   
     /* 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. 
        nhstepm is the number of hstepm from age to agelim 
        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 */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   
     agelim=AGESUP;
     /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepm matrices, stored
          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;*/
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
   
     for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
       nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
       /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
       hpxij(p3mat,nhstepma,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       
       printf("%d|",(int)age);fflush(stdout);
       fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
       
       /* Computing expectancies */
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3mat[i][j][h]+p3mat[i][j][h+1])/2.0*hf;
             
             /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   
           }
   
       fprintf(ficreseij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
         eip=0;
         for(j=1; j<=nlstate;j++){
           eip +=eij[i][j][(int)age];
           fprintf(ficreseij,"%9.4f", eij[i][j][(int)age] );
         }
         fprintf(ficreseij,"%9.4f", eip );
       }
       fprintf(ficreseij,"\n");
       
     }
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
     fprintf(ficlog,"\n");
     
   }
   
   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[] )
   
   {
     /* Covariances of health expectancies eij and of total life expectancies according
      to initial status i, ei. .
     */
     int i, j, nhstepm, hstepm, h, nstepm, k, cptj, cptj2, i2, j2, ij, ji;
     int nhstepma, nstepma; /* Decreasing with age */
     double age, agelim, hf;
     double ***p3matp, ***p3matm, ***varhe;
     double **dnewm,**doldm;
     double *xp, *xm;
     double **gp, **gm;
     double ***gradg, ***trgradg;
     int theta;
   
     double eip, vip;
   
     varhe=ma3x(1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int) fage);
     xp=vector(1,npar);
     xm=vector(1,npar);
     dnewm=matrix(1,nlstate*nlstate,1,npar);
     doldm=matrix(1,nlstate*nlstate,1,nlstate*nlstate);
     
     pstamp(ficresstdeij);
     fprintf(ficresstdeij,"# Health expectancies with standard errors\n");
     fprintf(ficresstdeij,"# Age");
     for(i=1; i<=nlstate;i++){
       for(j=1; j<=nlstate;j++)
         fprintf(ficresstdeij," e%1d%1d (SE)",i,j);
       fprintf(ficresstdeij," e%1d. ",i);
     }
     fprintf(ficresstdeij,"\n");
   
     pstamp(ficrescveij);
     fprintf(ficrescveij,"# Subdiagonal matrix of covariances of health expectancies by age: cov(eij,ekl)\n");
     fprintf(ficrescveij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++){
         cptj= (j-1)*nlstate+i;
         for(i2=1; i2<=nlstate;i2++)
           for(j2=1; j2<=nlstate;j2++){
             cptj2= (j2-1)*nlstate+i2;
             if(cptj2 <= cptj)
               fprintf(ficrescveij,"  %1d%1d,%1d%1d",i,j,i2,j2);
           }
       }
     fprintf(ficrescveij,"\n");
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* We compute the life expectancy from trapezoids spaced every estepm months
      * This is mainly to measure the difference between two models: for example
      * if stepm=24 months pijx are given only every 2 years and by summing them
      * 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
      * to compare the new estimate of Life expectancy with the same linear 
      * hypothesis. A more precise result, taking into account a more precise
      * curvature will be obtained if estepm is as small as stepm. */
   
     /* 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. 
        nhstepm is the number of hstepm from age to agelim 
        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 */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed only each two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
   
     /* If stepm=6 months */
     /* nhstepm age range expressed in number of stepm */
     agelim=AGESUP;
     nstepm=(int) rint((agelim-bage)*YEARM/stepm); 
     /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
     /* if (stepm >= YEARM) hstepm=1;*/
     nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
     
     p3matp=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     p3matm=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     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);
     gm=matrix(0,nhstepm,1,nlstate*nlstate);
   
     for (age=bage; age<=fage; age ++){ 
       nstepma=(int) rint((agelim-bage)*YEARM/stepm); /* Biggest nstepm */
       /* Typically if 20 years nstepm = 20*12/6=40 stepm */ 
       /* if (stepm >= YEARM) hstepm=1;*/
       nhstepma = nstepma/hstepm;/* Expressed in hstepm, typically nhstepma=40/4=10 */
   
       /* If stepm=6 months */
       /* Computed by stepm unit matrices, product of hstepma matrices, stored
          in an array of nhstepma length: nhstepma=10, hstepm=4, stepm=6 months */
       
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
   
       /* Computing  Variances of health expectancies */
       /* Gradient is computed with plus gp and minus gm. Code is duplicated in order to
          decrease memory allocation */
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ 
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
           xm[i] = x[i] - (i==theta ?delti[theta]:0);
         }
         hpxij(p3matp,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, cij);  
         hpxij(p3matm,nhstepm,age,hstepm,xm,nlstate,stepm,oldm,savm, cij);  
     
         for(j=1; j<= nlstate; j++){
           for(i=1; i<=nlstate; i++){
             for(h=0; h<=nhstepm-1; h++){
               gp[h][(j-1)*nlstate + i] = (p3matp[i][j][h]+p3matp[i][j][h+1])/2.;
               gm[h][(j-1)*nlstate + i] = (p3matm[i][j][h]+p3matm[i][j][h+1])/2.;
             }
           }
         }
        
         for(ij=1; ij<= nlstate*nlstate; ij++)
           for(h=0; h<=nhstepm-1; h++){
             gradg[h][theta][ij]= (gp[h][ij]-gm[h][ij])/2./delti[theta];
           }
       }/* End theta */
       
       
       for(h=0; h<=nhstepm-1; h++)
         for(j=1; j<=nlstate*nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
       
   
        for(ij=1;ij<=nlstate*nlstate;ij++)
         for(ji=1;ji<=nlstate*nlstate;ji++)
           varhe[ij][ji][(int)age] =0.;
   
        printf("%d|",(int)age);fflush(stdout);
        fprintf(ficlog,"%d|",(int)age);fflush(ficlog);
        for(h=0;h<=nhstepm-1;h++){
         for(k=0;k<=nhstepm-1;k++){
           matprod2(dnewm,trgradg[h],1,nlstate*nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate*nlstate,1,npar,1,nlstate*nlstate,gradg[k]);
           for(ij=1;ij<=nlstate*nlstate;ij++)
             for(ji=1;ji<=nlstate*nlstate;ji++)
               varhe[ij][ji][(int)age] += doldm[ij][ji]*hf*hf;
         }
       }
   
       /* Computing expectancies */
       hpxij(p3matm,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, cij);  
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++)
           for (h=0, eij[i][j][(int)age]=0; h<=nhstepm-1; h++){
             eij[i][j][(int)age] += (p3matm[i][j][h]+p3matm[i][j][h+1])/2.0*hf;
             
             /* if((int)age==70)printf("i=%2d,j=%2d,h=%2d,age=%3d,%9.4f,%9.4f,%9.4f\n",i,j,h,(int)age,p3mat[i][j][h],hf,eij[i][j][(int)age]);*/
   
           }
   
       fprintf(ficresstdeij,"%3.0f",age );
       for(i=1; i<=nlstate;i++){
         eip=0.;
         vip=0.;
         for(j=1; j<=nlstate;j++){
           eip += eij[i][j][(int)age];
           for(k=1; k<=nlstate;k++) /* Sum on j and k of cov(eij,eik) */
             vip += varhe[(j-1)*nlstate+i][(k-1)*nlstate+i][(int)age];
           fprintf(ficresstdeij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[(j-1)*nlstate+i][(j-1)*nlstate+i][(int)age]) );
         }
         fprintf(ficresstdeij," %9.4f (%.4f)", eip, sqrt(vip));
       }
       fprintf(ficresstdeij,"\n");
   
       fprintf(ficrescveij,"%3.0f",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           cptj= (j-1)*nlstate+i;
           for(i2=1; i2<=nlstate;i2++)
             for(j2=1; j2<=nlstate;j2++){
               cptj2= (j2-1)*nlstate+i2;
               if(cptj2 <= cptj)
                 fprintf(ficrescveij," %.4f", varhe[cptj][cptj2][(int)age]);
             }
         }
       fprintf(ficrescveij,"\n");
      
     }
     free_matrix(gm,0,nhstepm,1,nlstate*nlstate);
     free_matrix(gp,0,nhstepm,1,nlstate*nlstate);
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*nlstate);
     free_ma3x(trgradg,0,nhstepm,1,nlstate*nlstate,1,npar);
     free_ma3x(p3matm,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     free_ma3x(p3matp,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     printf("\n");
     fprintf(ficlog,"\n");
   
     free_vector(xm,1,npar);
     free_vector(xp,1,npar);
     free_matrix(dnewm,1,nlstate*nlstate,1,npar);
     free_matrix(doldm,1,nlstate*nlstate,1,nlstate*nlstate);
     free_ma3x(varhe,1,nlstate*nlstate,1,nlstate*nlstate,(int) bage, (int)fage);
   }
   
   /************ Variance ******************/
   void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
   {
     /* Variance of health expectancies */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
     /* double **newm;*/
     double **dnewm,**doldm;
     double **dnewmp,**doldmp;
     int i, j, nhstepm, hstepm, h, nstepm ;
     int k;
     double *xp;
     double **gp, **gm;  /* for var eij */
     double ***gradg, ***trgradg; /*for var eij */
     double **gradgp, **trgradgp; /* for var p point j */
     double *gpp, *gmp; /* for var p point j */
     double **varppt; /* for var p point j nlstate to nlstate+ndeath */
     double ***p3mat;
     double age,agelim, hf;
     double ***mobaverage;
     int theta;
     char digit[4];
     char digitp[25];
   
     char fileresprobmorprev[FILENAMELENGTH];
   
     if(popbased==1){
       if(mobilav!=0)
         strcpy(digitp,"-populbased-mobilav-");
       else strcpy(digitp,"-populbased-nomobil-");
     }
     else 
       strcpy(digitp,"-stablbased-");
   
     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);
       }
     }
   
     strcpy(fileresprobmorprev,"prmorprev"); 
     sprintf(digit,"%-d",ij);
     /*printf("DIGIT=%s, ij=%d ijr=%-d|\n",digit, ij,ij);*/
     strcat(fileresprobmorprev,digit); /* Tvar to be done */
     strcat(fileresprobmorprev,digitp); /* Popbased or not, mobilav or not */
     strcat(fileresprobmorprev,fileres);
     if((ficresprobmorprev=fopen(fileresprobmorprev,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobmorprev);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobmorprev);
     }
     printf("Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
    
     fprintf(ficlog,"Computing total mortality p.j=w1*p1j+w2*p2j+..: result on file '%s' \n",fileresprobmorprev);
     pstamp(ficresprobmorprev);
     fprintf(ficresprobmorprev,"# probabilities of dying before estepm=%d months for people of exact age and weighted probabilities w1*p1j+w2*p2j+... stand dev in()\n",estepm);
     fprintf(ficresprobmorprev,"# Age cov=%-d",ij);
     for(j=nlstate+1; j<=(nlstate+ndeath);j++){
       fprintf(ficresprobmorprev," p.%-d SE",j);
       for(i=1; i<=nlstate;i++)
         fprintf(ficresprobmorprev," w%1d p%-d%-d",i,i,j);
     }  
     fprintf(ficresprobmorprev,"\n");
     fprintf(ficgp,"\n# Routine varevsij");
     /* fprintf(fichtm, "#Local time at start: %s", strstart);*/
     fprintf(fichtm,"\n<li><h4> Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)</h4></li>\n");
     fprintf(fichtm,"\n<br>%s  <br>\n",digitp);
   /*   } */
     varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     pstamp(ficresvij);
     fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n#  (weighted average of eij where weights are ");
     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
       fprintf(ficresvij,"the age specific period (stable) prevalences in each health state \n");
     fprintf(ficresvij,"# Age");
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=nlstate;j++)
         fprintf(ficresvij," Cov(e.%1d, e.%1d)",i,j);
     fprintf(ficresvij,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     dnewmp= matrix(nlstate+1,nlstate+ndeath,1,npar);
     doldmp= matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
   
     gradgp=matrix(1,npar,nlstate+1,nlstate+ndeath);
     gpp=vector(nlstate+1,nlstate+ndeath);
     gmp=vector(nlstate+1,nlstate+ndeath);
     trgradgp =matrix(nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
     /* 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. 
        nhstepm is the number of hstepm from age to agelim 
        nstepm is the number of stepm from age to agelin. 
        Look at function hpijx to understand why (it is linked to memory size questions) */
     /* We decided (b) to get a life expectancy respecting the most precise curvature of the
        survival function given by stepm (the optimization length). Unfortunately it
        means that if the survival funtion is printed every two years of age and if
        you sum them up and add 1 year (area under the trapezoids) you won't get the same 
        results. So we changed our mind and took the option of the best precision.
     */
     hstepm=hstepm/stepm; /* Typically in stepm units, if stepm=6 & estepm=24 , = 24/6 months = 4 */ 
     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 */ 
       nhstepm = nstepm/hstepm;/* Expressed in hstepm, typically nhstepm=40/4=10 */
       p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
       gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
       gp=matrix(0,nhstepm,1,nlstate);
       gm=matrix(0,nhstepm,1,nlstate);
   
   
       for(theta=1; theta <=npar; theta++){
         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);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
   
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
     
         for(j=1; j<= nlstate; j++){
           for(h=0; h<=nhstepm; h++){
             for(i=1, gp[h][j]=0.;i<=nlstate;i++)
               gp[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gpp[j]=0.; i<= nlstate; i++)
             gpp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         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);  
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
    
         if (popbased==1) {
           if(mobilav ==0){
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=probs[(int)age][i][ij];
           }else{ /* mobilav */ 
             for(i=1; i<=nlstate;i++)
               prlim[i][i]=mobaverage[(int)age][i][ij];
           }
         }
   
         for(j=1; j<= nlstate; j++){  /* Sum of wi * eij = e.j */
           for(h=0; h<=nhstepm; h++){
             for(i=1, gm[h][j]=0.;i<=nlstate;i++)
               gm[h][j] += prlim[i][i]*p3mat[i][j][h];
           }
         }
         /* This for computing probability of death (h=1 means
            computed over hstepm matrices product = hstepm*stepm months) 
            as a weighted average of prlim.
         */
         for(j=nlstate+1;j<=nlstate+ndeath;j++){
           for(i=1,gmp[j]=0.; i<= nlstate; i++)
            gmp[j] += prlim[i][i]*p3mat[i][j][1];
         }    
         /* end probability of death */
   
         for(j=1; j<= nlstate; j++) /* vareij */
           for(h=0; h<=nhstepm; h++){
             gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
           }
   
         for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu */
           gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta];
         }
   
       } /* End theta */
   
       trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */
   
       for(h=0; h<=nhstepm; h++) /* veij */
         for(j=1; j<=nlstate;j++)
           for(theta=1; theta <=npar; theta++)
             trgradg[h][j][theta]=gradg[h][theta][j];
   
       for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */
         for(theta=1; theta <=npar; theta++)
           trgradgp[j][theta]=gradgp[theta][j];
     
   
       hf=hstepm*stepm/YEARM;  /* Duration of hstepm expressed in year unit. */
       for(i=1;i<=nlstate;i++)
         for(j=1;j<=nlstate;j++)
           vareij[i][j][(int)age] =0.;
   
       for(h=0;h<=nhstepm;h++){
         for(k=0;k<=nhstepm;k++){
           matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
           matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
           for(i=1;i<=nlstate;i++)
             for(j=1;j<=nlstate;j++)
               vareij[i][j][(int)age] += doldm[i][j]*hf*hf;
         }
       }
     
       /* pptj */
       matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov);
       matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp);
       for(j=nlstate+1;j<=nlstate+ndeath;j++)
         for(i=nlstate+1;i<=nlstate+ndeath;i++)
           varppt[j][i]=doldmp[j][i];
       /* end ppptj */
       /*  x centered again */
       hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);
    
       if (popbased==1) {
         if(mobilav ==0){
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=probs[(int)age][i][ij];
         }else{ /* mobilav */ 
           for(i=1; i<=nlstate;i++)
             prlim[i][i]=mobaverage[(int)age][i][ij];
         }
       }
                
       /* This for computing probability of death (h=1 means
          computed over hstepm (estepm) matrices product = hstepm*stepm months) 
          as a weighted average of prlim.
       */
       for(j=nlstate+1;j<=nlstate+ndeath;j++){
         for(i=1,gmp[j]=0.;i<= nlstate; i++) 
           gmp[j] += prlim[i][i]*p3mat[i][j][1]; 
       }    
       /* end probability of death */
   
       fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij);
       for(j=nlstate+1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));
         for(i=1; i<=nlstate;i++){
           fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]);
         }
       } 
       fprintf(ficresprobmorprev,"\n");
   
       fprintf(ficresvij,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         for(j=1; j<=nlstate;j++){
           fprintf(ficresvij," %.4f", vareij[i][j][(int)age]);
         }
       fprintf(ficresvij,"\n");
       free_matrix(gp,0,nhstepm,1,nlstate);
       free_matrix(gm,0,nhstepm,1,nlstate);
       free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
       free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
       free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
     } /* End age */
     free_vector(gpp,nlstate+1,nlstate+ndeath);
     free_vector(gmp,nlstate+1,nlstate+ndeath);
     free_matrix(gradgp,1,npar,nlstate+1,nlstate+ndeath);
     free_matrix(trgradgp,nlstate+1,nlstate+ndeath,1,npar); /* mu or p point j*/
     fprintf(ficgp,"\nunset parametric;unset label; set ter png small size 320, 240");
     /* for(j=nlstate+1; j<= nlstate+ndeath; j++){ *//* Only the first actually */
     fprintf(ficgp,"\n set log y; unset log x;set xlabel \"Age\"; set ylabel \"Force of mortality (year-1)\";");
   /*   fprintf(ficgp,"\n plot \"%s\"  u 1:($3*%6.3f) not w l 1 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)*%6.3f) t \"95\%% interval\" w l 2 ",fileresprobmorprev,YEARM/estepm); */
   /*   fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)*%6.3f) not w l 2 ",fileresprobmorprev,YEARM/estepm); */
     fprintf(ficgp,"\n plot \"%s\"  u 1:($3) not w l lt 1 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3+1.96*$4)) t \"95\%% interval\" w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(ficgp,"\n replot \"%s\"  u 1:(($3-1.96*$4)) not w l lt 2 ",subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> File (multiple files are possible if covariates are present): <A href=\"%s\">%s</a>\n",subdirf(fileresprobmorprev),subdirf(fileresprobmorprev));
     fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months. <br> <img src=\"%s%s.png\"> <br>\n", estepm,subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
     /*  fprintf(fichtm,"\n<br> Probability is computed over estepm=%d months and then divided by estepm and multiplied by %.0f in order to have the probability to die over a year <br> <img src=\"varmuptjgr%s%s.png\"> <br>\n", stepm,YEARM,digitp,digit);
   */
   /*   fprintf(ficgp,"\nset out \"varmuptjgr%s%s%s.png\";replot;",digitp,optionfilefiname,digit); */
     fprintf(ficgp,"\nset out \"%s%s.png\";replot;\n",subdirf3(optionfilefiname,"varmuptjgr",digitp),digit);
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,nlstate);
     free_matrix(dnewm,1,nlstate,1,npar);
     free_matrix(doldmp,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     free_matrix(dnewmp,nlstate+1,nlstate+ndeath,1,npar);
     free_matrix(varppt,nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath);
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficresprobmorprev);
     fflush(ficgp);
     fflush(fichtm); 
   }  /* end varevsij */
   
   /************ Variance of prevlim ******************/
   void varprevlim(char fileres[], double **varpl, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, char strstart[])
   {
     /* Variance of prevalence limit */
     /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
   
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     
     pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  k1, l1, tj;
     int k2, l2, j1,  z1;
     int k=0, l;
     int first=1, first1, first2;
     double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2, c12, tnalp;
     double **dnewm,**doldm;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double **mu;
     double age, cov[NCOVMAX+1];
     double std=2.0; /* Number of standard deviation wide of confidence ellipsoids */
     int theta;
     char fileresprob[FILENAMELENGTH];
     char fileresprobcov[FILENAMELENGTH];
     char fileresprobcor[FILENAMELENGTH];
     double ***varpij;
   
     strcpy(fileresprob,"prob"); 
     strcat(fileresprob,fileres);
     if((ficresprob=fopen(fileresprob,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprob);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprob);
     }
     strcpy(fileresprobcov,"probcov"); 
     strcat(fileresprobcov,fileres);
     if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcov);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcov);
     }
     strcpy(fileresprobcor,"probcor"); 
     strcat(fileresprobcor,fileres);
     if((ficresprobcor=fopen(fileresprobcor,"w"))==NULL) {
       printf("Problem with resultfile: %s\n", fileresprobcor);
       fprintf(ficlog,"Problem with resultfile: %s\n", fileresprobcor);
     }
     printf("Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     fprintf(ficlog,"Computing standard deviation of one-step probabilities: result on file '%s' \n",fileresprob);
     printf("Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     fprintf(ficlog,"Computing matrix of variance covariance of one-step probabilities: result on file '%s' \n",fileresprobcov);
     printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     fprintf(ficlog,"and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor);
     pstamp(ficresprob);
     fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n");
     fprintf(ficresprob,"# Age");
     pstamp(ficresprobcov);
     fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n");
     fprintf(ficresprobcov,"# Age");
     pstamp(ficresprobcor);
     fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n");
     fprintf(ficresprobcor,"# Age");
   
   
     for(i=1; i<=nlstate;i++)
       for(j=1; j<=(nlstate+ndeath);j++){
         fprintf(ficresprob," p%1d-%1d (SE)",i,j);
         fprintf(ficresprobcov," p%1d-%1d ",i,j);
         fprintf(ficresprobcor," p%1d-%1d ",i,j);
       }  
    /* fprintf(ficresprob,"\n");
     fprintf(ficresprobcov,"\n");
     fprintf(ficresprobcor,"\n");
    */
     xp=vector(1,npar);
     dnewm=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
     doldm=matrix(1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     mu=matrix(1,(nlstate)*(nlstate+ndeath), (int) bage, (int)fage);
     varpij=ma3x(1,nlstate*(nlstate+ndeath),1,nlstate*(nlstate+ndeath),(int) bage, (int) fage);
     first=1;
     fprintf(ficgp,"\n# Routine varprob");
     fprintf(fichtm,"\n<li><h4> Computing and drawing one step probabilities with their confidence intervals</h4></li>\n");
     fprintf(fichtm,"\n");
   
     fprintf(fichtm,"\n<li><h4> <a href=\"%s\">Matrix of variance-covariance of pairs of step probabilities (drawings)</a></h4></li>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\n<h4>Matrix of variance-covariance of pairs of step probabilities</h4>\n\
     file %s<br>\n",optionfilehtmcov);
     fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated\
   and drawn. It helps understanding how is the covariance between two incidences.\
    They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>\n");
     fprintf(fichtmcov,"\n<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. \
   It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \
   would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \
   standard deviations wide on each axis. <br>\
    Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix\
    and made the appropriate rotation to look at the uncorrelated principal directions.<br>\
   To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> \n");
   
     cov[1]=1;
     /* tj=cptcoveff; */
     tj = (int) pow(2,cptcoveff);
     if (cptcovn<1) {tj=1;ncodemax[1]=1;}
     j1=0;
     for(j1=1; j1<=tj;j1++){
       /*for(i1=1; i1<=ncodemax[t];i1++){ */
       /*j1++;*/
         if  (cptcovn>0) {
           fprintf(ficresprob, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprob, "**********\n#\n");
           fprintf(ficresprobcov, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcov, "**********\n#\n");
           
           fprintf(ficgp, "\n#********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficgp, "**********\n#\n");
           
           
           fprintf(fichtmcov, "\n<hr  size=\"2\" color=\"#EC5E5E\">********** Variable "); 
           for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(fichtmcov, "**********\n<hr size=\"2\" color=\"#EC5E5E\">");
           
           fprintf(ficresprobcor, "\n#********** Variable ");    
           for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
           fprintf(ficresprobcor, "**********\n#");    
         }
         
         gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath));
         trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar);
         gp=vector(1,(nlstate)*(nlstate+ndeath));
         gm=vector(1,(nlstate)*(nlstate+ndeath));
         for (age=bage; age<=fage; age ++){ 
           cov[2]=age;
           for (k=1; k<=cptcovn;k++) {
             cov[2+k]=nbcode[Tvar[k]][codtab[j1][Tvar[k]]];/* j1 1 2 3 4
                                                            * 1  1 1 1 1
                                                            * 2  2 1 1 1
                                                            * 3  1 2 1 1
                                                            */
             /* nbcode[1][1]=0 nbcode[1][2]=1;*/
           }
           for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
           for (k=1; k<=cptcovprod;k++)
             cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
           
       
           for(theta=1; theta <=npar; theta++){
             for(i=1; i<=npar; i++)
               xp[i] = x[i] + (i==theta ?delti[theta]:(double)0);
             
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             
             k=0;
             for(i=1; i<= (nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gp[k]=pmmij[i][j];
               }
             }
             
             for(i=1; i<=npar; i++)
               xp[i] = x[i] - (i==theta ?delti[theta]:(double)0);
       
             pmij(pmmij,cov,ncovmodel,xp,nlstate);
             k=0;
             for(i=1; i<=(nlstate); i++){
               for(j=1; j<=(nlstate+ndeath);j++){
                 k=k+1;
                 gm[k]=pmmij[i][j];
               }
             }
        
             for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) 
               gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta];  
           }
   
           for(j=1; j<=(nlstate)*(nlstate+ndeath);j++)
             for(theta=1; theta <=npar; theta++)
               trgradg[j][theta]=gradg[theta][j];
           
           matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); 
           matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg);
   
           pmij(pmmij,cov,ncovmodel,x,nlstate);
           
           k=0;
           for(i=1; i<=(nlstate); i++){
             for(j=1; j<=(nlstate+ndeath);j++){
               k=k+1;
               mu[k][(int) age]=pmmij[i][j];
             }
           }
           for(i=1;i<=(nlstate)*(nlstate+ndeath);i++)
             for(j=1;j<=(nlstate)*(nlstate+ndeath);j++)
               varpij[i][j][(int)age] = doldm[i][j];
   
           /*printf("\n%d ",(int)age);
             for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i]));
             }*/
   
           fprintf(ficresprob,"\n%d ",(int)age);
           fprintf(ficresprobcov,"\n%d ",(int)age);
           fprintf(ficresprobcor,"\n%d ",(int)age);
   
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
             fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
           for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
             fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
             fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
           }
           i=0;
           for (k=1; k<=(nlstate);k++){
             for (l=1; l<=(nlstate+ndeath);l++){ 
               i++;
               fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
               fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
               for (j=1; j<=i;j++){
                 /* printf(" k=%d l=%d i=%d j=%d\n",k,l,i,j);fflush(stdout); */
                 fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
                 fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
               }
             }
           }/* end of loop for state */
         } /* end of loop for age */
         free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
         free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
         free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
         
         /* Confidence intervalle of pij  */
         /*
           fprintf(ficgp,"\nunset parametric;unset label");
           fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
           fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
           fprintf(fichtm,"\n<br>Probability with  confidence intervals expressed in year<sup>-1</sup> :<a href=\"pijgr%s.png\">pijgr%s.png</A>, ",optionfilefiname,optionfilefiname);
           fprintf(fichtm,"\n<br><img src=\"pijgr%s.png\"> ",optionfilefiname);
           fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
           fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
         */
   
         /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
         first1=1;first2=2;
         for (k2=1; k2<=(nlstate);k2++){
           for (l2=1; l2<=(nlstate+ndeath);l2++){ 
             if(l2==k2) continue;
             j=(k2-1)*(nlstate+ndeath)+l2;
             for (k1=1; k1<=(nlstate);k1++){
               for (l1=1; l1<=(nlstate+ndeath);l1++){ 
                 if(l1==k1) continue;
                 i=(k1-1)*(nlstate+ndeath)+l1;
                 if(i<=j) continue;
                 for (age=bage; age<=fage; age ++){ 
                   if ((int)age %5==0){
                     v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
                     v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
                     mu1=mu[i][(int) age]/stepm*YEARM ;
                     mu2=mu[j][(int) age]/stepm*YEARM;
                     c12=cv12/sqrt(v1*v2);
                     /* Computing eigen value of matrix of covariance */
                     lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
                     if ((lc2 <0) || (lc1 <0) ){
                       if(first2==1){
                         first1=0;
                       printf("Strange: j1=%d 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. Probably WRONG RESULTS. See log file for details...\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
                       }
                       fprintf(ficlog,"Strange: j1=%d 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. Probably WRONG RESULTS.\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);fflush(ficlog);
                       /* lc1=fabs(lc1); */ /* If we want to have them positive */
                       /* lc2=fabs(lc2); */
                     }
   
                     /* Eigen vectors */
                     v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
                     /*v21=sqrt(1.-v11*v11); *//* error */
                     v21=(lc1-v1)/cv12*v11;
                     v12=-v21;
                     v22=v11;
                     tnalp=v21/v11;
                     if(first1==1){
                       first1=0;
                       printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     }
                     fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
                     /*printf(fignu*/
                     /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
                     /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
                     if(first==1){
                       first=0;
                       fprintf(ficgp,"\nset parametric;unset label");
                       fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
                       fprintf(ficgp,"\nset ter png small size 320, 240");
                       fprintf(fichtmcov,"\n<br>Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year<sup>-1</sup>\
    :<a href=\"%s%d%1d%1d-%1d%1d.png\">\
   %s%d%1d%1d-%1d%1d.png</A>, ",k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2,\
                               subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br><img src=\"%s%d%1d%1d-%1d%1d.png\"> ",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(fichtmcov,"\n<br> Correlation at age %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\"",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }else{
                       first=0;
                       fprintf(fichtmcov," %d (%.3f),",(int) age, c12);
                       fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2);
                       fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2);
                       fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not",\
                               mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),\
                               mu2,std,v21,sqrt(lc1),v22,sqrt(lc2));
                     }/* if first */
                   } /* age mod 5 */
                 } /* end loop age */
                 fprintf(ficgp,"\nset out \"%s%d%1d%1d-%1d%1d.png\";replot;",subdirf2(optionfilefiname,"varpijgr"), j1,k1,l1,k2,l2);
                 first=1;
               } /*l12 */
             } /* k12 */
           } /*l1 */
         }/* k1 */
         /* } /* loop covariates */
     }
     free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage);
     free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage);
     free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath));
     free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar);
     free_vector(xp,1,npar);
     fclose(ficresprob);
     fclose(ficresprobcov);
     fclose(ficresprobcor);
     fflush(ficgp);
     fflush(fichtmcov);
   }
   
   
   /******************* Printing html file ***********/
   void printinghtml(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,int jmin, int jmax, double jmeanint,char rfileres[],\
                     int popforecast, int estepm ,\
                     double jprev1, double mprev1,double anprev1, \
                     double jprev2, double mprev2,double anprev2){
     int jj1, k1, i1, cpt;
   
      fprintf(fichtm,"<ul><li><a href='#firstorder'>Result files (first order: no variance)</a>\n \
      <li><a href='#secondorder'>Result files (second order (variance)</a>\n \
   </ul>");
      fprintf(fichtm,"<ul><li><h4><a name='firstorder'>Result files (first order: no variance)</a></h4>\n \
    - Observed prevalence in each state (during the period defined between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf): <a href=\"%s\">%s</a> <br>\n ",
              jprev1, mprev1,anprev1,jprev2, mprev2,anprev2,subdirf2(fileres,"p"),subdirf2(fileres,"p"));
      fprintf(fichtm,"\
    - Estimated transition probabilities over %d (stepm) months: <a href=\"%s\">%s</a><br>\n ",
              stepm,subdirf2(fileres,"pij"),subdirf2(fileres,"pij"));
      fprintf(fichtm,"\
    - Period (stable) prevalence in each health state: <a href=\"%s\">%s</a> <br>\n",
              subdirf2(fileres,"pl"),subdirf2(fileres,"pl"));
      fprintf(fichtm,"\
    - (a) Life expectancies by health status at initial age, ei. (b) health expectancies by health status at initial age, eij . If one or more covariates are included, specific tables for each value of the covariate are output in sequences within the same file (estepm=%2d months): \
      <a href=\"%s\">%s</a> <br>\n",
              estepm,subdirf2(fileres,"e"),subdirf2(fileres,"e"));
      fprintf(fichtm,"\
    - Population projections by age and states: \
      <a href=\"%s\">%s</a> <br>\n</li>", subdirf2(fileres,"f"),subdirf2(fileres,"f"));
   
   fprintf(fichtm," \n<ul><li><b>Graphs</b></li><p>");
   
    m=pow(2,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%d_1.png\">%s%d_1.png</a><br> \
   <img src=\"%s%d_1.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%d_2.png\">%s%d_2.png</a><br> \
   <img src=\"%s%d_2.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>- Convergence to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
   <img src=\"%s%d_%d.png\">", cpt, cpt, nlstate, 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 in each alive state (1 to %d) : <a href=\"%s%d%d.png\">%s%d%d.png</a> <br> \
   <img src=\"%s%d%d.png\">",cpt,nlstate,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=pow(2,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 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*/
     fprintf(ficgp,"\n# 1st: Period (stable) prevalence with CI: 'vpl' files\n");
     for (cpt=1; cpt<= nlstate ; cpt ++) {
       for (k1=1; k1<= m ; k1 ++) { /* plot [100000000000000000000:-100000000000000000000] "mysbiaspar/vplrmysbiaspar.txt to check */
        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 size 320, 240\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 lt 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 lt 1,\"%s\" every :::%d::%d u 1:($2-1.96*$3) \"\%%lf",subdirf2(fileres,"vpl"),k1-1,k1-1); 
        for (i=1; i<= nlstate ; i ++) {
          if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");
          else fprintf(ficgp," \%%*lf (\%%*lf)");
        }  
        fprintf(ficgp,"\" t\"\" w l lt 1,\"%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l lt 2",subdirf2(fileres,"p"),k1-1,k1-1,2+4*(cpt-1));
      }
     }
     /*2 eme*/
     fprintf(ficgp,"\n# 2nd: Total life expectancy with CI: 't' files\n");
     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 size 320, 240\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 lt 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 lt 0");
         else fprintf(ficgp,"\" t\"\" w l lt 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 size 320, 240\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 each multivariate if any */
       for (cpt=1; cpt<=nlstate ; cpt ++) { /* For each life state */
         k=3;
         fprintf(ficgp,"\n#\n#\n#CV preval stable (period): 'pij' files, cov=%d state=%d",k1, cpt);
         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 size 320, 240\n\
   unset log y\n\
   plot [%.f:%.f]  ", ageminpar, agemaxpar);
         for (i=1; i<= nlstate ; i ++){
           if(i==1)
             fprintf(ficgp,"\"%s\"",subdirf2(fileres,"pij"));
           else
             fprintf(ficgp,", '' ");
           l=(nlstate+ndeath)*(i-1)+1;
           fprintf(ficgp," u ($1==%d ? ($3):1/0):($%d/($%d",k1,k+l+(cpt-1),k+l);
           for (j=1; j<= (nlstate-1) ; j ++)
             fprintf(ficgp,"+$%d",k+l+j);
           fprintf(ficgp,")) t \"prev(%d,%d)\" w l",i,cpt);
         } /* nlstate */
         fprintf(ficgp,"\n");
       } /* end cpt state*/ 
     } /* end covariate */  
     
     /* 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");
           }
         }
       }
      }
     /*goto avoid;*/
      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 size 320, 240\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;/* To be checked else nbcode[0][0] wrong */
                for(j=3; j <=ncovmodel; j++) {
                  /* if(((j-2)==Tage[ij]) &&(ij <=cptcovage)) { /\* Bug valgrind *\/ */
                  /*        /\*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 */
    /* avoid: */
      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, cptcod, i, h, i1;
     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];
     int i,j, k, 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 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 size 320, 240\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=0, j=0, n=0;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[MAXLINE], strb[MAXLINE];
     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 */
       strcpy(line, linetmp);
     
   
       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 %d 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 %d 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.",dummy) != 0){
           month=99;
           year=9999;
         }else{
           printf("Error reading data around '%s' at line number %d 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 %d 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 %d 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 %d 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.", dummy) != 0){
         month=99;
         year=9999;
       }else{
         printf("Error reading data around '%s' at line number %d 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 %d 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 %d 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 %d 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 %d, \"%s\" for individual %d\nShould be a weight.  Exiting.\n",dval, i,line,linei);
         fprintf(ficlog,"Error reading data around '%f' at line number %d, \"%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 '%ld' at line number %d 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 '%ld' at line number %d 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 '%ld' at line number %d 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 '%ld' at line number %d 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);
   
   
   
   }
   void removespace(char *str) {
     char *p1 = str, *p2 = str;
     do
       while (*p2 == ' ')
         p2++;
     while (*p1++ = *p2++);
   }
   
   int decodemodel ( char model[], int lastobs) /**< This routine decode the model and returns:
      * Model  V1+V2+V3+V8+V7*V8+V5*V6+V8*age+V3*age
      * - cptcovt total number of covariates of the model nbocc(+)+1 = 8
      * - cptcovn or number of covariates k of the models excluding age*products =6
      * - cptcovage number of covariates with age*products =2
      * - cptcovs number of simple covariates
      * - Tvar[k] is the id of the kth covariate Tvar[1]@12 {1, 2, 3, 8, 10, 11, 8, 3, 7, 8, 5, 6}, thus Tvar[5=V7*V8]=10
      *     which is a new column after the 9 (ncovcol) variables. 
      * - if k is a product Vn*Vm covar[k][i] is filled with correct values for each individual
      * - Tprod[l] gives the kth covariates of the product Vn*Vm l=1 to cptcovprod-cptcovage
      *    Tprod[1]@2 {5, 6}: position of first product V7*V8 is 5, and second V5*V6 is 6.
      * - Tvard[k]  p Tvard[1][1]@4 {7, 8, 5, 6} for V7*V8 and V5*V6 .
    */
   {
     int i, j, k, ks;
     int  j1, k1, k2;
     char modelsav[80];
     char stra[80], strb[80], strc[80], strd[80],stre[80];
   
     /*removespace(model);*/
     if (strlen(model) >1){ /* If there is at least 1 covariate */
       j=0, j1=0, k1=0, k2=-1, ks=0, cptcovn=0;
       j=nbocc(model,'+'); /**< j=Number of '+' */
       j1=nbocc(model,'*'); /**< j1=Number of '*' */
       cptcovs=j+1-j1; /**<  Number of simple covariates V1+V2*age+V3 +V3*V4=> V1 + V3 =2  */
       cptcovt= j+1; /* Number of total covariates in the model V1 + V2*age+ V3 + V3*V4=> 4*/
                     /* including age products which are counted in cptcovage.
                     /* but the covariates which are products must be treated separately: ncovn=4- 2=2 (V1+V3). */
       cptcovprod=j1; /**< Number of products  V1*V2 +v3*age = 2 */
       cptcovprodnoage=0; /**< Number of covariate products without age: V3*V4 =1  */
       strcpy(modelsav,model); 
       if (strstr(model,"AGE") !=0){
         printf("Error. AGE must be in lower case 'age' model=%s ",model);
         fprintf(ficlog,"Error. AGE must be in lower case model=%s ",model);fflush(ficlog);
         return 1;
       }
       if (strstr(model,"v") !=0){
         printf("Error. 'v' must be in upper case 'V' model=%s ",model);
         fprintf(ficlog,"Error. 'v' must be in upper case model=%s ",model);fflush(ficlog);
         return 1;
       }
       
       /*   Design
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9 Weight
        *  <          ncovcol=8                >
        * Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8
        *   k=  1    2      3       4     5       6      7        8
        *  cptcovn number of covariates (not including constant and age ) = # of + plus 1 = 7+1=8
        *  covar[k,i], value of kth covariate if not including age for individual i:
        *       covar[1][i]= (V2), covar[4][i]=(V3), covar[8][i]=(V8)
        *  Tvar[k] # of the kth covariate:  Tvar[1]=2  Tvar[4]=3 Tvar[8]=8
        *       if multiplied by age: V3*age Tvar[3=V3*age]=3 (V3) Tvar[7]=8 and 
        *  Tage[++cptcovage]=k
        *       if products, new covar are created after ncovcol with k1
        *  Tvar[k]=ncovcol+k1; # of the kth covariate product:  Tvar[5]=ncovcol+1=10  Tvar[6]=ncovcol+1=11
        *  Tprod[k1]=k; Tprod[1]=5 Tprod[2]= 6; gives the position of the k1th product
        *  Tvard[k1][1]=m Tvard[k1][2]=m; Tvard[1][1]=5 (V5) Tvard[1][2]=6 Tvard[2][1]=7 (V7) Tvard[2][2]=8
        *  Tvar[cptcovn+k2]=Tvard[k1][1];Tvar[cptcovn+k2+1]=Tvard[k1][2];
        *  Tvar[8+1]=5;Tvar[8+2]=6;Tvar[8+3]=7;Tvar[8+4]=8 inverted
        *  V1   V2   V3   V4  V5  V6  V7  V8  V9  V10  V11
        *  <          ncovcol=8                >
        *       Model V2 + V1 + V3*age + V3 + V5*V6 + V7*V8 + V8*age + V8    d1   d1   d2  d2
        *          k=  1    2      3       4     5       6      7        8    9   10   11  12
        *     Tvar[k]= 2    1      3       3    10      11      8        8    5    6    7   8
        * p Tvar[1]@12={2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        * p Tprod[1]@2={                         6, 5}
        *p Tvard[1][1]@4= {7, 8, 5, 6}
        * covar[k][i]= V2   V1      ?      V3    V5*V6?   V7*V8?  ?       V8   
        *  cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
        *How to reorganize?
        * Model V1 + V2 + V3 + V8 + V5*V6 + V7*V8 + V3*age + V8*age
        * Tvars {2,   1,     3,      3,   11,     10,     8,       8,   7,   8,   5,  6}
        *       {2,   1,     4,      8,    5,      6,     3,       7}
        * Struct []
        */
   
       /* This loop fills the array Tvar from the string 'model'.*/
       /* j is the number of + signs in the model V1+V2+V3 j=2 i=3 to 1 */
       /*   modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4  */
       /*  k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tage[cptcovage=1]=4 */
       /*  k=3 V4 Tvar[k=3]= 4 (from V4) */
       /*  k=2 V1 Tvar[k=2]= 1 (from V1) */
       /*  k=1 Tvar[1]=2 (from V2) */
       /*  k=5 Tvar[5] */
       /* for (k=1; k<=cptcovn;k++) { */
       /*  cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]]; */
       /*  } */
       /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
       /*
        * Treating invertedly V2+V1+V3*age+V2*V4 is as if written V2*V4 +V3*age + V1 + V2 */
       for(k=cptcovt; k>=1;k--) /**< Number of covariates */
           Tvar[k]=0;
       cptcovage=0;
       for(k=1; k<=cptcovt;k++){ /* Loop on total covariates of the model */
         cutl(stra,strb,modelsav,'+'); /* keeps in strb after the first '+' 
                                        modelsav==V2+V1+V4+V3*age strb=V3*age stra=V2+V1+V4 */ 
         if (nbocc(modelsav,'+')==0) strcpy(strb,modelsav); /* and analyzes it */
         /*      printf("i=%d a=%s b=%s sav=%s\n",i, stra,strb,modelsav);*/
         /*scanf("%d",i);*/
         if (strchr(strb,'*')) {  /**< Model includes a product V2+V1+V4+V3*age strb=V3*age */
           cutl(strc,strd,strb,'*'); /**< strd*strc  Vm*Vn: strb=V3*age(input) strc=age strd=V3 ; V3*V2 strc=V2, strd=V3 */
           if (strcmp(strc,"age")==0) { /**< Model includes age: Vn*age */
             /* covar is not filled and then is empty */
             cptcovprod--;
             cutl(stre,strb,strd,'V'); /* strd=V3(input): stre="3" */
             Tvar[k]=atoi(stre);  /* V2+V1+V4+V3*age Tvar[4]=3 ; V1+V2*age Tvar[2]=2 */
             cptcovage++; /* Sums the number of covariates which include age as a product */
             Tage[cptcovage]=k;  /* Tage[1] = 4 */
             /*printf("stre=%s ", stre);*/
           } else if (strcmp(strd,"age")==0) { /* or age*Vn */
             cptcovprod--;
             cutl(stre,strb,strc,'V');
             Tvar[k]=atoi(stre);
             cptcovage++;
             Tage[cptcovage]=k;
           } else {  /* Age is not in the model product V2+V1+V1*V4+V3*age+V3*V2  strb=V3*V2*/
             /* loops on k1=1 (V3*V2) and k1=2 V4*V3 */
             cptcovn++;
             cptcovprodnoage++;k1++;
             cutl(stre,strb,strc,'V'); /* strc= Vn, stre is n; strb=V3*V2 stre=3 strc=*/
             Tvar[k]=ncovcol+k1; /* For model-covariate k tells which data-covariate to use but
                                     because this model-covariate is a construction we invent a new column
                                     ncovcol + k1
                                     If already ncovcol=4 and model=V2+V1+V1*V4+age*V3+V3*V2
                                     Tvar[3=V1*V4]=4+1 Tvar[5=V3*V2]=4 + 2= 6, etc */
             cutl(strc,strb,strd,'V'); /* strd was Vm, strc is m */
             Tprod[k1]=k;  /* Tprod[1]=3(=V1*V4) for V2+V1+V1*V4+age*V3+V3*V2  */
             Tvard[k1][1] =atoi(strc); /* m 1 for V1*/
             Tvard[k1][2] =atoi(stre); /* n 4 for V4*/
             k2=k2+2;
             Tvar[cptcovt+k2]=Tvard[k1][1]; /* Tvar[(cptcovt=4+k2=1)=5]= 1 (V1) */
             Tvar[cptcovt+k2+1]=Tvard[k1][2];  /* Tvar[(cptcovt=4+(k2=1)+1)=6]= 4 (V4) */
             for (i=1; i<=lastobs;i++){
               /* Computes the new covariate which is a product of
                  covar[n][i]* covar[m][i] and stores it at ncovol+k1 May not be defined */
               covar[ncovcol+k1][i]=covar[atoi(stre)][i]*covar[atoi(strc)][i];
             }
           } /* End age is not in the model */
         } /* End if model includes a product */
         else { /* no more sum */
           /*printf("d=%s c=%s b=%s\n", strd,strc,strb);*/
          /*  scanf("%d",i);*/
           cutl(strd,strc,strb,'V');
           ks++; /**< Number of simple covariates */
           cptcovn++;
           Tvar[k]=atoi(strd);
         }
         strcpy(modelsav,stra);  /* modelsav=V2+V1+V4 stra=V2+V1+V4 */ 
         /*printf("a=%s b=%s sav=%s\n", stra,strb,modelsav);
           scanf("%d",i);*/
       } /* end of loop + */
     } /* end model */
     
     /*The number n of Vn is stored in Tvar. cptcovage =number of age covariate. Tage gives the position of age. cptcovprod= number of products.
       If model=V1+V1*age then Tvar[1]=1 Tvar[2]=1 cptcovage=1 Tage[1]=2 cptcovprod=0*/
   
     /* printf("tvar1=%d tvar2=%d tvar3=%d cptcovage=%d Tage=%d",Tvar[1],Tvar[2],Tvar[3],cptcovage,Tage[1]);
     printf("cptcovprod=%d ", cptcovprod);
     fprintf(ficlog,"cptcovprod=%d ", cptcovprod);
   
     scanf("%d ",i);*/
   
   
     return (0); /* with covar[new additional covariate if product] and Tage if age */ 
     /*endread:*/
       printf("Exiting decodemodel: ");
       return (1);
   }
   
   calandcheckages(int imx, int maxwav, double *agemin, double *agemax, int *nberr, int *nbwarn )
   {
     int i, m;
   
     for (i=1; i<=imx; i++) {
       for(m=2; (m<= maxwav); m++) {
         if (((int)mint[m][i]== 99) && (s[m][i] <= nlstate)){
           anint[m][i]=9999;
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]==9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           fprintf(ficlog,"Error! Date of death (month %2d and year %4d) of individual %ld on line %d was unknown, you must set an arbitrary year of death or he/she is skipped and results are biased\n",(int)moisdc[i],(int)andc[i],num[i],i);
           s[m][i]=-1;
         }
         if((int)moisdc[i]==99 && (int)andc[i]!=9999 && s[m][i]>nlstate){
           *nberr++;
           printf("Error! Month of death of individual %ld on line %d was unknown %2d, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,(int)moisdc[i]); 
           fprintf(ficlog,"Error! Month of death of individual %ld on line %d was unknown %f, you should set it otherwise the information on the death is skipped and results are biased.\n",num[i],i,moisdc[i]); 
           s[m][i]=-1; /* We prefer to skip it (and to skip it in version 0.8a1 too */
         }
       }
     }
   
     for (i=1; i<=imx; i++)  {
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
       for(m=firstpass; (m<= lastpass); m++){
         if(s[m][i] >0 || s[m][i]==-2 || s[m][i]==-4 || s[m][i]==-5){
           if (s[m][i] >= nlstate+1) {
             if(agedc[i]>0)
               if((int)moisdc[i]!=99 && (int)andc[i]!=9999)
                 agev[m][i]=agedc[i];
             /*if(moisdc[i]==99 && andc[i]==9999) s[m][i]=-1;*/
               else {
                 if ((int)andc[i]!=9999){
                   nbwarn++;
                   printf("Warning negative age at death: %ld line:%d\n",num[i],i);
                   fprintf(ficlog,"Warning negative age at death: %ld line:%d\n",num[i],i);
                   agev[m][i]=-1;
                 }
               }
           }
           else if(s[m][i] !=9){ /* Standard case, age in fractional
                                    years but with the precision of a month */
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
             if((int)mint[m][i]==99 || (int)anint[m][i]==9999)
               agev[m][i]=1;
             else if(agev[m][i] < *agemin){ 
               *agemin=agev[m][i];
               printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], *agemin);
             }
             else if(agev[m][i] >*agemax){
               *agemax=agev[m][i];
               /* printf(" Max anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.2f\n",m,i,anint[m][i], i,annais[i], *agemax);*/
             }
             /*agev[m][i]=anint[m][i]-annais[i];*/
             /*     agev[m][i] = age[i]+2*m;*/
           }
           else { /* =9 */
             agev[m][i]=1;
             s[m][i]=-1;
           }
         }
         else /*= 0 Unknown */
           agev[m][i]=1;
       }
       
     }
     for (i=1; i<=imx; i++)  {
       for(m=firstpass; (m<=lastpass); m++){
         if (s[m][i] > (nlstate+ndeath)) {
           *nberr++;
           printf("Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           fprintf(ficlog,"Error: on wave %d of individual %d status %d > (nlstate+ndeath)=(%d+%d)=%d\n",m,i,s[m][i],nlstate, ndeath, nlstate+ndeath);     
           return 1;
         }
       }
     }
   
     /*for (i=1; i<=imx; i++){
     for (m=firstpass; (m<lastpass); m++){
        printf("%ld %d %.lf %d %d\n", num[i],(covar[1][i]),agev[m][i],s[m][i],s[m+1][i]);
   }
   
   }*/
   
   
     printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax);
     fprintf(ficlog,"Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, *agemin, *agemax); 
   
     return (0);
    /* endread:*/
       printf("Exiting calandcheckages: ");
       return (1);
   }
   
   syscompilerinfo()
    {
      /* #include "syscompilerinfo.h"*/
   #include <gnu/libc-version.h>
   #if defined(__GNUC__)
   # if defined(__GNUC_PATCHLEVEL__)
   #  define __GNUC_VERSION__ (__GNUC__ * 10000 \
                               + __GNUC_MINOR__ * 100 \
                               + __GNUC_PATCHLEVEL__)
   # else
   #  define __GNUC_VERSION__ (__GNUC__ * 10000 \
                               + __GNUC_MINOR__ * 100)
   # endif
   #endif
   
   // http://stackoverflow.com/questions/4605842/how-to-identify-platform-compiler-from-preprocessor-macros
   #ifdef _WIN32 // note the underscore: without it, it's not msdn official!
       // Windows (x64 and x86)
   #elif __unix__ // all unices, not all compilers
       // Unix
   #elif __linux__
       // linux
   #elif __APPLE__
       // Mac OS, not sure if this is covered by __posix__ and/or __unix__ though...
   #endif
   
   /*  __MINGW32__   */
   /*  __CYGWIN__   */
   /* __MINGW64__  */
   // http://msdn.microsoft.com/en-us/library/b0084kay.aspx
   /* _MSC_VER  //the Visual C++ compiler is 17.00.51106.1, the _MSC_VER macro evaluates to 1700. Type cl /?  */
   /* _MSC_FULL_VER //the Visual C++ compiler is 15.00.20706.01, the _MSC_FULL_VER macro evaluates to 150020706 */
   /* _WIN64  // Defined for applications for Win64. */
   /* _M_X64 // Defined for compilations that target x64 processors. */
   /* _DEBUG // Defined when you compile with /LDd, /MDd, and /MTd. */
   #include <stdint.h>
   #if UINTPTR_MAX == 0xffffffff
      printf("32-bit \n"); /* 32-bit */
   #elif UINTPTR_MAX == 0xffffffffffffffff
     printf("64-bit \n");/* 64-bit */
   #else
    printf("wtf-bit \n"); /* wtf */
   #endif
   
   struct utsname sysInfo;
   
      if (uname(&sysInfo) != -1) {
         puts(sysInfo.sysname);
         puts(sysInfo.nodename);
         puts(sysInfo.release);
         puts(sysInfo.version);
         puts(sysInfo.machine);
      }
      else
         perror("uname() error");
      printf("GNU C version %d\n", __GNUC_VERSION__);
     printf("GNU libc version: %s\n", gnu_get_libc_version());
   
    }
   
   /***********************************************/
   /**************** 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=0,m,size=100, cptcod;
   
     int jj, ll, li, lj, lk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
   
     char line[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int c,  h , cpt;
     int jl;
     int i1, j1, jk, stepsize;
     int *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=0, fage=110, 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 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]="1234";
     int *dcwave;
   
     char z[1]="c";
   
     /*char  *strt;*/
     char strtend[80];
   
   
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     rstart_time = time(NULL);  
     /*  (void) gettimeofday(&start_time,&tzp);*/
     start_time = *localtime(&rstart_time);
     curr_time=start_time;
     /*tml = *localtime(&start_time.tm_sec);*/
     /* strcpy(strstart,asctime(&tml)); */
     strcpy(strstart,asctime(&start_time));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tm_sec = tp.tm_sec +86400; */
   /*  tm = *localtime(&start_time.tm_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.tm_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';
       i=strlen(pathr);
       if(pathr[i-1]==' ') /* This may happen when dragging on oS/X! */
         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);
   
     syscompilerinfo();
   
     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.tm_sec-start_time.tm_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' with errno='%s'\n",optionfile,strerror(errno));
       fprintf(ficlog,"Problem with optionfile '%s' with errno='%s'\n",optionfile,strerror(errno));
       fflush(ficlog);
       /* goto end; */
       exit(70); 
     }
   
   
   
     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++;
       fputs(line,stdout);
       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++;
       fputs(line, stdout);
       //puts(line);
       fputs(line,ficparo);
       fputs(line,ficlog);
     }
     ungetc(c,ficpar);
   
      
     covar=matrix(0,NCOVMAX,1,n);  /**< used in readdata */
     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) 
       ncovmodel=2+nbocc(model,'+')+1; /*Number of variables including intercept and age = cptcovn + intercept + age : v1+v2+v3+v2*v4+v5*age makes 5+2=7*/
     else
       ncovmodel=2;
     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 guessed parameters */
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         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);
   
       /* Reads scales values */
       p=param[1][1];
       
       /* Reads comments: lines beginning with '#' */
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         numlinepar++;
         fputs(line,stdout);
         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);
   
       /* Reads covariance matrix */
       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++;
         fputs(line,stdout);
         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,NCOVMAX); /* Number of code per covariate; if O and 1 only, 2**ncov; V1+V2+V3+V4=>16 */
   
     /* Reads data from file datafile */
     if (readdata(datafile, firstobs, lastobs, &imx)==1)
       goto end;
   
     /* Calculation of the number of parameters from char model */
       /*    modelsav=V2+V1+V4+age*V3 strb=age*V3 stra=V2+V1+V4 
           k=4 (age*V3) Tvar[k=4]= 3 (from V3) Tag[cptcovage=1]=4
           k=3 V4 Tvar[k=3]= 4 (from V4)
           k=2 V1 Tvar[k=2]= 1 (from V1)
           k=1 Tvar[1]=2 (from V2)
       */
     Tvar=ivector(1,NCOVMAX); /* Was 15 changed to NCOVMAX. */
     /*  V2+V1+V4+age*V3 is a model with 4 covariates (3 plus signs). 
         For each model-covariate stores the data-covariate id. Tvar[1]=2, Tvar[2]=1, Tvar[3]=4, 
         Tvar[4=age*V3] is 3 and 'age' is recorded in Tage.
     */
     /* For model-covariate k tells which data-covariate to use but
       because this model-covariate is a construction we invent a new column
       ncovcol + k1
       If already ncovcol=4 and model=V2+V1+V1*V4+age*V3
       Tvar[3=V1*V4]=4+1 etc */
     Tprod=ivector(1,NCOVMAX); /* Gives the position of a product */
     /* Tprod[k1=1]=3(=V1*V4) for V2+V1+V1*V4+age*V3
        if  V2+V1+V1*V4+age*V3+V3*V2   TProd[k1=2]=5 (V3*V2)
     */
     Tvaraff=ivector(1,NCOVMAX); /* Unclear */
     Tvard=imatrix(1,NCOVMAX,1,2); /* n=Tvard[k1][1]  and m=Tvard[k1][2] gives the couple n,m of the k1 th product Vn*Vm
                               * For V3*V2 (in V2+V1+V1*V4+age*V3+V3*V2), V3*V2 position is 2nd. 
                               * Tvard[k1=2][1]=3 (V3) Tvard[k1=2][2]=2(V2) */
     Tage=ivector(1,NCOVMAX); /* Gives the covariate id of covariates associated with age: V2 + V1 + age*V4 + V3*age
                            4 covariates (3 plus signs)
                            Tage[1=V3*age]= 4; Tage[2=age*V4] = 3
                         */  
   
     if(decodemodel(model, lastobs) == 1)
       goto end;
   
     if((double)(lastobs-imx)/(double)imx > 1.10){
       nbwarn++;
       printf("Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
       fprintf(ficlog,"Warning: The value of parameter lastobs=%d is big compared to the \n  effective number of cases imx=%d, please adjust, \n  otherwise you are allocating more memory than necessary.\n",lastobs, imx); 
     }
       /*  if(mle==1){*/
     if (weightopt != 1) { /* Maximisation without weights. We can have weights different from 1 but want no weight*/
       for(i=1;i<=imx;i++) weight[i]=1.0; /* changed to imx */
     }
   
       /*-calculation of age at interview from date of interview and age at death -*/
     agev=matrix(1,maxwav,1,imx);
   
     if(calandcheckages(imx, maxwav, &agemin, &agemax, &nberr, &nbwarn) == 1)
       goto end;
   
   
     agegomp=(int)agemin;
     free_vector(moisnais,1,n);
     free_vector(annais,1,n);
     /* free_matrix(mint,1,maxwav,1,n);
        free_matrix(anint,1,maxwav,1,n);*/
     free_vector(moisdc,1,n);
     free_vector(andc,1,n);
     /* */
     
     wav=ivector(1,imx);
     dh=imatrix(1,lastpass-firstpass+1,1,imx);
     bh=imatrix(1,lastpass-firstpass+1,1,imx);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);
      
     /* Concatenates waves */
     concatwav(wav, dh, bh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
     /* */
    
     /* Routine tricode is to calculate cptcoveff (real number of unique covariates) and to associate covariable number and modality */
   
     nbcode=imatrix(0,NCOVMAX,0,NCOVMAX); 
     ncodemax[1]=1;
     Ndum =ivector(-1,NCOVMAX);  
     if (ncovmodel > 2)
       tricode(Tvar,nbcode,imx, Ndum); /**< Fills nbcode[Tvar[j]][l]; */
   
     codtab=imatrix(1,100,1,10); /* codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) */
     /*printf(" codtab[1,1],codtab[100,10]=%d,%d\n", codtab[1][1],codtab[100][10]);*/
     h=0;
   
   
     /*if (cptcovn > 0) */
         
    
     m=pow(2,cptcoveff);
    
     for(k=1;k<=cptcoveff; k++){ /* scans any effective covariate */
       for(i=1; i <=pow(2,cptcoveff-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 ncodemax=2*/
           for(cpt=1; cpt <=pow(2,k-1); 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)  k   = codtab[h,k]=( (h-1) - mod(k-1,2**(k-1) )/2**(k-1) + 1
              *     h     1     2     3     4
              *______________________________  
              *     1 i=1 1 i=1 1 i=1 1 i=1 1
              *     2     2     1     1     1
              *     3 i=2 1     2     1     1
              *     4     2     2     1     1
              *     5 i=3 1 i=2 1     2     1
              *     6     2     1     2     1
              *     7 i=4 1     2     2     1
              *     8     2     2     2     1
              *     9 i=5 1 i=3 1 i=2 1     1
              *    10     2     1     1     1
              *    11 i=6 1     2     1     1
              *    12     2     2     1     1
              *    13 i=7 1 i=4 1     2     1    
              *    14     2     1     2     1
              *    15 i=8 1     2     2     1
              *    16     2     2     2     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);*/
   
    free_ivector(Ndum,-1,NCOVMAX);
   
   
       
     /*------------ 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");
       fprintf(ficgp,"set datafile 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");
   #else
       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");
   #else
       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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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);
         fputs(line,stdout);
         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) --------------*/
   #include "prevlim.h"  /* Use ficrespl, ficlog */
       fclose(ficrespl);
   
   #ifdef FREEEXIT2
   #include "freeexit2.h"
   #endif
   
       /*------------- h Pij x at various ages ------------*/
   #include "hpijx.h"
       fclose(ficrespij);
   
     /*-------------- Variance of one-step probabilities---*/
       k=1;
       varprob(optionfilefiname, matcov, p, delti, nlstate, bage, fage,k,Tvar,nbcode, ncodemax,strstart);
   
   
       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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           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);  
           /*
            */
           /* goto endfree; */
    
           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; /* Segmentation fault */
             cptcod= 0; /* To be deleted */
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart); /* cptcod not initialized Intel */
             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,NCOVMAX,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++){*/
             
       for (k=1; k <= (int) pow(2,cptcoveff); k++){
           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); /*here or after loop ? */
       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,NCOVMAX);
       free_ivector(Tvar,1,NCOVMAX);
       free_ivector(Tprod,1,NCOVMAX);
       free_ivector(Tvaraff,1,NCOVMAX);
       free_ivector(Tage,1,NCOVMAX);
   
       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);*/
     rend_time = time(NULL);  
     end_time = *localtime(&rend_time);
     /* tml = *localtime(&end_time.tm_sec); */
     strcpy(strtend,asctime(&end_time));
     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(rend_time -rstart_time,tmpout));
   
     printf("Total time was %.0lf Sec.\n", difftime(rend_time,rstart_time));
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(rend_time -rstart_time,tmpout));
     fprintf(ficlog,"Total time was %.0lf Sec.\n", difftime(rend_time,rstart_time));
     /*  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");
   #ifdef _WIN32
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error or gnuplot program not found: '%s'\n",plotcmd);fflush(stdout);
       if(!stat(getenv("GNUPLOTBIN"),&info)){
         printf("Error or 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("gnuplot command might not be in your path: '%s', err=%d\n", plotcmd, outcmd);
       printf("\n Trying if gnuplot resides on the same directory that IMaCh\n");
       sprintf(plotcmd,"%sgnuplot %s", pathimach, optionfilegnuplot);
       if((outcmd=system(plotcmd)) != 0)
         printf("\n Still a problem with gnuplot command %s, err=%d\n", plotcmd, outcmd);
     }
     printf(" Successful, please wait...");
     while (z[0] != 'q') {
       /* chdir(path); */
       printf("\nType e to edit results with your browser, g to graph again and q for exit: ");
       scanf("%s",z);
   /*     if (z[0] == 'c') system("./imach"); */
       if (z[0] == 'e') {
   #ifdef __APPLE__
         sprintf(pplotcmd, "open %s", optionfilehtm);
   #elif __linux
         sprintf(pplotcmd, "xdg-open %s", optionfilehtm);
   #else
         sprintf(pplotcmd, "%s", optionfilehtm);
   #endif
         printf("Starting browser with: %s",pplotcmd);fflush(stdout);
         system(pplotcmd);
       }
       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.1.4  
changed lines
  Added in v.1.168


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