Diff for /imach/src/imach.c between versions 1.2 and 1.155

version 1.2, 2001/03/13 18:10:26 version 1.155, 2014/08/25 18:32:34
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 1.155  2014/08/25 18:32:34  brouard
   individuals from different ages are interviewed on their health status    Summary: New compile, minor changes
   or degree of  disability. At least a second wave of interviews    Author: Brouard
   ("longitudinal") should  measure each new individual health status.  
   Health expectancies are computed from the transistions observed between    Revision 1.154  2014/06/20 17:32:08  brouard
   waves and are computed for each degree of severity of disability (number    Summary: Outputs now all graphs of convergence to period prevalence
   of life states). More degrees you consider, more time is necessary to  
   reach the Maximum Likelihood of the parameters involved in the model.    Revision 1.153  2014/06/20 16:45:46  brouard
   The simplest model is the multinomial logistic model where pij is    Summary: If 3 live state, convergence to period prevalence on same graph
   the probabibility to be observed in state j at the second wave conditional    Author: Brouard
   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 1.152  2014/06/18 17:54:09  brouard
   is a covariate. If you want to have a more complex model than "constant and    Summary: open browser, use gnuplot on same dir than imach if not found in the path
   age", you should modify the program where the markup  
     *Covariates have to be included here again* invites you to do it.    Revision 1.151  2014/06/18 16:43:30  brouard
   More covariates you add, less is the speed of the convergence.    *** empty log message ***
   
   The advantage that this computer programme claims, comes from that if the    Revision 1.150  2014/06/18 16:42:35  brouard
   delay between waves is not identical for each individual, or if some    Summary: If gnuplot is not in the path try on same directory than imach binary (OSX)
   individual missed an interview, the information is not rounded or lost, but    Author: brouard
   taken into account using an interpolation or extrapolation.  
   hPijx is the probability to be    Revision 1.149  2014/06/18 15:51:14  brouard
   observed in state i at age x+h conditional to the observed state i at age    Summary: Some fixes in parameter files errors
   x. The delay 'h' can be split into an exact number (nh*stepm) of    Author: Nicolas Brouard
   unobserved intermediate  states. This elementary transition (by month or  
   quarter trimester, semester or year) is model as a multinomial logistic.    Revision 1.148  2014/06/17 17:38:48  brouard
   The hPx matrix is simply the matrix product of nh*stepm elementary matrices    Summary: Nothing new
   and the contribution of each individual to the likelihood is simply hPijx.    Author: Brouard
   
   Also this programme outputs the covariance matrix of the parameters but also    Just a new packaging for OS/X version 0.98nS
   of the life expectancies. It also computes the prevalence limits.  
      Revision 1.147  2014/06/16 10:33:11  brouard
   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).    *** empty log message ***
            Institut national d'études démographiques, Paris.  
   This software have been partly granted by Euro-REVES, a concerted action    Revision 1.146  2014/06/16 10:20:28  brouard
   from the European Union.    Summary: Merge
   It is copyrighted identically to a GNU software product, ie programme and    Author: Brouard
   software can be distributed freely for non commercial use. Latest version  
   can be accessed at http://euroreves.ined.fr/imach .    Merge, before building revised version.
   **********************************************************************/  
      Revision 1.145  2014/06/10 21:23:15  brouard
 #include <math.h>    Summary: Debugging with valgrind
 #include <stdio.h>    Author: Nicolas Brouard
 #include <stdlib.h>  
 #include <unistd.h>    Lot of changes in order to output the results with some covariates
     After the Edimburgh REVES conference 2014, it seems mandatory to
 #define MAXLINE 256    improve the code.
 #define FILENAMELENGTH 80    No more memory valgrind error but a lot has to be done in order to
 /*#define DEBUG*/    continue the work of splitting the code into subroutines.
 #define windows    Also, decodemodel has been improved. Tricode is still not
     optimal. nbcode should be improved. Documentation has been added in
 #define MAXPARM 30 /* Maximum number of parameters for the optimization */    the source code.
 #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncovmodel */  
     Revision 1.143  2014/01/26 09:45:38  brouard
 #define NINTERVMAX 8    Summary: Version 0.98nR (to be improved, but gives same optimization results as 0.98k. Nice, promising
 #define NLSTATEMAX 8 /* Maximum number of live states (for func) */  
 #define NDEATHMAX 8 /* Maximum number of dead states (for func) */    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 #define NCOVMAX 8 /* Maximum number of covariates */    (Module): Version 0.98nR Running ok, but output format still only works for three covariates.
 #define MAXN 80000  
 #define YEARM 12. /* Number of months per year */    Revision 1.142  2014/01/26 03:57:36  brouard
 #define AGESUP 130    Summary: gnuplot changed plot w l 1 has to be changed to plot w l lt 2
 #define AGEBASE 40  
     * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
   
 int nvar;    Revision 1.141  2014/01/26 02:42:01  brouard
 static int cptcov;    * imach.c (Module): Trying to merge old staffs together while being at Tokyo. Not tested...
 int cptcovn;  
 int npar=NPARMAX;    Revision 1.140  2011/09/02 10:37:54  brouard
 int nlstate=2; /* Number of live states */    Summary: times.h is ok with mingw32 now.
 int ndeath=1; /* Number of dead states */  
 int ncovmodel, ncov;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */    Revision 1.139  2010/06/14 07:50:17  brouard
     After the theft of my laptop, I probably lost some lines of codes which were not uploaded to the CVS tree.
 int *wav; /* Number of waves for this individuual 0 is possible */    I remember having already fixed agemin agemax which are pointers now but not cvs saved.
 int maxwav; /* Maxim number of waves */  
 int mle, weightopt;    Revision 1.138  2010/04/30 18:19:40  brouard
 int **mw; /* mw[mi][i] is number of the mi wave for this individual */    *** empty log message ***
 int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */  
 double **oldm, **newm, **savm; /* Working pointers to matrices */    Revision 1.137  2010/04/29 18:11:38  brouard
 double **oldms, **newms, **savms; /* Fixed working pointers to matrices */    (Module): Checking covariates for more complex models
 FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;    than V1+V2. A lot of change to be done. Unstable.
 FILE *ficgp, *fichtm;  
 FILE *ficreseij;    Revision 1.136  2010/04/26 20:30:53  brouard
   char filerese[FILENAMELENGTH];    (Module): merging some libgsl code. Fixing computation
  FILE  *ficresvij;    of likelione (using inter/intrapolation if mle = 0) in order to
   char fileresv[FILENAMELENGTH];    get same likelihood as if mle=1.
  FILE  *ficresvpl;    Some cleaning of code and comments added.
   char fileresvpl[FILENAMELENGTH];  
     Revision 1.135  2009/10/29 15:33:14  brouard
     (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
   
     Revision 1.134  2009/10/29 13:18:53  brouard
 #define NR_END 1    (Module): Now imach stops if date of birth, at least year of birth, is not given. Some cleaning of the code.
 #define FREE_ARG char*  
 #define FTOL 1.0e-10    Revision 1.133  2009/07/06 10:21:25  brouard
     just nforces
 #define NRANSI  
 #define ITMAX 200    Revision 1.132  2009/07/06 08:22:05  brouard
     Many tings
 #define TOL 2.0e-4  
     Revision 1.131  2009/06/20 16:22:47  brouard
 #define CGOLD 0.3819660    Some dimensions resccaled
 #define ZEPS 1.0e-10  
 #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);    Revision 1.130  2009/05/26 06:44:34  brouard
     (Module): Max Covariate is now set to 20 instead of 8. A
 #define GOLD 1.618034    lot of cleaning with variables initialized to 0. Trying to make
 #define GLIMIT 100.0    V2+V3*age+V1+V4 strb=V3*age+V1+V4 working better.
 #define TINY 1.0e-20  
     Revision 1.129  2007/08/31 13:49:27  lievre
 static double maxarg1,maxarg2;    Modification of the way of exiting when the covariate is not binary in order to see on the window the error message before exiting
 #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))  
 #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))    Revision 1.128  2006/06/30 13:02:05  brouard
      (Module): Clarifications on computing e.j
 #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))  
 #define rint(a) floor(a+0.5)    Revision 1.127  2006/04/28 18:11:50  brouard
     (Module): Yes the sum of survivors was wrong since
 static double sqrarg;    imach-114 because nhstepm was no more computed in the age
 #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)    loop. Now we define nhstepma in the age loop.
 #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;}    (Module): In order to speed up (in case of numerous covariates) we
     compute health expectancies (without variances) in a first step
 int imx;    and then all the health expectancies with variances or standard
 int stepm;    deviation (needs data from the Hessian matrices) which slows the
 /* Stepm, step in month: minimum step interpolation*/    computation.
     In the future we should be able to stop the program is only health
 int m,nb;    expectancies and graph are needed without standard deviations.
 int *num, firstpass=0, lastpass=4,*cod, *ncodemax;  
 double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;    Revision 1.126  2006/04/28 17:23:28  brouard
 double **pmmij;    (Module): Yes the sum of survivors was wrong since
     imach-114 because nhstepm was no more computed in the age
 double *weight;    loop. Now we define nhstepma in the age loop.
 int **s; /* Status */    Version 0.98h
 double *agedc, **covar, idx;  
 int **nbcode, *Tcode, *Tvar, **codtab;    Revision 1.125  2006/04/04 15:20:31  lievre
     Errors in calculation of health expectancies. Age was not initialized.
 double ftol=FTOL; /* Tolerance for computing Max Likelihood */    Forecasting file added.
 double ftolhess; /* Tolerance for computing hessian */  
     Revision 1.124  2006/03/22 17:13:53  lievre
     Parameters are printed with %lf instead of %f (more numbers after the comma).
 /******************************************/    The log-likelihood is printed in the log file
   
 void replace(char *s, char*t)    Revision 1.123  2006/03/20 10:52:43  brouard
 {    * imach.c (Module): <title> changed, corresponds to .htm file
   int i;    name. <head> headers where missing.
   int lg=20;  
   i=0;    * imach.c (Module): Weights can have a decimal point as for
   lg=strlen(t);    English (a comma might work with a correct LC_NUMERIC environment,
   for(i=0; i<= lg; i++) {    otherwise the weight is truncated).
     (s[i] = t[i]);    Modification of warning when the covariates values are not 0 or
     if (t[i]== '\\') s[i]='/';    1.
   }    Version 0.98g
 }  
     Revision 1.122  2006/03/20 09:45:41  brouard
 int nbocc(char *s, char occ)    (Module): Weights can have a decimal point as for
 {    English (a comma might work with a correct LC_NUMERIC environment,
   int i,j=0;    otherwise the weight is truncated).
   int lg=20;    Modification of warning when the covariates values are not 0 or
   i=0;    1.
   lg=strlen(s);    Version 0.98g
   for(i=0; i<= lg; i++) {  
   if  (s[i] == occ ) j++;    Revision 1.121  2006/03/16 17:45:01  lievre
   }    * imach.c (Module): Comments concerning covariates added
   return j;  
 }    * imach.c (Module): refinements in the computation of lli if
     status=-2 in order to have more reliable computation if stepm is
 void cutv(char *u,char *v, char*t, char occ)    not 1 month. Version 0.98f
 {  
   int i,lg,j,p;    Revision 1.120  2006/03/16 15:10:38  lievre
   i=0;    (Module): refinements in the computation of lli if
   if (t[0]== occ) p=0;    status=-2 in order to have more reliable computation if stepm is
   for(j=0; j<=strlen(t)-1; j++) {    not 1 month. Version 0.98f
     if((t[j]!= occ) && (t[j+1]==occ)) p=j+1;  
   }    Revision 1.119  2006/03/15 17:42:26  brouard
     (Module): Bug if status = -2, the loglikelihood was
   lg=strlen(t);    computed as likelihood omitting the logarithm. Version O.98e
   for(j=0; j<p; j++) {  
     (u[j] = t[j]);    Revision 1.118  2006/03/14 18:20:07  brouard
     u[p]='\0';    (Module): varevsij Comments added explaining the second
   }    table of variances if popbased=1 .
     (Module): Covariances of eij, ekl added, graphs fixed, new html link.
    for(j=0; j<= lg; j++) {    (Module): Function pstamp added
     if (j>=(p+1))(v[j-p-1] = t[j]);    (Module): Version 0.98d
   }  
 }    Revision 1.117  2006/03/14 17:16:22  brouard
     (Module): varevsij Comments added explaining the second
     table of variances if popbased=1 .
 /********************** nrerror ********************/    (Module): Covariances of eij, ekl added, graphs fixed, new html link.
     (Module): Function pstamp added
 void nrerror(char error_text[])    (Module): Version 0.98d
 {  
   fprintf(stderr,"ERREUR ...\n");    Revision 1.116  2006/03/06 10:29:27  brouard
   fprintf(stderr,"%s\n",error_text);    (Module): Variance-covariance wrong links and
   exit(1);    varian-covariance of ej. is needed (Saito).
 }  
 /*********************** vector *******************/    Revision 1.115  2006/02/27 12:17:45  brouard
 double *vector(int nl, int nh)    (Module): One freematrix added in mlikeli! 0.98c
 {  
   double *v;    Revision 1.114  2006/02/26 12:57:58  brouard
   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));    (Module): Some improvements in processing parameter
   if (!v) nrerror("allocation failure in vector");    filename with strsep.
   return v-nl+NR_END;  
 }    Revision 1.113  2006/02/24 14:20:24  brouard
     (Module): Memory leaks checks with valgrind and:
 /************************ free vector ******************/    datafile was not closed, some imatrix were not freed and on matrix
 void free_vector(double*v, int nl, int nh)    allocation too.
 {  
   free((FREE_ARG)(v+nl-NR_END));    Revision 1.112  2006/01/30 09:55:26  brouard
 }    (Module): Back to gnuplot.exe instead of wgnuplot.exe
   
 /************************ivector *******************************/    Revision 1.111  2006/01/25 20:38:18  brouard
 int *ivector(long nl,long nh)    (Module): Lots of cleaning and bugs added (Gompertz)
 {    (Module): Comments can be added in data file. Missing date values
   int *v;    can be a simple dot '.'.
   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));  
   if (!v) nrerror("allocation failure in ivector");    Revision 1.110  2006/01/25 00:51:50  brouard
   return v-nl+NR_END;    (Module): Lots of cleaning and bugs added (Gompertz)
 }  
     Revision 1.109  2006/01/24 19:37:15  brouard
 /******************free ivector **************************/    (Module): Comments (lines starting with a #) are allowed in data.
 void free_ivector(int *v, long nl, long nh)  
 {    Revision 1.108  2006/01/19 18:05:42  lievre
   free((FREE_ARG)(v+nl-NR_END));    Gnuplot problem appeared...
 }    To be fixed
   
 /******************* imatrix *******************************/    Revision 1.107  2006/01/19 16:20:37  brouard
 int **imatrix(long nrl, long nrh, long ncl, long nch)    Test existence of gnuplot in imach path
      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */  
 {    Revision 1.106  2006/01/19 13:24:36  brouard
   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;    Some cleaning and links added in html output
   int **m;  
      Revision 1.105  2006/01/05 20:23:19  lievre
   /* allocate pointers to rows */    *** empty log message ***
   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));  
   if (!m) nrerror("allocation failure 1 in matrix()");    Revision 1.104  2005/09/30 16:11:43  lievre
   m += NR_END;    (Module): sump fixed, loop imx fixed, and simplifications.
   m -= nrl;    (Module): If the status is missing at the last wave but we know
      that the person is alive, then we can code his/her status as -2
      (instead of missing=-1 in earlier versions) and his/her
   /* allocate rows and set pointers to them */    contributions to the likelihood is 1 - Prob of dying from last
   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));    health status (= 1-p13= p11+p12 in the easiest case of somebody in
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    the healthy state at last known wave). Version is 0.98
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Revision 1.103  2005/09/30 15:54:49  lievre
      (Module): sump fixed, loop imx fixed, and simplifications.
   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;  
      Revision 1.102  2004/09/15 17:31:30  brouard
   /* return pointer to array of pointers to rows */    Add the possibility to read data file including tab characters.
   return m;  
 }    Revision 1.101  2004/09/15 10:38:38  brouard
     Fix on curr_time
 /****************** free_imatrix *************************/  
 void free_imatrix(m,nrl,nrh,ncl,nch)    Revision 1.100  2004/07/12 18:29:06  brouard
       int **m;    Add version for Mac OS X. Just define UNIX in Makefile
       long nch,ncl,nrh,nrl;  
      /* free an int matrix allocated by imatrix() */    Revision 1.99  2004/06/05 08:57:40  brouard
 {    *** empty log message ***
   free((FREE_ARG) (m[nrl]+ncl-NR_END));  
   free((FREE_ARG) (m+nrl-NR_END));    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
 /******************* matrix *******************************/    state at each age, but using a Gompertz model: log u =a + b*age .
 double **matrix(long nrl, long nrh, long ncl, long nch)    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
   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;    cross-longitudinal survey is different from the mortality estimated
   double **m;    from other sources like vital statistic data.
   
   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    The same imach parameter file can be used but the option for mle should be -3.
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Agnès, who wrote this part of the code, tried to keep most of the
   m -= nrl;    former routines in order to include the new code within the former code.
   
   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    The output is very simple: only an estimate of the intercept and of
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");    the slope with 95% confident intervals.
   m[nrl] += NR_END;  
   m[nrl] -= ncl;    Current limitations:
     A) Even if you enter covariates, i.e. with the
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;    model= V1+V2 equation for example, the programm does only estimate a unique global model without covariates.
   return m;    B) There is no computation of Life Expectancy nor Life Table.
 }  
     Revision 1.97  2004/02/20 13:25:42  lievre
 /*************************free matrix ************************/    Version 0.96d. Population forecasting command line is (temporarily)
 void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)    suppressed.
 {  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.96  2003/07/15 15:38:55  brouard
   free((FREE_ARG)(m+nrl-NR_END));    * imach.c (Repository): Errors in subdirf, 2, 3 while printing tmpout is
 }    rewritten within the same printf. Workaround: many printfs.
   
 /******************* ma3x *******************************/    Revision 1.95  2003/07/08 07:54:34  brouard
 double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)    * imach.c (Repository):
 {    (Repository): Using imachwizard code to output a more meaningful covariance
   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;    matrix (cov(a12,c31) instead of numbers.
   double ***m;  
     Revision 1.94  2003/06/27 13:00:02  brouard
   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));    Just cleaning
   if (!m) nrerror("allocation failure 1 in matrix()");  
   m += NR_END;    Revision 1.93  2003/06/25 16:33:55  brouard
   m -= nrl;    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));    (Module): Version 0.96b
   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");  
   m[nrl] += NR_END;    Revision 1.92  2003/06/25 16:30:45  brouard
   m[nrl] -= ncl;    (Module): On windows (cygwin) function asctime_r doesn't
     exist so I changed back to asctime which exists.
   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;  
     Revision 1.91  2003/06/25 15:30:29  brouard
   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));    * imach.c (Repository): Duplicated warning errors corrected.
   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");    (Repository): Elapsed time after each iteration is now output. It
   m[nrl][ncl] += NR_END;    helps to forecast when convergence will be reached. Elapsed time
   m[nrl][ncl] -= nll;    is stamped in powell.  We created a new html file for the graphs
   for (j=ncl+1; j<=nch; j++)    concerning matrix of covariance. It has extension -cov.htm.
     m[nrl][j]=m[nrl][j-1]+nlay;  
      Revision 1.90  2003/06/24 12:34:15  brouard
   for (i=nrl+1; i<=nrh; i++) {    (Module): Some bugs corrected for windows. Also, when
     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;    mle=-1 a template is output in file "or"mypar.txt with the design
     for (j=ncl+1; j<=nch; j++)    of the covariance matrix to be input.
       m[i][j]=m[i][j-1]+nlay;  
   }    Revision 1.89  2003/06/24 12:30:52  brouard
   return m;    (Module): Some bugs corrected for windows. Also, when
 }    mle=-1 a template is output in file "or"mypar.txt with the design
     of the covariance matrix to be input.
 /*************************free ma3x ************************/  
 void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)    Revision 1.88  2003/06/23 17:54:56  brouard
 {    * imach.c (Repository): Create a sub-directory where all the secondary files are. Only imach, htm, gp and r(imach) are on the main directory. Correct time and other things.
   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));  
   free((FREE_ARG)(m[nrl]+ncl-NR_END));    Revision 1.87  2003/06/18 12:26:01  brouard
   free((FREE_ARG)(m+nrl-NR_END));    Version 0.96
 }  
     Revision 1.86  2003/06/17 20:04:08  brouard
 /***************** f1dim *************************/    (Module): Change position of html and gnuplot routines and added
 extern int ncom;    routine fileappend.
 extern double *pcom,*xicom;  
 extern double (*nrfunc)(double []);    Revision 1.85  2003/06/17 13:12:43  brouard
      * imach.c (Repository): Check when date of death was earlier that
 double f1dim(double x)    current date of interview. It may happen when the death was just
 {    prior to the death. In this case, dh was negative and likelihood
   int j;    was wrong (infinity). We still send an "Error" but patch by
   double f;    assuming that the date of death was just one stepm after the
   double *xt;    interview.
      (Repository): Because some people have very long ID (first column)
   xt=vector(1,ncom);    we changed int to long in num[] and we added a new lvector for
   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j];    memory allocation. But we also truncated to 8 characters (left
   f=(*nrfunc)(xt);    truncation)
   free_vector(xt,1,ncom);    (Repository): No more line truncation errors.
   return f;  
 }    Revision 1.84  2003/06/13 21:44:43  brouard
     * imach.c (Repository): Replace "freqsummary" at a correct
 /*****************brent *************************/    place. It differs from routine "prevalence" which may be called
 double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin)    many times. Probs is memory consuming and must be used with
 {    parcimony.
   int iter;    Version 0.95a3 (should output exactly the same maximization than 0.8a2)
   double a,b,d,etemp;  
   double fu,fv,fw,fx;    Revision 1.83  2003/06/10 13:39:11  lievre
   double ftemp;    *** empty log message ***
   double p,q,r,tol1,tol2,u,v,w,x,xm;  
   double e=0.0;    Revision 1.82  2003/06/05 15:57:20  brouard
      Add log in  imach.c and  fullversion number is now printed.
   a=(ax < cx ? ax : cx);  
   b=(ax > cx ? ax : cx);  */
   x=w=v=bx;  /*
   fw=fv=fx=(*f)(x);     Interpolated Markov Chain
   for (iter=1;iter<=ITMAX;iter++) {  
     xm=0.5*(a+b);    Short summary of the programme:
     tol2=2.0*(tol1=tol*fabs(x)+ZEPS);    
     /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/    This program computes Healthy Life Expectancies from
     printf(".");fflush(stdout);    cross-longitudinal data. Cross-longitudinal data consist in: -1- a
 #ifdef DEBUG    first survey ("cross") where individuals from different ages are
     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);    interviewed on their health status or degree of disability (in the
     /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */    case of a health survey which is our main interest) -2- at least a
 #endif    second wave of interviews ("longitudinal") which measure each change
     if (fabs(x-xm) <= (tol2-0.5*(b-a))){    (if any) in individual health status.  Health expectancies are
       *xmin=x;    computed from the time spent in each health state according to a
       return fx;    model. More health states you consider, more time is necessary to reach the
     }    Maximum Likelihood of the parameters involved in the model.  The
     ftemp=fu;    simplest model is the multinomial logistic model where pij is the
     if (fabs(e) > tol1) {    probability to be observed in state j at the second wave
       r=(x-w)*(fx-fv);    conditional to be observed in state i at the first wave. Therefore
       q=(x-v)*(fx-fw);    the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where
       p=(x-v)*q-(x-w)*r;    'age' is age and 'sex' is a covariate. If you want to have a more
       q=2.0*(q-r);    complex model than "constant and age", you should modify the program
       if (q > 0.0) p = -p;    where the markup *Covariates have to be included here again* invites
       q=fabs(q);    you to do it.  More covariates you add, slower the
       etemp=e;    convergence.
       e=d;  
       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))    The advantage of this computer programme, compared to a simple
         d=CGOLD*(e=(x >= xm ? a-x : b-x));    multinomial logistic model, is clear when the delay between waves is not
       else {    identical for each individual. Also, if a individual missed an
         d=p/q;    intermediate interview, the information is lost, but taken into
         u=x+d;    account using an interpolation or extrapolation.  
         if (u-a < tol2 || b-u < tol2)  
           d=SIGN(tol1,xm-x);    hPijx is the probability to be observed in state i at age x+h
       }    conditional to the observed state i at age x. The delay 'h' can be
     } else {    split into an exact number (nh*stepm) of unobserved intermediate
       d=CGOLD*(e=(x >= xm ? a-x : b-x));    states. This elementary transition (by month, quarter,
     }    semester or year) is modelled as a multinomial logistic.  The hPx
     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));    matrix is simply the matrix product of nh*stepm elementary matrices
     fu=(*f)(u);    and the contribution of each individual to the likelihood is simply
     if (fu <= fx) {    hPijx.
       if (u >= x) a=x; else b=x;  
       SHFT(v,w,x,u)    Also this programme outputs the covariance matrix of the parameters but also
         SHFT(fv,fw,fx,fu)    of the life expectancies. It also computes the period (stable) prevalence. 
         } else {    
           if (u < x) a=u; else b=u;    Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
           if (fu <= fw || w == x) {             Institut national d'études démographiques, Paris.
             v=w;    This software have been partly granted by Euro-REVES, a concerted action
             w=u;    from the European Union.
             fv=fw;    It is copyrighted identically to a GNU software product, ie programme and
             fw=fu;    software can be distributed freely for non commercial use. Latest version
           } else if (fu <= fv || v == x || v == w) {    can be accessed at http://euroreves.ined.fr/imach .
             v=u;  
             fv=fu;    Help to debug: LD_PRELOAD=/usr/local/lib/libnjamd.so ./imach foo.imach
           }    or better on gdb : set env LD_PRELOAD=/usr/local/lib/libnjamd.so
         }    
   }    **********************************************************************/
   nrerror("Too many iterations in brent");  /*
   *xmin=x;    main
   return fx;    read parameterfile
 }    read datafile
     concatwav
 /****************** mnbrak ***********************/    freqsummary
     if (mle >= 1)
 void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc,      mlikeli
             double (*func)(double))    print results files
 {    if mle==1 
   double ulim,u,r,q, dum;       computes hessian
   double fu;    read end of parameter file: agemin, agemax, bage, fage, estepm
          begin-prev-date,...
   *fa=(*func)(*ax);    open gnuplot file
   *fb=(*func)(*bx);    open html file
   if (*fb > *fa) {    period (stable) prevalence      | pl_nom    1-1 2-2 etc by covariate
     SHFT(dum,*ax,*bx,dum)     for age prevalim()             | #****** V1=0  V2=1  V3=1  V4=0 ******
       SHFT(dum,*fb,*fa,dum)                                    | 65 1 0 2 1 3 1 4 0  0.96326 0.03674
       }      freexexit2 possible for memory heap.
   *cx=(*bx)+GOLD*(*bx-*ax);  
   *fc=(*func)(*cx);    h Pij x                         | pij_nom  ficrestpij
   while (*fb > *fc) {     # Cov Agex agex+h hpijx with i,j= 1-1 1-2     1-3     2-1     2-2     2-3
     r=(*bx-*ax)*(*fb-*fc);         1  85   85    1.00000             0.00000 0.00000 0.00000 1.00000 0.00000
     q=(*bx-*cx)*(*fb-*fa);         1  85   86    0.68299             0.22291 0.09410 0.71093 0.00000 0.28907
     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/  
       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r));         1  65   99    0.00364             0.00322 0.99314 0.00350 0.00310 0.99340
     ulim=(*bx)+GLIMIT*(*cx-*bx);         1  65  100    0.00214             0.00204 0.99581 0.00206 0.00196 0.99597
     if ((*bx-u)*(u-*cx) > 0.0) {    variance of p one-step probabilities varprob  | prob_nom   ficresprob #One-step probabilities and stand. devi in ()
       fu=(*func)(u);     Standard deviation of one-step probabilities | probcor_nom   ficresprobcor #One-step probabilities and correlation matrix
     } else if ((*cx-u)*(u-ulim) > 0.0) {     Matrix of variance covariance of one-step probabilities |  probcov_nom ficresprobcov #One-step probabilities and covariance matrix
       fu=(*func)(u);  
       if (fu < *fc) {    forecasting if prevfcast==1 prevforecast call prevalence()
         SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx))    health expectancies
           SHFT(*fb,*fc,fu,(*func)(u))    Variance-covariance of DFLE
           }    prevalence()
     } else if ((u-ulim)*(ulim-*cx) >= 0.0) {     movingaverage()
       u=ulim;    varevsij() 
       fu=(*func)(u);    if popbased==1 varevsij(,popbased)
     } else {    total life expectancies
       u=(*cx)+GOLD*(*cx-*bx);    Variance of period (stable) prevalence
       fu=(*func)(u);   end
     }  */
     SHFT(*ax,*bx,*cx,u)  
       SHFT(*fa,*fb,*fc,fu)  
       }  
 }   
   #include <math.h>
 /*************** linmin ************************/  #include <stdio.h>
   #include <stdlib.h>
 int ncom;  #include <string.h>
 double *pcom,*xicom;  #include <unistd.h>
 double (*nrfunc)(double []);  
    #include <limits.h>
 void linmin(double p[], double xi[], int n, double *fret,double (*func)(double []))  #include <sys/types.h>
 {  #include <sys/stat.h>
   double brent(double ax, double bx, double cx,  #include <errno.h>
                double (*f)(double), double tol, double *xmin);  extern int errno;
   double f1dim(double x);  
   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb,  #ifdef LINUX
               double *fc, double (*func)(double));  #include <time.h>
   int j;  #include "timeval.h"
   double xx,xmin,bx,ax;  #else
   double fx,fb,fa;  #include <sys/time.h>
    #endif
   ncom=n;  
   pcom=vector(1,n);  #ifdef GSL
   xicom=vector(1,n);  #include <gsl/gsl_errno.h>
   nrfunc=func;  #include <gsl/gsl_multimin.h>
   for (j=1;j<=n;j++) {  #endif
     pcom[j]=p[j];  
     xicom[j]=xi[j];  /* #include <libintl.h> */
   }  /* #define _(String) gettext (String) */
   ax=0.0;  
   xx=1.0;  #define MAXLINE 1024 /* Was 256. Overflow with 312 with 2 states and 4 covariates. Should be ok */
   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  
   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin);  #define GNUPLOTPROGRAM "gnuplot"
 #ifdef DEBUG  /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/
   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);  #define FILENAMELENGTH 132
 #endif  
   for (j=1;j<=n;j++) {  #define GLOCK_ERROR_NOPATH              -1      /* empty path */
     xi[j] *= xmin;  #define GLOCK_ERROR_GETCWD              -2      /* cannot get cwd */
     p[j] += xi[j];  
   }  #define MAXPARM 128 /**< Maximum number of parameters for the optimization */
   free_vector(xicom,1,n);  #define NPARMAX 64 /**< (nlstate+ndeath-1)*nlstate*ncovmodel */
   free_vector(pcom,1,n);  
 }  #define NINTERVMAX 8
   #define NLSTATEMAX 8 /**< Maximum number of live states (for func) */
 /*************** powell ************************/  #define NDEATHMAX 8 /**< Maximum number of dead states (for func) */
 void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret,  #define NCOVMAX 20 /**< Maximum number of covariates, including generated covariates V1*V2 */
             double (*func)(double []))  #define codtabm(h,k)  1 & (h-1) >> (k-1) ;
 {  #define MAXN 20000
   void linmin(double p[], double xi[], int n, double *fret,  #define YEARM 12. /**< Number of months per year */
               double (*func)(double []));  #define AGESUP 130
   int i,ibig,j;  #define AGEBASE 40
   double del,t,*pt,*ptt,*xit;  #define AGEGOMP 10. /**< Minimal age for Gompertz adjustment */
   double fp,fptt;  #ifdef UNIX
   double *xits;  #define DIRSEPARATOR '/'
   pt=vector(1,n);  #define CHARSEPARATOR "/"
   ptt=vector(1,n);  #define ODIRSEPARATOR '\\'
   xit=vector(1,n);  #else
   xits=vector(1,n);  #define DIRSEPARATOR '\\'
   *fret=(*func)(p);  #define CHARSEPARATOR "\\"
   for (j=1;j<=n;j++) pt[j]=p[j];  #define ODIRSEPARATOR '/'
   for (*iter=1;;++(*iter)) {  #endif
     fp=(*fret);  
     ibig=0;  /* $Id$ */
     del=0.0;  /* $State$ */
     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);  
     for (i=1;i<=n;i++)  char version[]="Imach version 0.98nV, August 2014,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121)";
       printf(" %d %.12f",i, p[i]);  char fullversion[]="$Revision$ $Date$"; 
     printf("\n");  char strstart[80];
     for (i=1;i<=n;i++) {  char optionfilext[10], optionfilefiname[FILENAMELENGTH];
       for (j=1;j<=n;j++) xit[j]=xi[j][i];  int erreur=0, nberr=0, nbwarn=0; /* Error number, number of errors number of warnings  */
       fptt=(*fret);  int nvar=0, nforce=0; /* Number of variables, number of forces */
 #ifdef DEBUG  /* Number of covariates model=V2+V1+ V3*age+V2*V4 */
       printf("fret=%lf \n",*fret);  int cptcovn=0; /**< cptcovn number of covariates added in the model (excepting constant and age and age*product) */
 #endif  int cptcovt=0; /**< cptcovt number of covariates added in the model (excepting constant and age) */
       printf("%d",i);fflush(stdout);  int cptcovs=0; /**< cptcovs number of simple covariates V2+V1 =2 */
       linmin(p,xit,n,fret,func);  int cptcovage=0; /**< Number of covariates with age: V3*age only =1 */
       if (fabs(fptt-(*fret)) > del) {  int cptcovprodnoage=0; /**< Number of covariate products without age */   
         del=fabs(fptt-(*fret));  int cptcoveff=0; /* Total number of covariates to vary for printing results */
         ibig=i;  int cptcov=0; /* Working variable */
       }  int npar=NPARMAX;
 #ifdef DEBUG  int nlstate=2; /* Number of live states */
       printf("%d %.12e",i,(*fret));  int ndeath=1; /* Number of dead states */
       for (j=1;j<=n;j++) {  int ncovmodel=0, ncovcol=0;     /* Total number of covariables including constant a12*1 +b12*x ncovmodel=2 */
         xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);  int popbased=0;
         printf(" x(%d)=%.12e",j,xit[j]);  
       }  int *wav; /* Number of waves for this individuual 0 is possible */
       for(j=1;j<=n;j++)  int maxwav=0; /* Maxim number of waves */
         printf(" p=%.12e",p[j]);  int jmin=0, jmax=0; /* min, max spacing between 2 waves */
       printf("\n");  int ijmin=0, ijmax=0; /* Individuals having jmin and jmax */ 
 #endif  int gipmx=0, gsw=0; /* Global variables on the number of contributions 
     }                     to the likelihood and the sum of weights (done by funcone)*/
     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {  int mle=1, weightopt=0;
 #ifdef DEBUG  int **mw; /* mw[mi][i] is number of the mi wave for this individual */
       int k[2],l;  int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
       k[0]=1;  int **bh; /* bh[mi][i] is the bias (+ or -) for this individual if the delay between
       k[1]=-1;             * wave mi and wave mi+1 is not an exact multiple of stepm. */
       printf("Max: %.12e",(*func)(p));  double jmean=1; /* Mean space between 2 waves */
       for (j=1;j<=n;j++)  double **matprod2(); /* test */
         printf(" %.12e",p[j]);  double **oldm, **newm, **savm; /* Working pointers to matrices */
       printf("\n");  double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
       for(l=0;l<=1;l++) {  /*FILE *fic ; */ /* Used in readdata only */
         for (j=1;j<=n;j++) {  FILE *ficpar, *ficparo,*ficres, *ficresp, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop;
           ptt[j]=p[j]+(p[j]-pt[j])*k[l];  FILE *ficlog, *ficrespow;
           printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);  int globpr=0; /* Global variable for printing or not */
         }  double fretone; /* Only one call to likelihood */
         printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));  long ipmx=0; /* Number of contributions */
       }  double sw; /* Sum of weights */
 #endif  char filerespow[FILENAMELENGTH];
   char fileresilk[FILENAMELENGTH]; /* File of individual contributions to the likelihood */
   FILE *ficresilk;
       free_vector(xit,1,n);  FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor;
       free_vector(xits,1,n);  FILE *ficresprobmorprev;
       free_vector(ptt,1,n);  FILE *fichtm, *fichtmcov; /* Html File */
       free_vector(pt,1,n);  FILE *ficreseij;
       return;  char filerese[FILENAMELENGTH];
     }  FILE *ficresstdeij;
     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");  char fileresstde[FILENAMELENGTH];
     for (j=1;j<=n;j++) {  FILE *ficrescveij;
       ptt[j]=2.0*p[j]-pt[j];  char filerescve[FILENAMELENGTH];
       xit[j]=p[j]-pt[j];  FILE  *ficresvij;
       pt[j]=p[j];  char fileresv[FILENAMELENGTH];
     }  FILE  *ficresvpl;
     fptt=(*func)(ptt);  char fileresvpl[FILENAMELENGTH];
     if (fptt < fp) {  char title[MAXLINE];
       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);  char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
       if (t < 0.0) {  char plotcmd[FILENAMELENGTH], pplotcmd[FILENAMELENGTH];
         linmin(p,xit,n,fret,func);  char tmpout[FILENAMELENGTH],  tmpout2[FILENAMELENGTH]; 
         for (j=1;j<=n;j++) {  char command[FILENAMELENGTH];
           xi[j][ibig]=xi[j][n];  int  outcmd=0;
           xi[j][n]=xit[j];  
         }  char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH];
 #ifdef DEBUG  
         printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);  char filelog[FILENAMELENGTH]; /* Log file */
         for(j=1;j<=n;j++)  char filerest[FILENAMELENGTH];
           printf(" %.12e",xit[j]);  char fileregp[FILENAMELENGTH];
         printf("\n");  char popfile[FILENAMELENGTH];
 #endif  
       }  char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH], optionfilehtmcov[FILENAMELENGTH] ;
     }  
   }  struct timeval start_time, end_time, curr_time, last_time, forecast_time;
 }  struct timezone tzp;
   extern int gettimeofday();
 /**** Prevalence limit ****************/  struct tm tmg, tm, tmf, *gmtime(), *localtime();
   long time_value;
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  extern long time();
 {  char strcurr[80], strfor[80];
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit  
      matrix by transitions matrix until convergence is reached */  char *endptr;
   long lval;
   int i, ii,j,k;  double dval;
   double min, max, maxmin, maxmax,sumnew=0.;  
   double **matprod2();  #define NR_END 1
   double **out, cov[NCOVMAX], **pmij();  #define FREE_ARG char*
   double **newm;  #define FTOL 1.0e-10
   double agefin, delaymax=50 ; /* Max number of years to converge */  
   #define NRANSI 
   for (ii=1;ii<=nlstate+ndeath;ii++)  #define ITMAX 200 
     for (j=1;j<=nlstate+ndeath;j++){  
       oldm[ii][j]=(ii==j ? 1.0 : 0.0);  #define TOL 2.0e-4 
     }  
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */  #define CGOLD 0.3819660 
   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){  #define ZEPS 1.0e-10 
     newm=savm;  #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
     /* Covariates have to be included here again */  
     cov[1]=1.;  #define GOLD 1.618034 
     cov[2]=agefin;  #define GLIMIT 100.0 
     if (cptcovn>0){  #define TINY 1.0e-20 
       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]]);*/}  
     }  static double maxarg1,maxarg2;
     out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);  #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
   #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
     savm=oldm;    
     oldm=newm;  #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
     maxmax=0.;  #define rint(a) floor(a+0.5)
     for(j=1;j<=nlstate;j++){  
       min=1.;  static double sqrarg;
       max=0.;  #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
       for(i=1; i<=nlstate; i++) {  #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
         sumnew=0;  int agegomp= AGEGOMP;
         for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];  
         prlim[i][j]= newm[i][j]/(1-sumnew);  int imx; 
         max=FMAX(max,prlim[i][j]);  int stepm=1;
         min=FMIN(min,prlim[i][j]);  /* Stepm, step in month: minimum step interpolation*/
       }  
       maxmin=max-min;  int estepm;
       maxmax=FMAX(maxmax,maxmin);  /* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/
     }  
     if(maxmax < ftolpl){  int m,nb;
       return prlim;  long *num;
     }  int firstpass=0, lastpass=4,*cod, *ncodemax, *Tage,*cens;
   }  double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
 }  double **pmmij, ***probs;
   double *ageexmed,*agecens;
 /*************** transition probabilities **********/  double dateintmean=0;
   
 double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )  double *weight;
 {  int **s; /* Status */
   double s1, s2;  double *agedc;
   /*double t34;*/  double  **covar; /**< covar[j,i], value of jth covariate for individual i,
   int i,j,j1, nc, ii, jj;                    * covar=matrix(0,NCOVMAX,1,n); 
                     * cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; */
     for(i=1; i<= nlstate; i++){  double  idx; 
     for(j=1; j<i;j++){  int **nbcode, *Tvar; /**< model=V2 => Tvar[1]= 2 */
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  int *Ndum; /** Freq of modality (tricode */
         /*s2 += param[i][j][nc]*cov[nc];*/  int **codtab; /**< codtab=imatrix(1,100,1,10); */
         s2 += x[(i-1)*nlstate*ncovmodel+(j-1)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  int **Tvard, *Tprod, cptcovprod, *Tvaraff;
         /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/  double *lsurv, *lpop, *tpop;
       }  
       ps[i][j]=s2;  double ftol=FTOL; /**< Tolerance for computing Max Likelihood */
       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/  double ftolhess; /**< Tolerance for computing hessian */
     }  
     for(j=i+1; j<=nlstate+ndeath;j++){  /**************** split *************************/
       for (nc=1, s2=0.;nc <=ncovmodel; nc++){  static  int split( char *path, char *dirc, char *name, char *ext, char *finame )
         s2 += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];  {
         /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/    /* From a file name with (full) path (either Unix or Windows) we extract the directory (dirc)
       }       the name of the file (name), its extension only (ext) and its first part of the name (finame)
       ps[i][j]=s2;    */ 
     }    char  *ss;                            /* pointer */
   }    int   l1, l2;                         /* length counters */
   for(i=1; i<= nlstate; i++){  
      s1=0;    l1 = strlen(path );                   /* length of path */
     for(j=1; j<i; j++)    if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH );
       s1+=exp(ps[i][j]);    ss= strrchr( path, DIRSEPARATOR );            /* find last / */
     for(j=i+1; j<=nlstate+ndeath; j++)    if ( ss == NULL ) {                   /* no directory, so determine current directory */
       s1+=exp(ps[i][j]);      strcpy( name, path );               /* we got the fullname name because no directory */
     ps[i][i]=1./(s1+1.);      /*if(strrchr(path, ODIRSEPARATOR )==NULL)
     for(j=1; j<i; j++)        printf("Warning you should use %s as a separator\n",DIRSEPARATOR);*/
       ps[i][j]= exp(ps[i][j])*ps[i][i];      /* get current working directory */
     for(j=i+1; j<=nlstate+ndeath; j++)      /*    extern  char* getcwd ( char *buf , int len);*/
       ps[i][j]= exp(ps[i][j])*ps[i][i];      if ( getcwd( dirc, FILENAME_MAX ) == NULL ) {
     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */        return( GLOCK_ERROR_GETCWD );
   } /* end i */      }
       /* got dirc from getcwd*/
   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){      printf(" DIRC = %s \n",dirc);
     for(jj=1; jj<= nlstate+ndeath; jj++){    } else {                              /* strip direcotry from path */
       ps[ii][jj]=0;      ss++;                               /* after this, the filename */
       ps[ii][ii]=1;      l2 = strlen( ss );                  /* length of filename */
     }      if ( l2 == 0 ) return( GLOCK_ERROR_NOPATH );
   }      strcpy( name, ss );         /* save file name */
       strncpy( dirc, path, l1 - l2 );     /* now the directory */
   /*   for(ii=1; ii<= nlstate+ndeath; ii++){      dirc[l1-l2] = 0;                    /* add zero */
     for(jj=1; jj<= nlstate+ndeath; jj++){      printf(" DIRC2 = %s \n",dirc);
      printf("%lf ",ps[ii][jj]);    }
    }    /* We add a separator at the end of dirc if not exists */
     printf("\n ");    l1 = strlen( dirc );                  /* length of directory */
     }    if( dirc[l1-1] != DIRSEPARATOR ){
     printf("\n ");printf("%lf ",cov[2]);*/      dirc[l1] =  DIRSEPARATOR;
 /*      dirc[l1+1] = 0; 
   for(i=1; i<= npar; i++) printf("%f ",x[i]);      printf(" DIRC3 = %s \n",dirc);
   goto end;*/    }
     return ps;    ss = strrchr( name, '.' );            /* find last / */
 }    if (ss >0){
       ss++;
 /**************** Product of 2 matrices ******************/      strcpy(ext,ss);                     /* save extension */
       l1= strlen( name);
 double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)      l2= strlen(ss)+1;
 {      strncpy( finame, name, l1-l2);
   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times      finame[l1-l2]= 0;
      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */    }
   /* in, b, out are matrice of pointers which should have been initialized  
      before: only the contents of out is modified. The function returns    return( 0 );                          /* we're done */
      a pointer to pointers identical to out */  }
   long i, j, k;  
   for(i=nrl; i<= nrh; i++)  
     for(k=ncolol; k<=ncoloh; k++)  /******************************************/
       for(j=ncl,out[i][k]=0.; j<=nch; j++)  
         out[i][k] +=in[i][j]*b[j][k];  void replace_back_to_slash(char *s, char*t)
   {
   return out;    int i;
 }    int lg=0;
     i=0;
     lg=strlen(t);
 /************* Higher Matrix Product ***************/    for(i=0; i<= lg; i++) {
       (s[i] = t[i]);
 double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )      if (t[i]== '\\') s[i]='/';
 {    }
   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month  }
      duration (i.e. until  
      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices.  char *trimbb(char *out, char *in)
      Output is stored in matrix po[i][j][h] for h every 'hstepm' step  { /* Trim multiple blanks in line but keeps first blanks if line starts with blanks */
      (typically every 2 years instead of every month which is too big).    char *s;
      Model is determined by parameters x and covariates have to be    s=out;
      included manually here.    while (*in != '\0'){
       while( *in == ' ' && *(in+1) == ' '){ /* && *(in+1) != '\0'){*/
      */        in++;
       }
   int i, j, d, h, k;      *out++ = *in++;
   double **out, cov[NCOVMAX];    }
   double **newm;    *out='\0';
     return s;
   /* Hstepm could be zero and should return the unit matrix */  }
   for (i=1;i<=nlstate+ndeath;i++)  
     for (j=1;j<=nlstate+ndeath;j++){  char *cutl(char *blocc, char *alocc, char *in, char occ)
       oldm[i][j]=(i==j ? 1.0 : 0.0);  {
       po[i][j][0]=(i==j ? 1.0 : 0.0);    /* cuts string in into blocc and alocc where blocc ends before first occurence of char 'occ' 
     }       and alocc starts after first occurence of char 'occ' : ex cutv(blocc,alocc,"abcdef2ghi2j",'2')
   /* Even if hstepm = 1, at least one multiplication by the unit matrix */       gives blocc="abcdef2ghi" and alocc="j".
   for(h=1; h <=nhstepm; h++){       If occ is not found blocc is null and alocc is equal to in. Returns blocc
     for(d=1; d <=hstepm; d++){    */
       newm=savm;    char *s, *t, *bl;
       /* Covariates have to be included here again */    t=in;s=in;
       cov[1]=1.;    while ((*in != occ) && (*in != '\0')){
       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;      *alocc++ = *in++;
       if (cptcovn>0){    }
       for (k=1; k<=cptcovn;k++) cov[2+k]=nbcode[Tvar[k]][codtab[ij][k]];    if( *in == occ){
     }      *(alocc)='\0';
       /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/      s=++in;
       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/    }
       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath,   
                    pmij(pmmij,cov,ncovmodel,x,nlstate));    if (s == t) {/* occ not found */
       savm=oldm;      *(alocc-(in-s))='\0';
       oldm=newm;      in=s;
     }    }
     for(i=1; i<=nlstate+ndeath; i++)    while ( *in != '\0'){
       for(j=1;j<=nlstate+ndeath;j++) {      *blocc++ = *in++;
         po[i][j][h]=newm[i][j];    }
         /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);  
          */    *blocc='\0';
       }    return t;
   } /* end h */  }
   return po;  char *cutv(char *blocc, char *alocc, char *in, char occ)
 }  {
     /* 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')
 /*************** log-likelihood *************/       gives blocc="abcdef2ghi" and alocc="j".
 double func( double *x)       If occ is not found blocc is null and alocc is equal to in. Returns alocc
 {    */
   int i, ii, j, k, mi, d;    char *s, *t;
   double l, ll[NLSTATEMAX], cov[NCOVMAX];    t=in;s=in;
   double **out;    while (*in != '\0'){
   double sw; /* Sum of weights */      while( *in == occ){
   double lli; /* Individual log likelihood */        *blocc++ = *in++;
   long ipmx;        s=in;
   /*extern weight */      }
   /* We are differentiating ll according to initial status */      *blocc++ = *in++;
   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/    }
   /*for(i=1;i<imx;i++)    if (s == t) /* occ not found */
 printf(" %d\n",s[4][i]);      *(blocc-(in-s))='\0';
   */    else
       *(blocc-(in-s)-1)='\0';
   for(k=1; k<=nlstate; k++) ll[k]=0.;    in=s;
   for (i=1,ipmx=0, sw=0.; i<=imx; i++){    while ( *in != '\0'){
        for(mi=1; mi<= wav[i]-1; mi++){      *alocc++ = *in++;
       for (ii=1;ii<=nlstate+ndeath;ii++)    }
         for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);  
             for(d=0; d<dh[mi][i]; d++){    *alocc='\0';
         newm=savm;    return s;
           cov[1]=1.;  }
           cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;  
           if (cptcovn>0){  int nbocc(char *s, char occ)
             for (k=1; k<=cptcovn;k++) {  {
               cov[2+k]=covar[Tvar[k]][i];    int i,j=0;
               /* printf("k=%d cptcovn=%d %lf\n",k,cptcovn,covar[Tvar[k]][i]);*/    int lg=20;
             }    i=0;
             }    lg=strlen(s);
           out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,    for(i=0; i<= lg; i++) {
                        1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));    if  (s[i] == occ ) j++;
           savm=oldm;    }
           oldm=newm;    return j;
       } /* end mult */  }
      
       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);  /* void cutv(char *u,char *v, char*t, char occ) */
       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/  /* { */
       ipmx +=1;  /*   /\* cuts string t into u and v where u ends before last occurence of char 'occ'  */
       sw += weight[i];  /*      and v starts after last occurence of char 'occ' : ex cutv(u,v,"abcdef2ghi2j",'2') */
       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;  /*      gives u="abcdef2ghi" and v="j" *\/ */
     } /* end of wave */  /*   int i,lg,j,p=0; */
   } /* end of individual */  /*   i=0; */
   /*   lg=strlen(t); */
   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];  /*   for(j=0; j<=lg-1; j++) { */
   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */  /*     if((t[j]!= occ) && (t[j+1]== occ)) p=j+1; */
   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */  /*   } */
   
   return -l;  /*   for(j=0; j<p; j++) { */
 }  /*     (u[j] = t[j]); */
   /*   } */
   /*      u[p]='\0'; */
 /*********** Maximum Likelihood Estimation ***************/  
   /*    for(j=0; j<= lg; j++) { */
 void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))  /*     if (j>=(p+1))(v[j-p-1] = t[j]); */
 {  /*   } */
   int i,j, iter;  /* } */
   double **xi,*delti;  
   double fret;  /********************** nrerror ********************/
   xi=matrix(1,npar,1,npar);  
   for (i=1;i<=npar;i++)  void nrerror(char error_text[])
     for (j=1;j<=npar;j++)  {
       xi[i][j]=(i==j ? 1.0 : 0.0);    fprintf(stderr,"ERREUR ...\n");
   printf("Powell\n");    fprintf(stderr,"%s\n",error_text);
   powell(p,xi,npar,ftol,&iter,&fret,func);    exit(EXIT_FAILURE);
   }
    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));  /*********************** vector *******************/
   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));  double *vector(int nl, int nh)
   {
 }    double *v;
     v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
 /**** Computes Hessian and covariance matrix ***/    if (!v) nrerror("allocation failure in vector");
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))    return v-nl+NR_END;
 {  }
   double  **a,**y,*x,pd;  
   double **hess;  /************************ free vector ******************/
   int i, j,jk;  void free_vector(double*v, int nl, int nh)
   int *indx;  {
     free((FREE_ARG)(v+nl-NR_END));
   double hessii(double p[], double delta, int theta, double delti[]);  }
   double hessij(double p[], double delti[], int i, int j);  
   void lubksb(double **a, int npar, int *indx, double b[]) ;  /************************ivector *******************************/
   void ludcmp(double **a, int npar, int *indx, double *d) ;  int *ivector(long nl,long nh)
   {
     int *v;
   hess=matrix(1,npar,1,npar);    v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
     if (!v) nrerror("allocation failure in ivector");
   printf("\nCalculation of the hessian matrix. Wait...\n");    return v-nl+NR_END;
   for (i=1;i<=npar;i++){  }
     printf("%d",i);fflush(stdout);  
     hess[i][i]=hessii(p,ftolhess,i,delti);  /******************free ivector **************************/
     /*printf(" %f ",p[i]);*/  void free_ivector(int *v, long nl, long nh)
   }  {
     free((FREE_ARG)(v+nl-NR_END));
   for (i=1;i<=npar;i++) {  }
     for (j=1;j<=npar;j++)  {  
       if (j>i) {  /************************lvector *******************************/
         printf(".%d%d",i,j);fflush(stdout);  long *lvector(long nl,long nh)
         hess[i][j]=hessij(p,delti,i,j);  {
         hess[j][i]=hess[i][j];    long *v;
       }    v=(long *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(long)));
     }    if (!v) nrerror("allocation failure in ivector");
   }    return v-nl+NR_END;
   printf("\n");  }
   
   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");  /******************free lvector **************************/
    void free_lvector(long *v, long nl, long nh)
   a=matrix(1,npar,1,npar);  {
   y=matrix(1,npar,1,npar);    free((FREE_ARG)(v+nl-NR_END));
   x=vector(1,npar);  }
   indx=ivector(1,npar);  
   for (i=1;i<=npar;i++)  /******************* imatrix *******************************/
     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];  int **imatrix(long nrl, long nrh, long ncl, long nch) 
   ludcmp(a,npar,indx,&pd);       /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
   { 
   for (j=1;j<=npar;j++) {    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
     for (i=1;i<=npar;i++) x[i]=0;    int **m; 
     x[j]=1;    
     lubksb(a,npar,indx,x);    /* allocate pointers to rows */ 
     for (i=1;i<=npar;i++){    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
       matcov[i][j]=x[i];    if (!m) nrerror("allocation failure 1 in matrix()"); 
     }    m += NR_END; 
   }    m -= nrl; 
     
   printf("\n#Hessian matrix#\n");    
   for (i=1;i<=npar;i++) {    /* allocate rows and set pointers to them */ 
     for (j=1;j<=npar;j++) {    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
       printf("%.3e ",hess[i][j]);    if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
     }    m[nrl] += NR_END; 
     printf("\n");    m[nrl] -= ncl; 
   }    
     for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
   /* Recompute Inverse */    
   for (i=1;i<=npar;i++)    /* return pointer to array of pointers to rows */ 
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    return m; 
   ludcmp(a,npar,indx,&pd);  } 
   
   /*  printf("\n#Hessian matrix recomputed#\n");  /****************** free_imatrix *************************/
   void free_imatrix(m,nrl,nrh,ncl,nch)
   for (j=1;j<=npar;j++) {        int **m;
     for (i=1;i<=npar;i++) x[i]=0;        long nch,ncl,nrh,nrl; 
     x[j]=1;       /* free an int matrix allocated by imatrix() */ 
     lubksb(a,npar,indx,x);  { 
     for (i=1;i<=npar;i++){    free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
       y[i][j]=x[i];    free((FREE_ARG) (m+nrl-NR_END)); 
       printf("%.3e ",y[i][j]);  } 
     }  
     printf("\n");  /******************* matrix *******************************/
   }  double **matrix(long nrl, long nrh, long ncl, long nch)
   */  {
     long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
   free_matrix(a,1,npar,1,npar);    double **m;
   free_matrix(y,1,npar,1,npar);  
   free_vector(x,1,npar);    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
   free_ivector(indx,1,npar);    if (!m) nrerror("allocation failure 1 in matrix()");
   free_matrix(hess,1,npar,1,npar);    m += NR_END;
     m -= nrl;
   
 }    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
     if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
 /*************** hessian matrix ****************/    m[nrl] += NR_END;
 double hessii( double x[], double delta, int theta, double delti[])    m[nrl] -= ncl;
 {  
   int i;    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
   int l=1, lmax=20;    return m;
   double k1,k2;    /* print *(*(m+1)+70) or print m[1][70]; print m+1 or print &(m[1]) or &(m[1][0])
   double p2[NPARMAX+1];  m[i] = address of ith row of the table. &(m[i]) is its value which is another adress
   double res;  that of m[i][0]. In order to get the value p m[i][0] but it is unitialized.
   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;     */
   double fx;  }
   int k=0,kmax=10;  
   double l1;  /*************************free matrix ************************/
   void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
   fx=func(x);  {
   for (i=1;i<=npar;i++) p2[i]=x[i];    free((FREE_ARG)(m[nrl]+ncl-NR_END));
   for(l=0 ; l <=lmax; l++){    free((FREE_ARG)(m+nrl-NR_END));
     l1=pow(10,l);  }
     delts=delt;  
     for(k=1 ; k <kmax; k=k+1){  /******************* ma3x *******************************/
       delt = delta*(l1*k);  double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
       p2[theta]=x[theta] +delt;  {
       k1=func(p2)-fx;    long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
       p2[theta]=x[theta]-delt;    double ***m;
       k2=func(p2)-fx;  
       /*res= (k1-2.0*fx+k2)/delt/delt; */    m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */    if (!m) nrerror("allocation failure 1 in matrix()");
          m += NR_END;
 #ifdef DEBUG    m -= nrl;
       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);  
 #endif    m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){    m[nrl] += NR_END;
         k=kmax;    m[nrl] -= ncl;
       }  
       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */    for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
         k=kmax; l=lmax*10.;  
       }    m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){    if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
         delts=delt;    m[nrl][ncl] += NR_END;
       }    m[nrl][ncl] -= nll;
     }    for (j=ncl+1; j<=nch; j++) 
   }      m[nrl][j]=m[nrl][j-1]+nlay;
   delti[theta]=delts;    
   return res;      for (i=nrl+1; i<=nrh; i++) {
 }      m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
       for (j=ncl+1; j<=nch; j++) 
 double hessij( double x[], double delti[], int thetai,int thetaj)        m[i][j]=m[i][j-1]+nlay;
 {    }
   int i;    return m; 
   int l=1, l1, lmax=20;    /*  gdb: p *(m+1) <=> p m[1] and p (m+1) <=> p (m+1) <=> p &(m[1])
   double k1,k2,k3,k4,res,fx;             &(m[i][j][k]) <=> *((*(m+i) + j)+k)
   double p2[NPARMAX+1];    */
   int k;  }
   
   fx=func(x);  /*************************free ma3x ************************/
   for (k=1; k<=2; k++) {  void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
     for (i=1;i<=npar;i++) p2[i]=x[i];  {
     p2[thetai]=x[thetai]+delti[thetai]/k;    free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    free((FREE_ARG)(m[nrl]+ncl-NR_END));
     k1=func(p2)-fx;    free((FREE_ARG)(m+nrl-NR_END));
    }
     p2[thetai]=x[thetai]+delti[thetai]/k;  
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  /*************** function subdirf ***********/
     k2=func(p2)-fx;  char *subdirf(char fileres[])
    {
     p2[thetai]=x[thetai]-delti[thetai]/k;    /* Caution optionfilefiname is hidden */
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;    strcpy(tmpout,optionfilefiname);
     k3=func(p2)-fx;    strcat(tmpout,"/"); /* Add to the right */
      strcat(tmpout,fileres);
     p2[thetai]=x[thetai]-delti[thetai]/k;    return tmpout;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;  }
     k4=func(p2)-fx;  
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */  /*************** function subdirf2 ***********/
 #ifdef DEBUG  char *subdirf2(char fileres[], char *preop)
     printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);  {
 #endif    
   }    /* Caution optionfilefiname is hidden */
   return res;    strcpy(tmpout,optionfilefiname);
 }    strcat(tmpout,"/");
     strcat(tmpout,preop);
 /************** Inverse of matrix **************/    strcat(tmpout,fileres);
 void ludcmp(double **a, int n, int *indx, double *d)    return tmpout;
 {  }
   int i,imax,j,k;  
   double big,dum,sum,temp;  /*************** function subdirf3 ***********/
   double *vv;  char *subdirf3(char fileres[], char *preop, char *preop2)
    {
   vv=vector(1,n);    
   *d=1.0;    /* Caution optionfilefiname is hidden */
   for (i=1;i<=n;i++) {    strcpy(tmpout,optionfilefiname);
     big=0.0;    strcat(tmpout,"/");
     for (j=1;j<=n;j++)    strcat(tmpout,preop);
       if ((temp=fabs(a[i][j])) > big) big=temp;    strcat(tmpout,preop2);
     if (big == 0.0) nrerror("Singular matrix in routine ludcmp");    strcat(tmpout,fileres);
     vv[i]=1.0/big;    return tmpout;
   }  }
   for (j=1;j<=n;j++) {  
     for (i=1;i<j;i++) {  /***************** f1dim *************************/
       sum=a[i][j];  extern int ncom; 
       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j];  extern double *pcom,*xicom;
       a[i][j]=sum;  extern double (*nrfunc)(double []); 
     }   
     big=0.0;  double f1dim(double x) 
     for (i=j;i<=n;i++) {  { 
       sum=a[i][j];    int j; 
       for (k=1;k<j;k++)    double f;
         sum -= a[i][k]*a[k][j];    double *xt; 
       a[i][j]=sum;   
       if ( (dum=vv[i]*fabs(sum)) >= big) {    xt=vector(1,ncom); 
         big=dum;    for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
         imax=i;    f=(*nrfunc)(xt); 
       }    free_vector(xt,1,ncom); 
     }    return f; 
     if (j != imax) {  } 
       for (k=1;k<=n;k++) {  
         dum=a[imax][k];  /*****************brent *************************/
         a[imax][k]=a[j][k];  double brent(double ax, double bx, double cx, double (*f)(double), double tol,  double *xmin) 
         a[j][k]=dum;  { 
       }    int iter; 
       *d = -(*d);    double a,b,d,etemp;
       vv[imax]=vv[j];    double fu,fv,fw,fx;
     }    double ftemp;
     indx[j]=imax;    double p,q,r,tol1,tol2,u,v,w,x,xm; 
     if (a[j][j] == 0.0) a[j][j]=TINY;    double e=0.0; 
     if (j != n) {   
       dum=1.0/(a[j][j]);    a=(ax < cx ? ax : cx); 
       for (i=j+1;i<=n;i++) a[i][j] *= dum;    b=(ax > cx ? ax : cx); 
     }    x=w=v=bx; 
   }    fw=fv=fx=(*f)(x); 
   free_vector(vv,1,n);  /* Doesn't work */    for (iter=1;iter<=ITMAX;iter++) { 
 ;      xm=0.5*(a+b); 
 }      tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
       /*          if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
 void lubksb(double **a, int n, int *indx, double b[])      printf(".");fflush(stdout);
 {      fprintf(ficlog,".");fflush(ficlog);
   int i,ii=0,ip,j;  #ifdef DEBUG
   double sum;      printf("br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
        fprintf(ficlog,"br %d,x=%.10e xm=%.10e b=%.10e a=%.10e tol=%.10e tol1=%.10e tol2=%.10e x-xm=%.10e fx=%.12e fu=%.12e,fw=%.12e,ftemp=%.12e,ftol=%.12e\n",iter,x,xm,b,a,tol,tol1,tol2,(x-xm),fx,fu,fw,ftemp,ftol);
   for (i=1;i<=n;i++) {      /*          if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
     ip=indx[i];  #endif
     sum=b[ip];      if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
     b[ip]=b[i];        *xmin=x; 
     if (ii)        return fx; 
       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j];      } 
     else if (sum) ii=i;      ftemp=fu;
     b[i]=sum;      if (fabs(e) > tol1) { 
   }        r=(x-w)*(fx-fv); 
   for (i=n;i>=1;i--) {        q=(x-v)*(fx-fw); 
     sum=b[i];        p=(x-v)*q-(x-w)*r; 
     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j];        q=2.0*(q-r); 
     b[i]=sum/a[i][i];        if (q > 0.0) p = -p; 
   }        q=fabs(q); 
 }        etemp=e; 
         e=d; 
 /************ Frequencies ********************/        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
 void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx, int *Tvar, int **nbcode, int *ncodemax)          d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
 {  /* Some frequencies */        else { 
            d=p/q; 
   int i, m, jk, k1, i1, j1, bool, z1,z2,j;          u=x+d; 
   double ***freq; /* Frequencies */          if (u-a < tol2 || b-u < tol2) 
   double *pp;            d=SIGN(tol1,xm-x); 
   double pos;        } 
   FILE *ficresp;      } else { 
   char fileresp[FILENAMELENGTH];        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
       } 
   pp=vector(1,nlstate);      u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
       fu=(*f)(u); 
   strcpy(fileresp,"p");      if (fu <= fx) { 
   strcat(fileresp,fileres);        if (u >= x) a=x; else b=x; 
   if((ficresp=fopen(fileresp,"w"))==NULL) {        SHFT(v,w,x,u) 
     printf("Problem with prevalence resultfile: %s\n", fileresp);          SHFT(fv,fw,fx,fu) 
     exit(0);          } else { 
   }            if (u < x) a=u; else b=u; 
   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);            if (fu <= fw || w == x) { 
   j1=0;              v=w; 
               w=u; 
   j=cptcovn;              fv=fw; 
   if (cptcovn<1) {j=1;ncodemax[1]=1;}              fw=fu; 
             } else if (fu <= fv || v == x || v == w) { 
   for(k1=1; k1<=j;k1++){              v=u; 
    for(i1=1; i1<=ncodemax[k1];i1++){              fv=fu; 
        j1++;            } 
           } 
         for (i=-1; i<=nlstate+ndeath; i++)      } 
          for (jk=-1; jk<=nlstate+ndeath; jk++)      nrerror("Too many iterations in brent"); 
            for(m=agemin; m <= agemax+3; m++)    *xmin=x; 
              freq[i][jk][m]=0;    return fx; 
          } 
        for (i=1; i<=imx; i++) {  
          bool=1;  /****************** mnbrak ***********************/
          if  (cptcovn>0) {  
            for (z1=1; z1<=cptcovn; z1++)  void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
              if (covar[Tvar[z1]][i]!= nbcode[Tvar[z1]][codtab[j1][z1]]) bool=0;              double (*func)(double)) 
          }  { 
           if (bool==1) {    double ulim,u,r,q, dum;
            for(m=firstpass; m<=lastpass-1; m++){    double fu; 
              if(agev[m][i]==0) agev[m][i]=agemax+1;   
              if(agev[m][i]==1) agev[m][i]=agemax+2;    *fa=(*func)(*ax); 
              freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];    *fb=(*func)(*bx); 
              freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];    if (*fb > *fa) { 
            }      SHFT(dum,*ax,*bx,dum) 
          }        SHFT(dum,*fb,*fa,dum) 
        }        } 
         if  (cptcovn>0) {    *cx=(*bx)+GOLD*(*bx-*ax); 
          fprintf(ficresp, "\n#Variable");    *fc=(*func)(*cx); 
          for (z1=1; z1<=cptcovn; z1++) fprintf(ficresp, " V%d=%d",Tvar[z1],nbcode[Tvar[z1]][codtab[j1][z1]]);    while (*fb > *fc) { 
        }      r=(*bx-*ax)*(*fb-*fc); 
        fprintf(ficresp, "\n#");      q=(*bx-*cx)*(*fb-*fa); 
        for(i=1; i<=nlstate;i++)      u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
          fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);        (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
        fprintf(ficresp, "\n");      ulim=(*bx)+GLIMIT*(*cx-*bx); 
              if ((*bx-u)*(u-*cx) > 0.0) { 
   for(i=(int)agemin; i <= (int)agemax+3; i++){        fu=(*func)(u); 
     if(i==(int)agemax+3)      } else if ((*cx-u)*(u-ulim) > 0.0) { 
       printf("Total");        fu=(*func)(u); 
     else        if (fu < *fc) { 
       printf("Age %d", i);          SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
     for(jk=1; jk <=nlstate ; jk++){            SHFT(*fb,*fc,fu,(*func)(u)) 
       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)            } 
         pp[jk] += freq[jk][m][i];      } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
     }        u=ulim; 
     for(jk=1; jk <=nlstate ; jk++){        fu=(*func)(u); 
       for(m=-1, pos=0; m <=0 ; m++)      } else { 
         pos += freq[jk][m][i];        u=(*cx)+GOLD*(*cx-*bx); 
       if(pp[jk]>=1.e-10)        fu=(*func)(u); 
         printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);      } 
       else      SHFT(*ax,*bx,*cx,u) 
         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);        SHFT(*fa,*fb,*fc,fu) 
     }        } 
     for(jk=1; jk <=nlstate ; jk++){  } 
       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)  
         pp[jk] += freq[jk][m][i];  /*************** linmin ************************/
     }  
     for(jk=1,pos=0; jk <=nlstate ; jk++)  int ncom; 
       pos += pp[jk];  double *pcom,*xicom;
     for(jk=1; jk <=nlstate ; jk++){  double (*nrfunc)(double []); 
       if(pos>=1.e-5)   
         printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);  void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
       else  { 
         printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);    double brent(double ax, double bx, double cx, 
       if( i <= (int) agemax){                 double (*f)(double), double tol, double *xmin); 
         if(pos>=1.e-5)    double f1dim(double x); 
           fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);    void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
       else                double *fc, double (*func)(double)); 
           fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);    int j; 
       }    double xx,xmin,bx,ax; 
     }    double fx,fb,fa;
     for(jk=-1; jk <=nlstate+ndeath; jk++)   
       for(m=-1; m <=nlstate+ndeath; m++)    ncom=n; 
         if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);    pcom=vector(1,n); 
     if(i <= (int) agemax)    xicom=vector(1,n); 
       fprintf(ficresp,"\n");    nrfunc=func; 
     printf("\n");    for (j=1;j<=n;j++) { 
     }      pcom[j]=p[j]; 
     }      xicom[j]=xi[j]; 
  }    } 
      ax=0.0; 
   fclose(ficresp);    xx=1.0; 
   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);    mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
   free_vector(pp,1,nlstate);    *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
   #ifdef DEBUG
 }  /* End of Freq */    printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
     fprintf(ficlog,"retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
 /************* Waves Concatenation ***************/  #endif
     for (j=1;j<=n;j++) { 
 void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)      xi[j] *= xmin; 
 {      p[j] += xi[j]; 
   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.    } 
      Death is a valid wave (if date is known).    free_vector(xicom,1,n); 
      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i    free_vector(pcom,1,n); 
      dh[m][i] of 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.  
      */  char *asc_diff_time(long time_sec, char ascdiff[])
   {
   int i, mi, m;    long sec_left, days, hours, minutes;
   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;    days = (time_sec) / (60*60*24);
 float sum=0.;    sec_left = (time_sec) % (60*60*24);
     hours = (sec_left) / (60*60) ;
   for(i=1; i<=imx; i++){    sec_left = (sec_left) %(60*60);
     mi=0;    minutes = (sec_left) /60;
     m=firstpass;    sec_left = (sec_left) % (60);
     while(s[m][i] <= nlstate){    sprintf(ascdiff,"%ld day(s) %ld hour(s) %ld minute(s) %ld second(s)",days, hours, minutes, sec_left);  
       if(s[m][i]>=1)    return ascdiff;
         mw[++mi][i]=m;  }
       if(m >=lastpass)  
         break;  /*************** powell ************************/
       else  void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
         m++;              double (*func)(double [])) 
     }/* end while */  { 
     if (s[m][i] > nlstate){    void linmin(double p[], double xi[], int n, double *fret, 
       mi++;     /* Death is another wave */                double (*func)(double [])); 
       /* if(mi==0)  never been interviewed correctly before death */    int i,ibig,j; 
          /* Only death is a correct wave */    double del,t,*pt,*ptt,*xit;
       mw[mi][i]=m;    double fp,fptt;
     }    double *xits;
     int niterf, itmp;
     wav[i]=mi;  
     if(mi==0)    pt=vector(1,n); 
       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);    ptt=vector(1,n); 
   }    xit=vector(1,n); 
     xits=vector(1,n); 
   for(i=1; i<=imx; i++){    *fret=(*func)(p); 
     for(mi=1; mi<wav[i];mi++){    for (j=1;j<=n;j++) pt[j]=p[j]; 
       if (stepm <=0)    for (*iter=1;;++(*iter)) { 
         dh[mi][i]=1;      fp=(*fret); 
       else{      ibig=0; 
         if (s[mw[mi+1][i]][i] > nlstate) {      del=0.0; 
           j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12);      last_time=curr_time;
           if(j=0) j=1;  /* Survives at least one month after exam */      (void) gettimeofday(&curr_time,&tzp);
         }      printf("\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec);fflush(stdout);
         else{      fprintf(ficlog,"\nPowell iter=%d -2*LL=%.12f %ld sec. %ld sec.",*iter,*fret, curr_time.tv_sec-last_time.tv_sec, curr_time.tv_sec-start_time.tv_sec); fflush(ficlog);
           j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));  /*     fprintf(ficrespow,"%d %.12f %ld",*iter,*fret,curr_time.tv_sec-start_time.tv_sec); */
           /*printf("i=%d agevi+1=%lf agevi=%lf j=%d\n", i,agev[mw[mi+1][i]][i],agev[mw[mi][i]][i],j);*/     for (i=1;i<=n;i++) {
         printf(" %d %.12f",i, p[i]);
           k=k+1;        fprintf(ficlog," %d %.12lf",i, p[i]);
           if (j >= jmax) jmax=j;        fprintf(ficrespow," %.12lf", p[i]);
           else if (j <= jmin)jmin=j;      }
           sum=sum+j;      printf("\n");
         }      fprintf(ficlog,"\n");
         jk= j/stepm;      fprintf(ficrespow,"\n");fflush(ficrespow);
         jl= j -jk*stepm;      if(*iter <=3){
         ju= j -(jk+1)*stepm;        tm = *localtime(&curr_time.tv_sec);
         if(jl <= -ju)        strcpy(strcurr,asctime(&tm));
           dh[mi][i]=jk;  /*       asctime_r(&tm,strcurr); */
         else        forecast_time=curr_time; 
           dh[mi][i]=jk+1;        itmp = strlen(strcurr);
         if(dh[mi][i]==0)        if(strcurr[itmp-1]=='\n')  /* Windows outputs with a new line */
           dh[mi][i]=1; /* At least one step */          strcurr[itmp-1]='\0';
       }        printf("\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
     }        fprintf(ficlog,"\nConsidering the time needed for this last iteration #%d: %ld seconds,\n",*iter,curr_time.tv_sec-last_time.tv_sec);
   }        for(niterf=10;niterf<=30;niterf+=10){
   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);          forecast_time.tv_sec=curr_time.tv_sec+(niterf-*iter)*(curr_time.tv_sec-last_time.tv_sec);
 }          tmf = *localtime(&forecast_time.tv_sec);
 /*********** Tricode ****************************/  /*      asctime_r(&tmf,strfor); */
 void tricode(int *Tvar, int **nbcode, int imx)          strcpy(strfor,asctime(&tmf));
 {          itmp = strlen(strfor);
   int Ndum[80],ij, k, j, i;          if(strfor[itmp-1]=='\n')
   int cptcode=0;          strfor[itmp-1]='\0';
   for (k=0; k<79; k++) Ndum[k]=0;          printf("   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
   for (k=1; k<=7; k++) ncodemax[k]=0;          fprintf(ficlog,"   - if your program needs %d iterations to converge, convergence will be \n   reached in %s i.e.\n   on %s (current time is %s);\n",niterf, asc_diff_time(forecast_time.tv_sec-curr_time.tv_sec,tmpout),strfor,strcurr);
          }
   for (j=1; j<=cptcovn; j++) {      }
     for (i=1; i<=imx; i++) {      for (i=1;i<=n;i++) { 
       ij=(int)(covar[Tvar[j]][i]);        for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
       Ndum[ij]++;        fptt=(*fret); 
       if (ij > cptcode) cptcode=ij;  #ifdef DEBUG
     }        printf("fret=%lf \n",*fret);
     /*printf("cptcode=%d cptcovn=%d ",cptcode,cptcovn);*/        fprintf(ficlog,"fret=%lf \n",*fret);
     for (i=0; i<=cptcode; i++) {  #endif
       if(Ndum[i]!=0) ncodemax[j]++;        printf("%d",i);fflush(stdout);
     }        fprintf(ficlog,"%d",i);fflush(ficlog);
          linmin(p,xit,n,fret,func); 
     ij=1;        if (fabs(fptt-(*fret)) > del) { 
     for (i=1; i<=ncodemax[j]; i++) {          del=fabs(fptt-(*fret)); 
       for (k=0; k<=79; k++) {          ibig=i; 
         if (Ndum[k] != 0) {        } 
           nbcode[Tvar[j]][ij]=k;  #ifdef DEBUG
           ij++;        printf("%d %.12e",i,(*fret));
         }        fprintf(ficlog,"%d %.12e",i,(*fret));
         if (ij > ncodemax[j]) break;        for (j=1;j<=n;j++) {
       }            xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
     }          printf(" x(%d)=%.12e",j,xit[j]);
   }            fprintf(ficlog," x(%d)=%.12e",j,xit[j]);
         }
   }        for(j=1;j<=n;j++) {
           printf(" p=%.12e",p[j]);
 /*********** Health Expectancies ****************/          fprintf(ficlog," p=%.12e",p[j]);
         }
 void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij)        printf("\n");
 {        fprintf(ficlog,"\n");
   /* Health expectancies */  #endif
   int i, j, nhstepm, hstepm, h;      } 
   double age, agelim,hf;      if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
   double ***p3mat;  #ifdef DEBUG
          int k[2],l;
   fprintf(ficreseij,"# Health expectancies\n");        k[0]=1;
   fprintf(ficreseij,"# 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(ficreseij," %1d-%1d",i,j);        for (j=1;j<=n;j++) {
   fprintf(ficreseij,"\n");          printf(" %.12e",p[j]);
           fprintf(ficlog," %.12e",p[j]);
   hstepm=1*YEARM; /*  Every j years of age (in month) */        }
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        printf("\n");
         fprintf(ficlog,"\n");
   agelim=AGESUP;        for(l=0;l<=1;l++) {
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */          for (j=1;j<=n;j++) {
     /* nhstepm age range expressed in number of stepm */            ptt[j]=p[j]+(p[j]-pt[j])*k[l];
     nhstepm=(int) rint((agelim-age)*YEARM/stepm);            printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     /* Typically if 20 years = 20*12/6=40 stepm */            fprintf(ficlog,"l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
     if (stepm >= YEARM) hstepm=1;          }
     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */          printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          fprintf(ficlog,"func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
     /* Computed by stepm unit matrices, product of hstepm matrices, stored        }
        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */  #endif
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij);    
   
         free_vector(xit,1,n); 
     for(i=1; i<=nlstate;i++)        free_vector(xits,1,n); 
       for(j=1; j<=nlstate;j++)        free_vector(ptt,1,n); 
         for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){        free_vector(pt,1,n); 
           eij[i][j][(int)age] +=p3mat[i][j][h];        return; 
         }      } 
          if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
     hf=1;      for (j=1;j<=n;j++) { 
     if (stepm >= YEARM) hf=stepm/YEARM;        ptt[j]=2.0*p[j]-pt[j]; 
     fprintf(ficreseij,"%.0f",age );        xit[j]=p[j]-pt[j]; 
     for(i=1; i<=nlstate;i++)        pt[j]=p[j]; 
       for(j=1; j<=nlstate;j++){      } 
         fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);      fptt=(*func)(ptt); 
       }      if (fptt < fp) { 
     fprintf(ficreseij,"\n");        t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);        if (t < 0.0) { 
   }          linmin(p,xit,n,fret,func); 
 }          for (j=1;j<=n;j++) { 
             xi[j][ibig]=xi[j][n]; 
 /************ Variance ******************/            xi[j][n]=xit[j]; 
 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)          }
 {  #ifdef DEBUG
   /* Variance of health expectancies */          printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/          fprintf(ficlog,"Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
   double **newm;          for(j=1;j<=n;j++){
   double **dnewm,**doldm;            printf(" %.12e",xit[j]);
   int i, j, nhstepm, hstepm, h;            fprintf(ficlog," %.12e",xit[j]);
   int k, cptcode;          }
    double *xp;          printf("\n");
   double **gp, **gm;          fprintf(ficlog,"\n");
   double ***gradg, ***trgradg;  #endif
   double ***p3mat;        }
   double age,agelim;      } 
   int theta;    } 
   } 
    fprintf(ficresvij,"# Covariances of life expectancies\n");  
   fprintf(ficresvij,"# Age");  /**** Prevalence limit (stable or period prevalence)  ****************/
   for(i=1; i<=nlstate;i++)  
     for(j=1; j<=nlstate;j++)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)
       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);  {
   fprintf(ficresvij,"\n");    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
        matrix by transitions matrix until convergence is reached */
   xp=vector(1,npar);  
   dnewm=matrix(1,nlstate,1,npar);    int i, ii,j,k;
   doldm=matrix(1,nlstate,1,nlstate);    double min, max, maxmin, maxmax,sumnew=0.;
      /* double **matprod2(); */ /* test */
   hstepm=1*YEARM; /* Every year of age */    double **out, cov[NCOVMAX+1], **pmij();
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */    double **newm;
   agelim = AGESUP;    double agefin, delaymax=50 ; /* Max number of years to converge */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */  
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */    for (ii=1;ii<=nlstate+ndeath;ii++)
     if (stepm >= YEARM) hstepm=1;      for (j=1;j<=nlstate+ndeath;j++){
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */        oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);      }
     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);  
     gp=matrix(0,nhstepm,1,nlstate);     cov[1]=1.;
     gm=matrix(0,nhstepm,1,nlstate);   
    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
     for(theta=1; theta <=npar; theta++){    for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
       for(i=1; i<=npar; i++){ /* Computes gradient */      newm=savm;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);      /* Covariates have to be included here again */
       }      cov[2]=agefin;
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      for (k=1; k<=cptcovn;k++) {
       for(j=1; j<= nlstate; j++){        cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
         for(h=0; h<=nhstepm; h++){        /*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]]);*/
           for(i=1, gp[h][j]=0.;i<=nlstate;i++)      }
             gp[h][j] += prlim[i][i]*p3mat[i][j][h];      /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */
         }      /* 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]]]; */
          
       for(i=1; i<=npar; i++) /* Computes gradient */      /*printf("ij=%d cptcovprod=%d tvar=%d ", ij, cptcovprod, Tvar[1]);*/
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      /*printf("ij=%d cov[3]=%lf cov[4]=%lf \n",ij, cov[3],cov[4]);*/
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);        /*printf("ij=%d cov[3]=%lf \n",ij, cov[3]);*/
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
       for(j=1; j<= nlstate; j++){      /* out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /\* Bug Valgrind *\/ */
         for(h=0; h<=nhstepm; h++){      out=matprod2(newm, pmij(pmmij,cov,ncovmodel,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm); /* Bug Valgrind */
           for(i=1, gm[h][j]=0.;i<=nlstate;i++)      
             gm[h][j] += prlim[i][i]*p3mat[i][j][h];      savm=oldm;
         }      oldm=newm;
       }      maxmax=0.;
       for(j=1; j<= nlstate; j++)      for(j=1;j<=nlstate;j++){
         for(h=0; h<=nhstepm; h++){        min=1.;
           gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];        max=0.;
         }        for(i=1; i<=nlstate; i++) {
     } /* End theta */          sumnew=0;
           for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);          prlim[i][j]= newm[i][j]/(1-sumnew);
           /*printf(" prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d \n", i, j, i, j, prlim[i][j],(int)agefin);*/
     for(h=0; h<=nhstepm; h++)          max=FMAX(max,prlim[i][j]);
       for(j=1; j<=nlstate;j++)          min=FMIN(min,prlim[i][j]);
         for(theta=1; theta <=npar; theta++)        }
           trgradg[h][j][theta]=gradg[h][theta][j];        maxmin=max-min;
         maxmax=FMAX(maxmax,maxmin);
     for(i=1;i<=nlstate;i++)      }
       for(j=1;j<=nlstate;j++)      if(maxmax < ftolpl){
         vareij[i][j][(int)age] =0.;        return prlim;
     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++)  /*************** transition probabilities ***************/ 
           for(j=1;j<=nlstate;j++)  
             vareij[i][j][(int)age] += doldm[i][j];  double **pmij(double **ps, double *cov, int ncovmodel, double *x, int nlstate )
       }  {
     }    /* According to parameters values stored in x and the covariate's values stored in cov,
     h=1;       computes the probability to be observed in state j being in state i by appying the
     if (stepm >= YEARM) h=stepm/YEARM;       model to the ncovmodel covariates (including constant and age).
     fprintf(ficresvij,"%.0f ",age );       lnpijopii=ln(pij/pii)= aij+bij*age+cij*v1+dij*v2+... = sum_nc=1^ncovmodel xij(nc)*cov[nc]
     for(i=1; i<=nlstate;i++)       and, according on how parameters are entered, the position of the coefficient xij(nc) of the
       for(j=1; j<=nlstate;j++){       ncth covariate in the global vector x is given by the formula:
         fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);       j<i nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel
       }       j>=i nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel
     fprintf(ficresvij,"\n");       Computes ln(pij/pii) (lnpijopii), deduces pij/pii by exponentiation,
     free_matrix(gp,0,nhstepm,1,nlstate);       sums on j different of i to get 1-pii/pii, deduces pii, and then all pij.
     free_matrix(gm,0,nhstepm,1,nlstate);       Outputs ps[i][j] the probability to be observed in j being in j according to
     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);       the values of the covariates cov[nc] and corresponding parameter values x[nc+shiftij]
     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);    */
     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);    double s1, lnpijopii;
   } /* End age */    /*double t34;*/
      int i,j,j1, nc, ii, jj;
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);      for(i=1; i<= nlstate; i++){
   free_matrix(dnewm,1,nlstate,1,nlstate);        for(j=1; j<i;j++){
           for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
 }            /*lnpijopii += param[i][j][nc]*cov[nc];*/
             lnpijopii += x[nc+((i-1)*(nlstate+ndeath-1)+j-1)*ncovmodel]*cov[nc];
 /************ Variance of prevlim ******************/  /*       printf("Int j<i s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
 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)          }
 {          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   /* Variance of prevalence limit */  /*      printf("s1=%.17e, lnpijopii=%.17e\n",s1,lnpijopii); */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/        }
   double **newm;        for(j=i+1; j<=nlstate+ndeath;j++){
   double **dnewm,**doldm;          for (nc=1, lnpijopii=0.;nc <=ncovmodel; nc++){
   int i, j, nhstepm, hstepm;            /*lnpijopii += x[(i-1)*nlstate*ncovmodel+(j-2)*ncovmodel+nc+(i-1)*(ndeath-1)*ncovmodel]*cov[nc];*/
   int k, cptcode;            lnpijopii += x[nc + ((i-1)*(nlstate+ndeath-1)+(j-2))*ncovmodel]*cov[nc];
   double *xp;  /*        printf("Int j>i s1=%.17e, lnpijopii=%.17e %lx %lx\n",s1,lnpijopii,s1,lnpijopii); */
   double *gp, *gm;          }
   double **gradg, **trgradg;          ps[i][j]=lnpijopii; /* In fact ln(pij/pii) */
   double age,agelim;        }
   int theta;      }
          
   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");      for(i=1; i<= nlstate; i++){
   fprintf(ficresvpl,"# Age");        s1=0;
   for(i=1; i<=nlstate;i++)        for(j=1; j<i; j++){
       fprintf(ficresvpl," %1d-%1d",i,i);          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   fprintf(ficresvpl,"\n");          /*printf("debug1 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
         }
   xp=vector(1,npar);        for(j=i+1; j<=nlstate+ndeath; j++){
   dnewm=matrix(1,nlstate,1,npar);          s1+=exp(ps[i][j]); /* In fact sums pij/pii */
   doldm=matrix(1,nlstate,1,nlstate);          /*printf("debug2 %d %d ps=%lf exp(ps)=%lf s1+=%lf\n",i,j,ps[i][j],exp(ps[i][j]),s1); */
          }
   hstepm=1*YEARM; /* Every year of age */        /* s1= sum_{j<>i} pij/pii=(1-pii)/pii and thus pii is known from s1 */
   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */        ps[i][i]=1./(s1+1.);
   agelim = AGESUP;        /* Computing other pijs */
   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */        for(j=1; j<i; j++)
     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          ps[i][j]= exp(ps[i][j])*ps[i][i];
     if (stepm >= YEARM) hstepm=1;        for(j=i+1; j<=nlstate+ndeath; j++)
     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */          ps[i][j]= exp(ps[i][j])*ps[i][i];
     gradg=matrix(1,npar,1,nlstate);        /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
     gp=vector(1,nlstate);      } /* end i */
     gm=vector(1,nlstate);      
       for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
     for(theta=1; theta <=npar; theta++){        for(jj=1; jj<= nlstate+ndeath; jj++){
       for(i=1; i<=npar; i++){ /* Computes gradient */          ps[ii][jj]=0;
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          ps[ii][ii]=1;
       }        }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      }
       for(i=1;i<=nlstate;i++)      
         gp[i] = prlim[i][i];      
          /* for(ii=1; ii<= nlstate+ndeath; ii++){ */
       for(i=1; i<=npar; i++) /* Computes gradient */      /*   for(jj=1; jj<= nlstate+ndeath; jj++){ */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);      /*  printf(" pmij  ps[%d][%d]=%lf ",ii,jj,ps[ii][jj]); */
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);      /*   } */
       for(i=1;i<=nlstate;i++)      /*   printf("\n "); */
         gm[i] = prlim[i][i];      /* } */
       /* printf("\n ");printf("%lf ",cov[2]);*/
       for(i=1;i<=nlstate;i++)      /*
         gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];        for(i=1; i<= npar; i++) printf("%f ",x[i]);
     } /* End theta */        goto end;*/
       return ps;
     trgradg =matrix(1,nlstate,1,npar);  }
   
     for(j=1; j<=nlstate;j++)  /**************** Product of 2 matrices ******************/
       for(theta=1; theta <=npar; theta++)  
         trgradg[j][theta]=gradg[theta][j];  double **matprod2(double **out, double **in,int nrl, int nrh, int ncl, int nch, int ncolol, int ncoloh, double **b)
   {
     for(i=1;i<=nlstate;i++)    /* Computes the matrix product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
       varpl[i][(int)age] =0.;       b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);    /* in, b, out are matrice of pointers which should have been initialized 
     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);       before: only the contents of out is modified. The function returns
     for(i=1;i<=nlstate;i++)       a pointer to pointers identical to out */
       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */    int i, j, k;
     for(i=nrl; i<= nrh; i++)
     fprintf(ficresvpl,"%.0f ",age );      for(k=ncolol; k<=ncoloh; k++){
     for(i=1; i<=nlstate;i++)        out[i][k]=0.;
       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));        for(j=ncl; j<=nch; j++)
     fprintf(ficresvpl,"\n");          out[i][k] +=in[i][j]*b[j][k];
     free_vector(gp,1,nlstate);      }
     free_vector(gm,1,nlstate);    return out;
     free_matrix(gradg,1,npar,1,nlstate);  }
     free_matrix(trgradg,1,nlstate,1,npar);  
   } /* End age */  
   /************* Higher Matrix Product ***************/
   free_vector(xp,1,npar);  
   free_matrix(doldm,1,nlstate,1,npar);  double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm, int ij )
   free_matrix(dnewm,1,nlstate,1,nlstate);  {
     /* Computes the transition matrix starting at age 'age' over 
 }       'nhstepm*hstepm*stepm' months (i.e. until
        age (in years)  age+nhstepm*hstepm*stepm/12) by multiplying 
        nhstepm*hstepm matrices. 
        Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
 /***********************************************/       (typically every 2 years instead of every month which is too big 
 /**************** Main Program *****************/       for the memory).
 /***********************************************/       Model is determined by parameters x and covariates have to be 
        included manually here. 
 /*int main(int argc, char *argv[])*/  
 int main()       */
 {  
     int i, j, d, h, k;
   int i,j, k, n=MAXN,iter,m,size,cptcode, aaa, cptcod;    double **out, cov[NCOVMAX+1];
   double agedeb, agefin,hf;    double **newm;
   double agemin=1.e20, agemax=-1.e20;  
     /* Hstepm could be zero and should return the unit matrix */
   double fret;    for (i=1;i<=nlstate+ndeath;i++)
   double **xi,tmp,delta;      for (j=1;j<=nlstate+ndeath;j++){
         oldm[i][j]=(i==j ? 1.0 : 0.0);
   double dum; /* Dummy variable */        po[i][j][0]=(i==j ? 1.0 : 0.0);
   double ***p3mat;      }
   int *indx;    /* Even if hstepm = 1, at least one multiplication by the unit matrix */
   char line[MAXLINE], linepar[MAXLINE];    for(h=1; h <=nhstepm; h++){
   char title[MAXLINE];      for(d=1; d <=hstepm; d++){
   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];        newm=savm;
   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];        /* Covariates have to be included here again */
   char filerest[FILENAMELENGTH];        cov[1]=1.;
   char fileregp[FILENAMELENGTH];        cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
   char path[80],pathc[80],pathcd[80],pathtot[80],model[20];        for (k=1; k<=cptcovn;k++) 
   int firstobs=1, lastobs=10;          cov[2+k]=nbcode[Tvar[k]][codtab[ij][Tvar[k]]];
   int sdeb, sfin; /* Status at beginning and end */        for (k=1; k<=cptcovage;k++)
   int c,  h , cpt,l;          cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2];
   int ju,jl, mi;        for (k=1; k<=cptcovprod;k++) /* Useless because included in cptcovn */
   int i1,j1, k1,jk,aa,bb, stepsize;          cov[2+Tprod[k]]=nbcode[Tvard[k][1]][codtab[ij][Tvard[k][1]]]*nbcode[Tvard[k][2]][codtab[ij][Tvard[k][2]]];
   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;  
    
   int hstepm, nhstepm;        /*printf("hxi cptcov=%d cptcode=%d\n",cptcov,cptcode);*/
   double bage, fage, age, agelim, agebase;        /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
   double ftolpl=FTOL;        out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
   double **prlim;                     pmij(pmmij,cov,ncovmodel,x,nlstate));
   double *severity;        savm=oldm;
   double ***param; /* Matrix of parameters */        oldm=newm;
   double  *p;      }
   double **matcov; /* Matrix of covariance */      for(i=1; i<=nlstate+ndeath; i++)
   double ***delti3; /* Scale */        for(j=1;j<=nlstate+ndeath;j++) {
   double *delti; /* Scale */          po[i][j][h]=newm[i][j];
   double ***eij, ***vareij;          /*if(h==nhstepm) printf("po[%d][%d][%d]=%f ",i,j,h,po[i][j][h]);*/
   double **varpl; /* Variances of prevalence limits by age */        }
   double *epj, vepp;      /*printf("h=%d ",h);*/
   char version[80]="Imach version 62c, May 1999, INED-EUROREVES ";    } /* end h */
   char *alph[]={"a","a","b","c","d","e"}, str[4];  /*     printf("\n H=%d \n",h); */
   char z[1]="c", occ;    return po;
 #include <sys/time.h>  }
 #include <time.h>  
   char stra[80], strb[80], strc[80], strd[80],stre[80],modelsav[80];  
   /* long total_usecs;  /*************** log-likelihood *************/
   struct timeval start_time, end_time;  double func( double *x)
    {
   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */    int i, ii, j, k, mi, d, kk;
     double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
     double **out;
   printf("\nIMACH, Version 0.63");    double sw; /* Sum of weights */
   printf("\nEnter the parameter file name: ");    double lli; /* Individual log likelihood */
     int s1, s2;
 #ifdef windows    double bbh, survp;
   scanf("%s",pathtot);    long ipmx;
   getcwd(pathcd, size);    /*extern weight */
   cutv(path,optionfile,pathtot,'\\');    /* We are differentiating ll according to initial status */
   chdir(path);    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
   replace(pathc,path);    /*for(i=1;i<imx;i++) 
 #endif      printf(" %d\n",s[4][i]);
 #ifdef unix    */
   scanf("%s",optionfile);    cov[1]=1.;
 #endif  
     for(k=1; k<=nlstate; k++) ll[k]=0.;
 /*-------- arguments in the command line --------*/  
     if(mle==1){
   strcpy(fileres,"r");      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
   strcat(fileres, optionfile);        /* 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[]
   /*---------arguments file --------*/           Then computes with function pmij which return a matrix p[i][j] giving the elementary probability
            to be observed in j being in i according to the model.
   if((ficpar=fopen(optionfile,"r"))==NULL)    {         */
     printf("Problem with optionfile %s\n",optionfile);        for (k=1; k<=cptcovn;k++){ /* Simple and product covariates without age* products */
     goto end;          cov[2+k]=covar[Tvar[k]][i];
   }        }
         /* In model V2+V1*V4+age*V3+V3*V2 Tvar[1] is V2, Tvar[2=V1*V4] 
   strcpy(filereso,"o");           is 6, Tvar[3=age*V3] should not be computed because of age Tvar[4=V3*V2] 
   strcat(filereso,fileres);           has been calculated etc */
   if((ficparo=fopen(filereso,"w"))==NULL) {        for(mi=1; mi<= wav[i]-1; mi++){
     printf("Problem with Output resultfile: %s\n", filereso);goto end;          for (ii=1;ii<=nlstate+ndeath;ii++)
   }            for (j=1;j<=nlstate+ndeath;j++){
               oldm[ii][j]=(ii==j ? 1.0 : 0.0);
   /* Reads comments: lines beginning with '#' */              savm[ii][j]=(ii==j ? 1.0 : 0.0);
   while((c=getc(ficpar))=='#' && c!= EOF){            }
     ungetc(c,ficpar);          for(d=0; d<dh[mi][i]; d++){
     fgets(line, MAXLINE, ficpar);            newm=savm;
     puts(line);            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     fputs(line,ficparo);            for (kk=1; kk<=cptcovage;kk++) {
   }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2]; /* Tage[kk] gives the data-covariate associated with age */
   ungetc(c,ficpar);            }
             out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   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);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
   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);            savm=oldm;
   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);            oldm=newm;
           } /* end mult */
   covar=matrix(1,NCOVMAX,1,n);            
   if (strlen(model)<=1) cptcovn=0;          /*lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/ /* Original formula */
   else {          /* But now since version 0.9 we anticipate for bias at large stepm.
     j=0;           * If stepm is larger than one month (smallest stepm) and if the exact delay 
     j=nbocc(model,'+');           * (in months) between two waves is not a multiple of stepm, we rounded to 
     cptcovn=j+1;           * the nearest (and in case of equal distance, to the lowest) interval but now
   }           * we keep into memory the bias bh[mi][i] and also the previous matrix product
            * (i.e to dh[mi][i]-1) saved in 'savm'. Then we inter(extra)polate the
   ncovmodel=2+cptcovn;           * probability in order to take into account the bias as a fraction of the way
   nvar=ncovmodel-1; /* Suppressing age as a basic covariate */           * from savm to out if bh is negative or even beyond if bh is positive. bh varies
             * -stepm/2 to stepm/2 .
   /* Read guess parameters */           * For stepm=1 the results are the same as for previous versions of Imach.
   /* Reads comments: lines beginning with '#' */           * For stepm > 1 the results are less biased than in previous versions. 
   while((c=getc(ficpar))=='#' && c!= EOF){           */
     ungetc(c,ficpar);          s1=s[mw[mi][i]][i];
     fgets(line, MAXLINE, ficpar);          s2=s[mw[mi+1][i]][i];
     puts(line);          bbh=(double)bh[mi][i]/(double)stepm; 
     fputs(line,ficparo);          /* bias bh is positive if real duration
   }           * is higher than the multiple of stepm and negative otherwise.
   ungetc(c,ficpar);           */
            /* lli= (savm[s1][s2]>1.e-8 ?(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]):log((1.+bbh)*out[s1][s2]));*/
   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);          if( s2 > nlstate){ 
     for(i=1; i <=nlstate; i++)            /* i.e. if s2 is a death state and if the date of death is known 
     for(j=1; j <=nlstate+ndeath-1; j++){               then the contribution to the likelihood is the probability to 
       fscanf(ficpar,"%1d%1d",&i1,&j1);               die between last step unit time and current  step unit time, 
       fprintf(ficparo,"%1d%1d",i1,j1);               which is also equal to probability to die before dh 
       printf("%1d%1d",i,j);               minus probability to die before dh-stepm . 
       for(k=1; k<=ncovmodel;k++){               In version up to 0.92 likelihood was computed
         fscanf(ficpar," %lf",&param[i][j][k]);          as if date of death was unknown. Death was treated as any other
         printf(" %lf",param[i][j][k]);          health state: the date of the interview describes the actual state
         fprintf(ficparo," %lf",param[i][j][k]);          and not the date of a change in health state. The former idea was
       }          to consider that at each interview the state was recorded
       fscanf(ficpar,"\n");          (healthy, disable or death) and IMaCh was corrected; but when we
       printf("\n");          introduced the exact date of death then we should have modified
       fprintf(ficparo,"\n");          the contribution of an exact death to the likelihood. This new
     }          contribution is smaller and very dependent of the step unit
            stepm. It is no more the probability to die between last interview
   npar= (nlstate+ndeath-1)*nlstate*ncovmodel;          and month of death but the probability to survive from last
   p=param[1][1];          interview up to one month before death multiplied by the
            probability to die within a month. Thanks to Chris
   /* Reads comments: lines beginning with '#' */          Jackson for correcting this bug.  Former versions increased
   while((c=getc(ficpar))=='#' && c!= EOF){          mortality artificially. The bad side is that we add another loop
     ungetc(c,ficpar);          which slows down the processing. The difference can be up to 10%
     fgets(line, MAXLINE, ficpar);          lower mortality.
     puts(line);            */
     fputs(line,ficparo);            lli=log(out[s1][s2] - savm[s1][s2]);
   }  
   ungetc(c,ficpar);  
           } else if  (s2==-2) {
   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);            for (j=1,survp=0. ; j<=nlstate; j++) 
   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
   for(i=1; i <=nlstate; i++){            /*survp += out[s1][j]; */
     for(j=1; j <=nlstate+ndeath-1; j++){            lli= log(survp);
       fscanf(ficpar,"%1d%1d",&i1,&j1);          }
       printf("%1d%1d",i,j);          
       fprintf(ficparo,"%1d%1d",i1,j1);          else if  (s2==-4) { 
       for(k=1; k<=ncovmodel;k++){            for (j=3,survp=0. ; j<=nlstate; j++)  
         fscanf(ficpar,"%le",&delti3[i][j][k]);              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
         printf(" %le",delti3[i][j][k]);            lli= log(survp); 
         fprintf(ficparo," %le",delti3[i][j][k]);          } 
       }  
       fscanf(ficpar,"\n");          else if  (s2==-5) { 
       printf("\n");            for (j=1,survp=0. ; j<=2; j++)  
       fprintf(ficparo,"\n");              survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     }            lli= log(survp); 
   }          } 
   delti=delti3[1][1];          
            else{
   /* Reads comments: lines beginning with '#' */            lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
   while((c=getc(ficpar))=='#' && c!= EOF){            /*  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 */
     ungetc(c,ficpar);          } 
     fgets(line, MAXLINE, ficpar);          /*lli=(1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]);*/
     puts(line);          /*if(lli ==000.0)*/
     fputs(line,ficparo);          /*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); */
   }          ipmx +=1;
   ungetc(c,ficpar);          sw += weight[i];
            ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
   matcov=matrix(1,npar,1,npar);        } /* end of wave */
   for(i=1; i <=npar; i++){      } /* end of individual */
     fscanf(ficpar,"%s",&str);    }  else if(mle==2){
     printf("%s",str);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     fprintf(ficparo,"%s",str);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     for(j=1; j <=i; j++){        for(mi=1; mi<= wav[i]-1; mi++){
       fscanf(ficpar," %le",&matcov[i][j]);          for (ii=1;ii<=nlstate+ndeath;ii++)
       printf(" %.5le",matcov[i][j]);            for (j=1;j<=nlstate+ndeath;j++){
       fprintf(ficparo," %.5le",matcov[i][j]);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     }              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     fscanf(ficpar,"\n");            }
     printf("\n");          for(d=0; d<=dh[mi][i]; d++){
     fprintf(ficparo,"\n");            newm=savm;
   }            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
   for(i=1; i <=npar; i++)            for (kk=1; kk<=cptcovage;kk++) {
     for(j=i+1;j<=npar;j++)              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       matcov[i][j]=matcov[j][i];            }
                out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
   printf("\n");                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
             savm=oldm;
             oldm=newm;
    if(mle==1){          } /* end mult */
     /*-------- data file ----------*/        
     if((ficres =fopen(fileres,"w"))==NULL) {          s1=s[mw[mi][i]][i];
       printf("Problem with resultfile: %s\n", fileres);goto end;          s2=s[mw[mi+1][i]][i];
     }          bbh=(double)bh[mi][i]/(double)stepm; 
     fprintf(ficres,"#%s\n",version);          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;
     if((fic=fopen(datafile,"r"))==NULL)    {          sw += weight[i];
       printf("Problem with datafile: %s\n", datafile);goto end;          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     }        } /* end of wave */
       } /* end of individual */
     n= lastobs;    }  else if(mle==3){  /* exponential inter-extrapolation */
     severity = vector(1,maxwav);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
     outcome=imatrix(1,maxwav+1,1,n);        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
     num=ivector(1,n);        for(mi=1; mi<= wav[i]-1; mi++){
     moisnais=vector(1,n);          for (ii=1;ii<=nlstate+ndeath;ii++)
     annais=vector(1,n);            for (j=1;j<=nlstate+ndeath;j++){
     moisdc=vector(1,n);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
     andc=vector(1,n);              savm[ii][j]=(ii==j ? 1.0 : 0.0);
     agedc=vector(1,n);            }
     cod=ivector(1,n);          for(d=0; d<dh[mi][i]; d++){
     weight=vector(1,n);            newm=savm;
     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     mint=matrix(1,maxwav,1,n);            for (kk=1; kk<=cptcovage;kk++) {
     anint=matrix(1,maxwav,1,n);              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
     s=imatrix(1,maxwav+1,1,n);            }
     adl=imatrix(1,maxwav+1,1,n);                out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
     tab=ivector(1,NCOVMAX);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     ncodemax=ivector(1,NCOVMAX);            savm=oldm;
             oldm=newm;
     i=1;          } /* end mult */
     while (fgets(line, MAXLINE, fic) != NULL)    {        
       if ((i >= firstobs) && (i <=lastobs)) {          s1=s[mw[mi][i]][i];
                  s2=s[mw[mi+1][i]][i];
         for (j=maxwav;j>=1;j--){          bbh=(double)bh[mi][i]/(double)stepm; 
           cutv(stra, strb,line,' '); s[j][i]=atoi(strb);          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 */
           strcpy(line,stra);          ipmx +=1;
           cutv(stra, strb,line,'/'); anint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          sw += weight[i];
           cutv(stra, strb,line,' '); mint[j][i]=(double)(atoi(strb)); strcpy(line,stra);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
         }        } /* end of wave */
              } /* end of individual */
         cutv(stra, strb,line,'/'); andc[i]=(double)(atoi(strb)); strcpy(line,stra);    }else if (mle==4){  /* ml=4 no inter-extrapolation */
         cutv(stra, strb,line,' '); moisdc[i]=(double)(atoi(strb)); strcpy(line,stra);      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         cutv(stra, strb,line,'/'); annais[i]=(double)(atoi(strb)); strcpy(line,stra);        for(mi=1; mi<= wav[i]-1; mi++){
         cutv(stra, strb,line,' '); moisnais[i]=(double)(atoi(strb)); strcpy(line,stra);          for (ii=1;ii<=nlstate+ndeath;ii++)
             for (j=1;j<=nlstate+ndeath;j++){
         cutv(stra, strb,line,' '); weight[i]=(double)(atoi(strb)); strcpy(line,stra);              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
         for (j=ncov;j>=1;j--){              savm[ii][j]=(ii==j ? 1.0 : 0.0);
           cutv(stra, strb,line,' '); covar[j][i]=(double)(atoi(strb)); strcpy(line,stra);            }
         }          for(d=0; d<dh[mi][i]; d++){
         num[i]=atol(stra);            newm=savm;
             cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
         /* printf("%d %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]), (weight[i]), (moisnais[i]), (annais[i]), (moisdc[i]), (andc[i]), (mint[1][i]), (anint[1][i]), (s[1][i]),  (mint[2][i]), (anint[2][i]), (s[2][i]),  (mint[3][i]), (anint[3][i]), (s[3][i]),  (mint[4][i]), (anint[4][i]), (s[4][i]));*/            for (kk=1; kk<=cptcovage;kk++) {
               cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         /*printf("%d %.lf %.lf %.lf %.lf %.lf %.lf/%.lf %.lf/%.lf %.lf/%.lf %d %.lf/%.lf %d\n",num[i],(covar[1][i]), (covar[2][i]),(covar[3][i]), (covar[4][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]));*/            }
           
         i=i+1;            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       }                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     }            savm=oldm;
     /*scanf("%d",i);*/            oldm=newm;
           } /* end mult */
   imx=i-1; /* Number of individuals */        
            s1=s[mw[mi][i]][i];
   /* Calculation of the number of parameter from char model*/          s2=s[mw[mi+1][i]][i];
   Tvar=ivector(1,8);              if( s2 > nlstate){ 
                lli=log(out[s1][s2] - savm[s1][s2]);
   if (strlen(model) >1){          }else{
     j=0;            lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
     j=nbocc(model,'+');          }
     cptcovn=j+1;          ipmx +=1;
            sw += weight[i];
     strcpy(modelsav,model);          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     if (j==0) {  /*      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]); */
       cutv(stra,strb,modelsav,'V'); Tvar[1]=atoi(strb);        } /* end of wave */
     }      } /* end of individual */
     else {    }else{  /* ml=5 no inter-extrapolation no jackson =0.8a */
       for(i=j; i>=1;i--){      for (i=1,ipmx=0, sw=0.; i<=imx; i++){
         cutv(stra,strb,modelsav,'+');        for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
         if (strchr(strb,'*')) {        for(mi=1; mi<= wav[i]-1; mi++){
           cutv(strd,strc,strb,'*');          for (ii=1;ii<=nlstate+ndeath;ii++)
           cutv(strb,stre,strc,'V');Tvar[i+1]=ncov+1;            for (j=1;j<=nlstate+ndeath;j++){
           cutv(strb,strc,strd,'V');              oldm[ii][j]=(ii==j ? 1.0 : 0.0);
           for (k=1; k<=lastobs;k++)              savm[ii][j]=(ii==j ? 1.0 : 0.0);
             covar[ncov+1][k]=covar[atoi(stre)][k]*covar[atoi(strc)][k];            }
         }          for(d=0; d<dh[mi][i]; d++){
         else {            newm=savm;
           cutv(strd,strc,strb,'V');            cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
           Tvar[i+1]=atoi(strc);            for (kk=1; kk<=cptcovage;kk++) {
         }              cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
         strcpy(modelsav,stra);              }
       }          
       /*cutv(strd,strc,stra,'V');*/            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
       Tvar[1]=atoi(strc);                         1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
     }            savm=oldm;
   }            oldm=newm;
   /*printf("tvar=%d ",Tvar[1]);*/          } /* end mult */
   /*scanf("%d ",i);*/        
     fclose(fic);          s1=s[mw[mi][i]][i];
           s2=s[mw[mi+1][i]][i];
     if (weightopt != 1) { /* Maximisation without weights*/          lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* Original formula */
       for(i=1;i<=n;i++) weight[i]=1.0;          ipmx +=1;
     }          sw += weight[i];
     /*-calculation of age at interview from date of interview and age at death -*/          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
     agev=matrix(1,maxwav,1,imx);          /*printf("i=%6d s1=%1d s2=%1d mi=%1d mw=%1d dh=%3d prob=%10.6f w=%6.4f out=%10.6f sav=%10.6f\n",i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],out[s1][s2],savm[s1][s2]);*/
            } /* end of wave */
     for (i=1; i<=imx; i++)  {      } /* end of individual */
       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);    } /* End of if */
       for(m=1; (m<= maxwav); m++){    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
         if (mint[m][i]==99 || anint[m][i]==9999) s[m][i]=-1;      /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
         if(s[m][i] >0){    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
           if (s[m][i] == nlstate+1) {    return -l;
             if(agedc[i]>0)  }
               if(moisdc[i]!=99 && andc[i]!=9999)  
               agev[m][i]=agedc[i];  /*************** log-likelihood *************/
             else{  double funcone( double *x)
               printf("Warning negative age at death: %d line:%d\n",num[i],i);  {
               agev[m][i]=-1;    /* Same as likeli but slower because of a lot of printf and if */
             }    int i, ii, j, k, mi, d, kk;
           }    double l, ll[NLSTATEMAX+1], cov[NCOVMAX+1];
           else if(s[m][i] !=9){ /* Should no more exist */    double **out;
             agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);    double lli; /* Individual log likelihood */
             if(mint[m][i]==99 || anint[m][i]==9999){    double llt;
               agev[m][i]=1;    int s1, s2;
               /* printf("i=%d m=%d agev=%lf \n",i,m, agev[m][i]);    */    double bbh, survp;
             }    /*extern weight */
             else if(agev[m][i] <agemin){    /* We are differentiating ll according to initial status */
               agemin=agev[m][i];    /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
               /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/    /*for(i=1;i<imx;i++) 
             }      printf(" %d\n",s[4][i]);
             else if(agev[m][i] >agemax){    */
               agemax=agev[m][i];    cov[1]=1.;
              /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/  
             }    for(k=1; k<=nlstate; k++) ll[k]=0.;
             /*agev[m][i]=anint[m][i]-annais[i];*/  
             /*   agev[m][i] = age[i]+2*m;*/    for (i=1,ipmx=0, sw=0.; i<=imx; i++){
           }      for (k=1; k<=cptcovn;k++) cov[2+k]=covar[Tvar[k]][i];
           else { /* =9 */      for(mi=1; mi<= wav[i]-1; mi++){
             agev[m][i]=1;        for (ii=1;ii<=nlstate+ndeath;ii++)
             s[m][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);
         else /*= 0 Unknown */          }
           agev[m][i]=1;        for(d=0; d<dh[mi][i]; d++){
       }          newm=savm;
              cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
     }          for (kk=1; kk<=cptcovage;kk++) {
     for (i=1; i<=imx; i++)  {            cov[Tage[kk]+2]=covar[Tvar[Tage[kk]]][i]*cov[2];
       for(m=1; (m<= maxwav); m++){          }
         if (s[m][i] > (nlstate+ndeath)) {          /* savm=pmij(pmmij,cov,ncovmodel,x,nlstate); */
           printf("Error: Wrong value in nlstate or ndeath\n");            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
           goto end;                       1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate));
         }          /* out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath, */
       }          /*           1,nlstate+ndeath,pmij(pmmij,cov,ncovmodel,x,nlstate)); */
     }          savm=oldm;
           oldm=newm;
 printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);        } /* end mult */
         
     free_vector(severity,1,maxwav);        s1=s[mw[mi][i]][i];
     free_imatrix(outcome,1,maxwav+1,1,n);        s2=s[mw[mi+1][i]][i];
     free_vector(moisnais,1,n);        bbh=(double)bh[mi][i]/(double)stepm; 
     free_vector(annais,1,n);        /* bias is positive if real duration
     free_matrix(mint,1,maxwav,1,n);         * is higher than the multiple of stepm and negative otherwise.
     free_matrix(anint,1,maxwav,1,n);         */
     free_vector(moisdc,1,n);        if( s2 > nlstate && (mle <5) ){  /* Jackson */
     free_vector(andc,1,n);          lli=log(out[s1][s2] - savm[s1][s2]);
         } else if  (s2==-2) {
              for (j=1,survp=0. ; j<=nlstate; j++) 
     wav=ivector(1,imx);            survp += (1.+bbh)*out[s1][j]- bbh*savm[s1][j];
     dh=imatrix(1,lastpass-firstpass+1,1,imx);          lli= log(survp);
     mw=imatrix(1,lastpass-firstpass+1,1,imx);        }else if (mle==1){
              lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
     /* Concatenates waves */        } else if(mle==2){
       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);          lli= (savm[s1][s2]>(double)1.e-8 ?log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]):log((1.+bbh)*out[s1][s2])); /* linear interpolation */
         } else if(mle==3){  /* exponential inter-extrapolation */
           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 */
 Tcode=ivector(1,100);        } else if (mle==4){  /* mle=4 no inter-extrapolation */
    nbcode=imatrix(1,nvar,1,8);            lli=log(out[s1][s2]); /* Original formula */
    ncodemax[1]=1;        } else{  /* mle=0 back to 1 */
    if (cptcovn > 0) tricode(Tvar,nbcode,imx);          lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
            /*lli=log(out[s1][s2]); */ /* Original formula */
    codtab=imatrix(1,100,1,10);        } /* End of if */
    h=0;        ipmx +=1;
    m=pow(2,cptcovn);        sw += weight[i];
          ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
    for(k=1;k<=cptcovn; k++){        /*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(i=1; i <=(m/pow(2,k));i++){        if(globpr){
        for(j=1; j <= ncodemax[k]; j++){          fprintf(ficresilk,"%9ld %6d %2d %2d %1d %1d %3d %11.6f %8.4f\
          for(cpt=1; cpt <=(m/pow(2,cptcovn+1-k)); cpt++){   %11.6f %11.6f %11.6f ", \
            h++;                  num[i],i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],
            if (h>m) h=1;codtab[h][k]=j;                  2*weight[i]*lli,out[s1][s2],savm[s1][s2]);
          }          for(k=1,llt=0.,l=0.; k<=nlstate; k++){
        }            llt +=ll[k]*gipmx/gsw;
      }            fprintf(ficresilk," %10.6f",-ll[k]*gipmx/gsw);
    }          }
           fprintf(ficresilk," %10.6f\n", -llt);
    /*for(i=1; i <=m ;i++){        }
      for(k=1; k <=cptcovn; k++){      } /* end of wave */
        printf("i=%d k=%d %d ",i,k,codtab[i][k]);    } /* end of individual */
      }    for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
      printf("\n");    /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
    }    l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
   scanf("%d",i);*/    if(globpr==0){ /* First time we count the contributions and weights */
          gipmx=ipmx;
    /* Calculates basic frequencies. Computes observed prevalence at single age      gsw=sw;
        and prints on file fileres'p'. */    }
   freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx,Tvar,nbcode, ncodemax);    return -l;
   }
     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 */  /*************** function likelione ***********/
     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  void likelione(FILE *ficres,double p[], int npar, int nlstate, int *globpri, long *ipmx, double *sw, double *fretone, double (*funcone)(double []))
     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */  {
        /* This routine should help understanding what is done with 
     /* For Powell, parameters are in a vector p[] starting at p[1]       the selection of individuals/waves and
        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */       to check the exact contribution to the likelihood.
     p=param[1][1]; /* *(*(*(param +1)+1)+0) */       Plotting could be done.
     /*scanf("%d",i);*/     */
     mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);    int k;
   
        if(*globpri !=0){ /* Just counts and sums, no printings */
     /*--------- results files --------------*/      strcpy(fileresilk,"ilk"); 
     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);      strcat(fileresilk,fileres);
          if((ficresilk=fopen(fileresilk,"w"))==NULL) {
    jk=1;        printf("Problem with resultfile: %s\n", fileresilk);
    fprintf(ficres,"# Parameters\n");        fprintf(ficlog,"Problem with resultfile: %s\n", fileresilk);
    printf("# Parameters\n");      }
    for(i=1,jk=1; i <=nlstate; i++){      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(k=1; k <=(nlstate+ndeath); k++){      fprintf(ficresilk, "#num_i i s1 s2 mi mw dh likeli weight 2wlli out sav ");
        if (k != i)      /*  i,s1,s2,mi,mw[mi][i],dh[mi][i],exp(lli),weight[i],2*weight[i]*lli,out[s1][s2],savm[s1][s2]); */
          {      for(k=1; k<=nlstate; k++) 
            printf("%d%d ",i,k);        fprintf(ficresilk," -2*gipw/gsw*weight*ll[%d]++",k);
            fprintf(ficres,"%1d%1d ",i,k);      fprintf(ficresilk," -2*gipw/gsw*weight*ll(total)\n");
            for(j=1; j <=ncovmodel; j++){    }
              printf("%f ",p[jk]);  
              fprintf(ficres,"%f ",p[jk]);    *fretone=(*funcone)(p);
              jk++;    if(*globpri !=0){
            }      fclose(ficresilk);
            printf("\n");      fprintf(fichtm,"\n<br>File of contributions to the likelihood: <a href=\"%s\">%s</a><br>\n",subdirf(fileresilk),subdirf(fileresilk));
            fprintf(ficres,"\n");      fflush(fichtm); 
          }    } 
      }    return;
    }  }
   
     /* Computing hessian and covariance matrix */  
     ftolhess=ftol; /* Usually correct */  /*********** Maximum Likelihood Estimation ***************/
     hesscov(matcov, p, npar, delti, ftolhess, func);  
     fprintf(ficres,"# Scales\n");  void mlikeli(FILE *ficres,double p[], int npar, int ncovmodel, int nlstate, double ftol, double (*func)(double []))
     printf("# Scales\n");  {
      for(i=1,jk=1; i <=nlstate; i++){    int i,j, iter;
       for(j=1; j <=nlstate+ndeath; j++){    double **xi;
         if (j!=i) {    double fret;
           fprintf(ficres,"%1d%1d",i,j);    double fretone; /* Only one call to likelihood */
           printf("%1d%1d",i,j);    /*  char filerespow[FILENAMELENGTH];*/
           for(k=1; k<=ncovmodel;k++){    xi=matrix(1,npar,1,npar);
             printf(" %.5e",delti[jk]);    for (i=1;i<=npar;i++)
             fprintf(ficres," %.5e",delti[jk]);      for (j=1;j<=npar;j++)
             jk++;        xi[i][j]=(i==j ? 1.0 : 0.0);
           }    printf("Powell\n");  fprintf(ficlog,"Powell\n");
           printf("\n");    strcpy(filerespow,"pow"); 
           fprintf(ficres,"\n");    strcat(filerespow,fileres);
         }    if((ficrespow=fopen(filerespow,"w"))==NULL) {
       }      printf("Problem with resultfile: %s\n", filerespow);
       }      fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
        }
     k=1;    fprintf(ficrespow,"# Powell\n# iter -2*LL");
     fprintf(ficres,"# Covariance\n");    for (i=1;i<=nlstate;i++)
     printf("# Covariance\n");      for(j=1;j<=nlstate+ndeath;j++)
     for(i=1;i<=npar;i++){        if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       /*  if (k>nlstate) k=1;    fprintf(ficrespow,"\n");
       i1=(i-1)/(ncovmodel*nlstate)+1;  
       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);    powell(p,xi,npar,ftol,&iter,&fret,func);
       printf("%s%d%d",alph[k],i1,tab[i]);*/  
       fprintf(ficres,"%3d",i);    free_matrix(xi,1,npar,1,npar);
       printf("%3d",i);    fclose(ficrespow);
       for(j=1; j<=i;j++){    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
         fprintf(ficres," %.5e",matcov[i][j]);    fprintf(ficlog,"\n#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
         printf(" %.5e",matcov[i][j]);    fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f \n",iter,func(p));
       }  
       fprintf(ficres,"\n");  }
       printf("\n");  
       k++;  /**** Computes Hessian and covariance matrix ***/
     }  void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
      {
     while((c=getc(ficpar))=='#' && c!= EOF){    double  **a,**y,*x,pd;
       ungetc(c,ficpar);    double **hess;
       fgets(line, MAXLINE, ficpar);    int i, j,jk;
       puts(line);    int *indx;
       fputs(line,ficparo);  
     }    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
     ungetc(c,ficpar);    double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);
      void lubksb(double **a, int npar, int *indx, double b[]) ;
     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    void ludcmp(double **a, int npar, int *indx, double *d) ;
        double gompertz(double p[]);
     if (fage <= 2) {    hess=matrix(1,npar,1,npar);
       bage = agemin;  
       fage = agemax;    printf("\nCalculation of the hessian matrix. Wait...\n");
     }    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
     for (i=1;i<=npar;i++){
     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");      printf("%d",i);fflush(stdout);
     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      fprintf(ficlog,"%d",i);fflush(ficlog);
 /*------------ gnuplot -------------*/     
 chdir(pathcd);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
   if((ficgp=fopen("graph.plt","w"))==NULL) {      
     printf("Problem with file graph.gp");goto end;      /*  printf(" %f ",p[i]);
   }          printf(" %lf %lf %lf",hess[i][i],ftolhess,delti[i]);*/
 #ifdef windows    }
   fprintf(ficgp,"cd \"%s\" \n",pathc);    
 #endif    for (i=1;i<=npar;i++) {
 m=pow(2,cptcovn);      for (j=1;j<=npar;j++)  {
          if (j>i) { 
  /* 1eme*/          printf(".%d%d",i,j);fflush(stdout);
   for (cpt=1; cpt<= nlstate ; cpt ++) {          fprintf(ficlog,".%d%d",i,j);fflush(ficlog);
    for (k1=1; k1<= m ; k1 ++) {          hess[i][j]=hessij(p,delti,i,j,func,npar);
           
 #ifdef windows          hess[j][i]=hess[i][j];    
     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);          /*printf(" %lf ",hess[i][j]);*/
 #endif        }
 #ifdef unix      }
 fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:2 \"\%%lf",agemin,fage,fileres);    }
 #endif    printf("\n");
     fprintf(ficlog,"\n");
 for (i=1; i<= nlstate ; i ++) {  
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
   else fprintf(ficgp," \%%*lf (\%%*lf)");    fprintf(ficlog,"\nInverting the hessian to get the covariance matrix. Wait...\n");
 }    
     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" every :::%d::%d u 1:($2+2*$3) \"\%%lf",fileres,k1-1,k1-1);    a=matrix(1,npar,1,npar);
     for (i=1; i<= nlstate ; i ++) {    y=matrix(1,npar,1,npar);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");    x=vector(1,npar);
   else fprintf(ficgp," \%%*lf (\%%*lf)");    indx=ivector(1,npar);
 }    for (i=1;i<=npar;i++)
   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" every :::%d::%d u 1:($2-2*$3) \"\%%lf",fileres,k1-1,k1-1);      for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
      for (i=1; i<= nlstate ; i ++) {    ludcmp(a,npar,indx,&pd);
   if (i==cpt) fprintf(ficgp," \%%lf (\%%lf)");  
   else fprintf(ficgp," \%%*lf (\%%*lf)");    for (j=1;j<=npar;j++) {
 }        for (i=1;i<=npar;i++) x[i]=0;
      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" every :::%d::%d u 1:($%d) t\"Observed prevalence \" w l 2",fileres,k1-1,k1-1,2+4*(cpt-1));      x[j]=1;
 #ifdef unix      lubksb(a,npar,indx,x);
 fprintf(ficgp,"\nset ter gif small size 400,300");      for (i=1;i<=npar;i++){ 
 #endif        matcov[i][j]=x[i];
 fprintf(ficgp,"\nset out \"v%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);      }
    }    }
   }  
   /*2 eme*/    printf("\n#Hessian matrix#\n");
     fprintf(ficlog,"\n#Hessian matrix#\n");
   for (k1=1; k1<= m ; k1 ++) {    for (i=1;i<=npar;i++) { 
     fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);      for (j=1;j<=npar;j++) { 
            printf("%.3e ",hess[i][j]);
     for (i=1; i<= nlstate+1 ; i ++) {        fprintf(ficlog,"%.3e ",hess[i][j]);
       k=2*i;      }
       fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:2 \"\%%lf",fileres,k1-1,k1-1);      printf("\n");
       for (j=1; j<= nlstate+1 ; j ++) {      fprintf(ficlog,"\n");
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    }
   else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }      /* Recompute Inverse */
       if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");    for (i=1;i<=npar;i++)
       else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);      for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
     fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2-$3*2) \"\%%lf",fileres,k1-1,k1-1);    ludcmp(a,npar,indx,&pd);
       for (j=1; j<= nlstate+1 ; j ++) {  
         if (j==i) fprintf(ficgp," \%%lf (\%%lf)");    /*  printf("\n#Hessian matrix recomputed#\n");
         else fprintf(ficgp," \%%*lf (\%%*lf)");  
 }      for (j=1;j<=npar;j++) {
       fprintf(ficgp,"\" t\"\" w l 0,");      for (i=1;i<=npar;i++) x[i]=0;
      fprintf(ficgp,"\"t%s\" every :::%d::%d u 1:($2+$3*2) \"\%%lf",fileres,k1-1,k1-1);      x[j]=1;
       for (j=1; j<= nlstate+1 ; j ++) {      lubksb(a,npar,indx,x);
   if (j==i) fprintf(ficgp," \%%lf (\%%lf)");      for (i=1;i<=npar;i++){ 
   else fprintf(ficgp," \%%*lf (\%%*lf)");        y[i][j]=x[i];
 }          printf("%.3e ",y[i][j]);
       if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");        fprintf(ficlog,"%.3e ",y[i][j]);
       else fprintf(ficgp,"\" t\"\" w l 0,");      }
     }      printf("\n");
     fprintf(ficgp,"\nset out \"e%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),k1);      fprintf(ficlog,"\n");
   }    }
      */
   /*3eme*/  
     free_matrix(a,1,npar,1,npar);
   for (k1=1; k1<= m ; k1 ++) {    free_matrix(y,1,npar,1,npar);
     for (cpt=1; cpt<= nlstate ; cpt ++) {    free_vector(x,1,npar);
       k=2+nlstate*(cpt-1);    free_ivector(indx,1,npar);
       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);    free_matrix(hess,1,npar,1,npar);
       for (i=1; i< nlstate ; i ++) {  
         fprintf(ficgp,",\"e%s\" every :::%d::%d u 1:%d t \"e%d%d\" w l",fileres,k1-1,k1-1,k+i,cpt,i+1);  
       }  }
       fprintf(ficgp,"\nset out \"exp%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);  
     }  /*************** hessian matrix ****************/
   }  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
    {
   /* CV preval stat */    int i;
   for (k1=1; k1<= m ; k1 ++) {    int l=1, lmax=20;
     for (cpt=1; cpt<nlstate ; cpt ++) {    double k1,k2;
       k=3;    double p2[MAXPARM+1]; /* identical to x */
       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/($%d",agemin,agemax,fileres,k1,k+cpt+1,k+1);    double res;
       for (i=1; i< nlstate ; i ++)    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
         fprintf(ficgp,"+$%d",k+i+1);    double fx;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);    int k=0,kmax=10;
          double l1;
       l=3+(nlstate+ndeath)*cpt;  
       fprintf(ficgp,",\"pij%s\" u ($1==%d ? ($3):1/0):($%d/($%d",fileres,k1,l+cpt+1,l+1);    fx=func(x);
       for (i=1; i< nlstate ; i ++) {    for (i=1;i<=npar;i++) p2[i]=x[i];
         l=3+(nlstate+ndeath)*cpt;    for(l=0 ; l <=lmax; l++){  /* Enlarging the zone around the Maximum */
         fprintf(ficgp,"+$%d",l+i+1);      l1=pow(10,l);
       }      delts=delt;
       fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);        for(k=1 ; k <kmax; k=k+1){
       fprintf(ficgp,"set out \"p%s%d%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt,k1);        delt = delta*(l1*k);
     }        p2[theta]=x[theta] +delt;
   }        k1=func(p2)-fx;   /* Might be negative if too close to the theoretical maximum */
         p2[theta]=x[theta]-delt;
   /* proba elementaires */        k2=func(p2)-fx;
   for(i=1,jk=1; i <=nlstate; i++){        /*res= (k1-2.0*fx+k2)/delt/delt; */
     for(k=1; k <=(nlstate+ndeath); k++){        res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
       if (k != i) {        
         /*  fprintf(ficgp,"%1d%1d ",i,k);*/  #ifdef DEBUGHESS
         for(j=1; j <=ncovmodel; j++){        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(ficgp,"%s%1d%1d=%f ",alph[j],i,k,p[jk]);        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);
           jk++;  #endif
           fprintf(ficgp,"\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. */
   for(jk=1; jk <=m; jk++) {          k=kmax; l=lmax*10.;
   fprintf(ficgp,"\nset ter gif small size 400,300\nset log y\nplot  [%.f:%.f] ",agemin,agemax);        }
   for(i=1; i <=nlstate; i++) {        else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
     for(k=1; k <=(nlstate+ndeath); k++){          delts=delt;
       if (k != i) {        }
         fprintf(ficgp," exp(a%d%d+b%d%d*x",i,k,i,k);      }
         for(j=3; j <=ncovmodel; j++)    }
           fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);    delti[theta]=delts;
         fprintf(ficgp,")/(1");    return res; 
         for(k1=1; k1 <=(nlstate+ndeath); k1++)    
           if (k1 != i) {  }
             fprintf(ficgp,"+exp(a%d%d+b%d%d*x",i,k1,i,k1);  
             for(j=3; j <=ncovmodel; j++)  double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
               fprintf(ficgp,"+%s%d%d*%d",alph[j],i,k,nbcode[Tvar[j-2]][codtab[jk][j-2]]);  {
             fprintf(ficgp,")");    int i;
           }    int l=1, l1, lmax=20;
         fprintf(ficgp,") t \"p%d%d\" ", i,k);    double k1,k2,k3,k4,res,fx;
       if ((i+k)!= (nlstate*2+ndeath)) fprintf(ficgp,",");    double p2[MAXPARM+1];
       }    int k;
     }  
   }    fx=func(x);
 fprintf(ficgp,"\nset out \"pe%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),jk);      for (k=1; k<=2; k++) {
   }      for (i=1;i<=npar;i++) p2[i]=x[i];
   fclose(ficgp);      p2[thetai]=x[thetai]+delti[thetai]/k;
          p2[thetaj]=x[thetaj]+delti[thetaj]/k;
 chdir(path);      k1=func(p2)-fx;
     free_matrix(agev,1,maxwav,1,imx);    
     free_ivector(wav,1,imx);      p2[thetai]=x[thetai]+delti[thetai]/k;
     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);      k2=func(p2)-fx;
        
     free_imatrix(s,1,maxwav+1,1,n);      p2[thetai]=x[thetai]-delti[thetai]/k;
          p2[thetaj]=x[thetaj]+delti[thetaj]/k;
          k3=func(p2)-fx;
     free_ivector(num,1,n);    
     free_vector(agedc,1,n);      p2[thetai]=x[thetai]-delti[thetai]/k;
     free_vector(weight,1,n);      p2[thetaj]=x[thetaj]-delti[thetaj]/k;
     /*free_matrix(covar,1,NCOVMAX,1,n);*/      k4=func(p2)-fx;
     fclose(ficparo);      res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
     fclose(ficres);  #ifdef DEBUG
    }      printf("%d %d k=%d, k1=%.12e k2=%.12e k3=%.12e k4=%.12e delti/k=%.12e deltj/k=%.12e, xi-de/k=%.12e xj-de/k=%.12e  res=%.12e k1234=%.12e,k1-2=%.12e,k3-4=%.12e\n",thetai,thetaj,k,k1,k2,k3,k4,delti[thetai]/k,delti[thetaj]/k,x[thetai]-delti[thetai]/k,x[thetaj]-delti[thetaj]/k, res,k1-k2-k3+k4,k1-k2,k3-k4);
          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);
    /*________fin mle=1_________*/  #endif
        }
     return res;
    }
     /* No more information from the sample is required now */  
   /* Reads comments: lines beginning with '#' */  /************** Inverse of matrix **************/
   while((c=getc(ficpar))=='#' && c!= EOF){  void ludcmp(double **a, int n, int *indx, double *d) 
     ungetc(c,ficpar);  { 
     fgets(line, MAXLINE, ficpar);    int i,imax,j,k; 
     puts(line);    double big,dum,sum,temp; 
     fputs(line,ficparo);    double *vv; 
   }   
   ungetc(c,ficpar);    vv=vector(1,n); 
      *d=1.0; 
   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);    for (i=1;i<=n;i++) { 
   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);      big=0.0; 
   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);      for (j=1;j<=n;j++) 
 /*--------- index.htm --------*/        if ((temp=fabs(a[i][j])) > big) big=temp; 
       if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
   if((fichtm=fopen("index.htm","w"))==NULL)    {      vv[i]=1.0/big; 
     printf("Problem with index.htm \n");goto end;    } 
   }    for (j=1;j<=n;j++) { 
       for (i=1;i<j;i++) { 
  fprintf(fichtm,"<body><ul> Imach, Version 0.63<hr> <li>Outputs files<br><br>\n        sum=a[i][j]; 
         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n        for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
 - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>        a[i][j]=sum; 
         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>      } 
         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>      big=0.0; 
         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>      for (i=j;i<=n;i++) { 
         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>        sum=a[i][j]; 
         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>        for (k=1;k<j;k++) 
         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>          sum -= a[i][k]*a[k][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);        a[i][j]=sum; 
         if ( (dum=vv[i]*fabs(sum)) >= big) { 
  fprintf(fichtm," <li>Graphs</li>\n<p>");          big=dum; 
           imax=i; 
  m=cptcovn;        } 
  if (cptcovn < 1) {m=1;ncodemax[1]=1;}      } 
       if (j != imax) { 
  j1=0;        for (k=1;k<=n;k++) { 
  for(k1=1; k1<=m;k1++){          dum=a[imax][k]; 
    for(i1=1; i1<=ncodemax[k1];i1++){          a[imax][k]=a[j][k]; 
        j1++;          a[j][k]=dum; 
        if (cptcovn > 0) {        } 
          fprintf(fichtm,"<hr>************ Results for covariates");        *d = -(*d); 
          for (cpt=1; cpt<=cptcovn;cpt++)        vv[imax]=vv[j]; 
            fprintf(fichtm," V%d=%d ",Tvar[cpt],nbcode[Tvar[cpt]][codtab[j1][cpt]]);      } 
          fprintf(fichtm," ************\n<hr>");      indx[j]=imax; 
        }      if (a[j][j] == 0.0) a[j][j]=TINY; 
        fprintf(fichtm,"<br>- Probabilities: pe%s%d.gif<br>      if (j != n) { 
 <img src=\"pe%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);            dum=1.0/(a[j][j]); 
        for(cpt=1; cpt<nlstate;cpt++){        for (i=j+1;i<=n;i++) a[i][j] *= dum; 
          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);    } 
        }    free_vector(vv,1,n);  /* Doesn't work */
     for(cpt=1; cpt<=nlstate;cpt++) {  ;
        fprintf(fichtm,"<br>- Observed and stationary prevalence (with confident  } 
 interval) in state (%d): v%s%d%d.gif <br>  
 <img src=\"v%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);    void lubksb(double **a, int n, int *indx, double b[]) 
      }  { 
      for(cpt=1; cpt<=nlstate;cpt++) {    int i,ii=0,ip,j; 
         fprintf(fichtm,"\n<br>- Health life expectancies by age and initial health state (%d): exp%s%d%d.gif <br>    double sum; 
 <img src=\"exp%s%d%d.gif\">",cpt,strtok(optionfile, "."),cpt,j1,strtok(optionfile, "."),cpt,j1);   
      }    for (i=1;i<=n;i++) { 
      fprintf(fichtm,"\n<br>- Total life expectancy by age and      ip=indx[i]; 
 health expectancies in states (1) and (2): e%s%d.gif<br>      sum=b[ip]; 
 <img src=\"e%s%d.gif\">",strtok(optionfile, "."),j1,strtok(optionfile, "."),j1);      b[ip]=b[i]; 
 fprintf(fichtm,"\n</body>");      if (ii) 
    }        for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
  }      else if (sum) ii=i; 
 fclose(fichtm);      b[i]=sum; 
     } 
   /*--------------- Prevalence limit --------------*/    for (i=n;i>=1;i--) { 
        sum=b[i]; 
   strcpy(filerespl,"pl");      for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
   strcat(filerespl,fileres);      b[i]=sum/a[i][i]; 
   if((ficrespl=fopen(filerespl,"w"))==NULL) {    } 
     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;  } 
   }  
   printf("Computing prevalence limit: result on file '%s' \n", filerespl);  void pstamp(FILE *fichier)
   fprintf(ficrespl,"#Prevalence limit\n");  {
   fprintf(ficrespl,"#Age ");    fprintf(fichier,"# %s.%s\n#%s\n#%s\n# %s", optionfilefiname,optionfilext,version,fullversion,strstart);
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);  }
   fprintf(ficrespl,"\n");  
    /************ Frequencies ********************/
   prlim=matrix(1,nlstate,1,nlstate);  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[])
   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */  {  /* Some frequencies */
   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    
   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    int i, m, jk, k1,i1, j1, bool, z1,j;
   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */    int first;
   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */    double ***freq; /* Frequencies */
   k=0;    double *pp, **prop;
   agebase=agemin;    double pos,posprop, k2, dateintsum=0,k2cpt=0;
   agelim=agemax;    char fileresp[FILENAMELENGTH];
   ftolpl=1.e-10;    
   i1=cptcovn;    pp=vector(1,nlstate);
   if (cptcovn < 1){i1=1;}    prop=matrix(1,nlstate,iagemin,iagemax+3);
     strcpy(fileresp,"p");
   for(cptcov=1;cptcov<=i1;cptcov++){    strcat(fileresp,fileres);
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    if((ficresp=fopen(fileresp,"w"))==NULL) {
         k=k+1;      printf("Problem with prevalence resultfile: %s\n", fileresp);
         /*printf("cptcov=%d cptcod=%d codtab=%d nbcode=%d\n",cptcov, cptcod,Tcode[cptcode],codtab[cptcod][cptcov]);*/      fprintf(ficlog,"Problem with prevalence resultfile: %s\n", fileresp);
         fprintf(ficrespl,"\n#****** ");      exit(0);
         for(j=1;j<=cptcovn;j++)    }
           fprintf(ficrespl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);    freq= ma3x(-5,nlstate+ndeath,-5,nlstate+ndeath,iagemin,iagemax+3);
         fprintf(ficrespl,"******\n");    j1=0;
            
         for (age=agebase; age<=agelim; age++){    j=cptcoveff;
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);    if (cptcovn<1) {j=1;ncodemax[1]=1;}
           fprintf(ficrespl,"%.0f",age );  
           for(i=1; i<=nlstate;i++)    first=1;
           fprintf(ficrespl," %.5f", prlim[i][i]);  
           fprintf(ficrespl,"\n");    /* for(k1=1; k1<=j ; k1++){   /* Loop on covariates */
         }    /*  for(i1=1; i1<=ncodemax[k1];i1++){ /* Now it is 2 */
       }    /*    j1++;
     }  */
   fclose(ficrespl);    for (j1 = 1; j1 <= (int) pow(2,cptcoveff); j1++){
   /*------------- h Pij x at various ages ------------*/        /*printf("cptcoveff=%d Tvaraff=%d", cptcoveff,Tvaraff[1]);
            scanf("%d", i);*/
   strcpy(filerespij,"pij");  strcat(filerespij,fileres);        for (i=-5; i<=nlstate+ndeath; i++)  
   if((ficrespij=fopen(filerespij,"w"))==NULL) {          for (jk=-5; jk<=nlstate+ndeath; jk++)  
     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;            for(m=iagemin; m <= iagemax+3; m++)
   }              freq[i][jk][m]=0;
   printf("Computing pij: result on file '%s' \n", filerespij);        
          for (i=1; i<=nlstate; i++)  
   stepsize=(int) (stepm+YEARM-1)/YEARM;          for(m=iagemin; m <= iagemax+3; m++)
   if (stepm<=24) stepsize=2;            prop[i][m]=0;
         
   agelim=AGESUP;        dateintsum=0;
   hstepm=stepsize*YEARM; /* Every year of age */        k2cpt=0;
   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */        for (i=1; i<=imx; i++) {
            bool=1;
   k=0;          if  (cptcovn>0) { /* Filter is here: Must be looked at for model=V1+V2+V3+V4 */
   for(cptcov=1;cptcov<=i1;cptcov++){            for (z1=1; z1<=cptcoveff; z1++)       
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]){
       k=k+1;                  /* Tests if the value of each of the covariates of i is equal to filter j1 */
         fprintf(ficrespij,"\n#****** ");                bool=0;
         for(j=1;j<=cptcovn;j++)                /* 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", 
           fprintf(ficrespij,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);                  bool,i,z1, z1, Tvaraff[z1],i,covar[Tvaraff[z1]][i],j1,z1,codtab[j1][z1],
         fprintf(ficrespij,"******\n");                  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*/
         for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */              } 
           nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */          }
           nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */   
           p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);          if (bool==1){
           oldm=oldms;savm=savms;            for(m=firstpass; m<=lastpass; m++){
           hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);                k2=anint[m][i]+(mint[m][i]/12.);
           fprintf(ficrespij,"# Age");              /*if ((k2>=dateprev1) && (k2<=dateprev2)) {*/
           for(i=1; i<=nlstate;i++)                if(agev[m][i]==0) agev[m][i]=iagemax+1;
             for(j=1; j<=nlstate+ndeath;j++)                if(agev[m][i]==1) agev[m][i]=iagemax+2;
               fprintf(ficrespij," %1d-%1d",i,j);                if (s[m][i]>0 && s[m][i]<=nlstate) prop[s[m][i]][(int)agev[m][i]] += weight[i];
           fprintf(ficrespij,"\n");                if (m<lastpass) {
           for (h=0; h<=nhstepm; h++){                  freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
             fprintf(ficrespij,"%d %.0f %.0f",k,agedeb, agedeb+ h*hstepm/YEARM*stepm );                  freq[s[m][i]][s[m+1][i]][iagemax+3] += weight[i];
             for(i=1; i<=nlstate;i++)                }
               for(j=1; j<=nlstate+ndeath;j++)                
                 fprintf(ficrespij," %.5f", p3mat[i][j][h]);                if ((agev[m][i]>1) && (agev[m][i]< (iagemax+3))) {
             fprintf(ficrespij,"\n");                  dateintsum=dateintsum+k2;
           }                  k2cpt++;
           free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);                }
           fprintf(ficrespij,"\n");                /*}*/
         }            }
     }          }
   }        } /* end i */
          
   fclose(ficrespij);        /*      fprintf(ficresp, "#Count between %.lf/%.lf/%.lf and %.lf/%.lf/%.lf\n",jprev1, mprev1,anprev1,jprev2, mprev2,anprev2);*/
         pstamp(ficresp);
   /*---------- Health expectancies and variances ------------*/        if  (cptcovn>0) {
           fprintf(ficresp, "\n#********** Variable "); 
   strcpy(filerest,"t");          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresp, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   strcat(filerest,fileres);          fprintf(ficresp, "**********\n#");
   if((ficrest=fopen(filerest,"w"))==NULL) {          fprintf(ficlog, "\n#********** Variable "); 
     printf("Problem with total LE resultfile: %s\n", filerest);goto end;          for (z1=1; z1<=cptcoveff; z1++) fprintf(ficlog, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]);
   }          fprintf(ficlog, "**********\n#");
   printf("Computing Total LEs with variances: file '%s' \n", filerest);        }
         for(i=1; i<=nlstate;i++) 
           fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
   strcpy(filerese,"e");        fprintf(ficresp, "\n");
   strcat(filerese,fileres);        
   if((ficreseij=fopen(filerese,"w"))==NULL) {        for(i=iagemin; i <= iagemax+3; i++){
     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);          if(i==iagemax+3){
   }            fprintf(ficlog,"Total");
   printf("Computing Health Expectancies: result on file '%s' \n", filerese);          }else{
             if(first==1){
  strcpy(fileresv,"v");              first=0;
   strcat(fileresv,fileres);              printf("See log file for details...\n");
   if((ficresvij=fopen(fileresv,"w"))==NULL) {            }
     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);            fprintf(ficlog,"Age %d", i);
   }          }
   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);          for(jk=1; jk <=nlstate ; jk++){
             for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
   k=0;              pp[jk] += freq[jk][m][i]; 
   for(cptcov=1;cptcov<=i1;cptcov++){          }
     for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){          for(jk=1; jk <=nlstate ; jk++){
       k=k+1;            for(m=-1, pos=0; m <=0 ; m++)
       fprintf(ficrest,"\n#****** ");              pos += freq[jk][m][i];
       for(j=1;j<=cptcovn;j++)            if(pp[jk]>=1.e-10){
         fprintf(ficrest,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);              if(first==1){
       fprintf(ficrest,"******\n");                printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
               }
       fprintf(ficreseij,"\n#****** ");              fprintf(ficlog," %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
       for(j=1;j<=cptcovn;j++)            }else{
         fprintf(ficreseij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);              if(first==1)
       fprintf(ficreseij,"******\n");                printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
               fprintf(ficlog," %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
       fprintf(ficresvij,"\n#****** ");            }
       for(j=1;j<=cptcovn;j++)          }
         fprintf(ficresvij,"V%d=%d ",j,nbcode[j][codtab[k][j]]);  
       fprintf(ficresvij,"******\n");          for(jk=1; jk <=nlstate ; jk++){
             for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++)
       eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);              pp[jk] += freq[jk][m][i];
       oldm=oldms;savm=savms;          }       
       evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm, k);            for(jk=1,pos=0,posprop=0; jk <=nlstate ; jk++){
       vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);            pos += pp[jk];
       oldm=oldms;savm=savms;            posprop += prop[jk][i];
       varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);          }
                for(jk=1; jk <=nlstate ; jk++){
       fprintf(ficrest,"#Total LEs with variances: e.. (std) ");            if(pos>=1.e-5){
       for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);              if(first==1)
       fprintf(ficrest,"\n");                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);
       hf=1;            }else{
       if (stepm >= YEARM) hf=stepm/YEARM;              if(first==1)
       epj=vector(1,nlstate+1);                printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
       for(age=bage; age <=fage ;age++){              fprintf(ficlog," %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
         prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            }
         fprintf(ficrest," %.0f",age);            if( i <= iagemax){
         for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){              if(pos>=1.e-5){
           for(i=1, epj[j]=0.;i <=nlstate;i++) {                fprintf(ficresp," %d %.5f %.0f %.0f",i,prop[jk][i]/posprop, prop[jk][i],posprop);
             epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];                /*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]);*/
           epj[nlstate+1] +=epj[j];              }
         }              else
         for(i=1, vepp=0.;i <=nlstate;i++)                fprintf(ficresp," %d NaNq %.0f %.0f",i,prop[jk][i],posprop);
           for(j=1;j <=nlstate;j++)            }
             vepp += vareij[i][j][(int)age];          }
         fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));          
         for(j=1;j <=nlstate;j++){          for(jk=-1; jk <=nlstate+ndeath; jk++)
           fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));            for(m=-1; m <=nlstate+ndeath; m++)
         }              if(freq[jk][m][i] !=0 ) {
         fprintf(ficrest,"\n");              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)
  fclose(ficreseij);            fprintf(ficresp,"\n");
  fclose(ficresvij);          if(first==1)
   fclose(ficrest);            printf("Others in log...\n");
   fclose(ficpar);          fprintf(ficlog,"\n");
   free_vector(epj,1,nlstate+1);        }
   /*  scanf("%d ",i); */        /*}*/
     }
   /*------- Variance limit prevalence------*/      dateintmean=dateintsum/k2cpt; 
    
 strcpy(fileresvpl,"vpl");    fclose(ficresp);
   strcat(fileresvpl,fileres);    free_ma3x(freq,-5,nlstate+ndeath,-5,nlstate+ndeath, iagemin, iagemax+3);
   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {    free_vector(pp,1,nlstate);
     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);    free_matrix(prop,1,nlstate,iagemin, iagemax+3);
     exit(0);    /* End of Freq */
   }  }
   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);  
   /************ Prevalence ********************/
  k=0;  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)
  for(cptcov=1;cptcov<=i1;cptcov++){  {  
    for(cptcod=1;cptcod<=ncodemax[cptcov];cptcod++){    /* Compute observed prevalence between dateprev1 and dateprev2 by counting the number of people
      k=k+1;       in each health status at the date of interview (if between dateprev1 and dateprev2).
      fprintf(ficresvpl,"\n#****** ");       We still use firstpass and lastpass as another selection.
      for(j=1;j<=cptcovn;j++)    */
        fprintf(ficresvpl,"V%d=%d ",Tvar[j],nbcode[Tvar[j]][codtab[k][j]]);   
      fprintf(ficresvpl,"******\n");    int i, m, jk, k1, i1, j1, bool, z1,j;
          double ***freq; /* Frequencies */
      varpl=matrix(1,nlstate,(int) bage, (int) fage);    double *pp, **prop;
      oldm=oldms;savm=savms;    double pos,posprop; 
      varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k);    double  y2; /* in fractional years */
    }    int iagemin, iagemax;
  }    int first; /** to stop verbosity which is redirected to log file */
   
   fclose(ficresvpl);    iagemin= (int) agemin;
     iagemax= (int) agemax;
   /*---------- End : free ----------------*/    /*pp=vector(1,nlstate);*/
   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);    prop=matrix(1,nlstate,iagemin,iagemax+3); 
      /*  freq=ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,iagemin,iagemax+3);*/
   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);    j1=0;
   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);    
      /*j=cptcoveff;*/
      if (cptcovn<1) {j=1;ncodemax[1]=1;}
   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);    
   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);    first=1;
   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);    for(j1=1; j1<= (int) pow(2,cptcoveff);j1++){
   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);      /*for(i1=1; i1<=ncodemax[k1];i1++){
          j1++;*/
   free_matrix(matcov,1,npar,1,npar);        
   free_vector(delti,1,npar);        for (i=1; i<=nlstate; i++)  
            for(m=iagemin; m <= iagemax+3; m++)
   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);            prop[i][m]=0.0;
        
   printf("End of Imach\n");        for (i=1; i<=imx; i++) { /* Each individual */
   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */          bool=1;
            if  (cptcovn>0) {
   /* 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);*/            for (z1=1; z1<=cptcoveff; z1++) 
   /*printf("Total time was %d uSec.\n", total_usecs);*/              if (covar[Tvaraff[z1]][i]!= nbcode[Tvaraff[z1]][codtab[j1][z1]]) 
   /*------ End -----------*/                bool=0;
           } 
  end:          if (bool==1) { 
 #ifdef windows            for(m=firstpass; m<=lastpass; m++){/* Other selection (we can limit to certain interviews*/
  chdir(pathcd);              y2=anint[m][i]+(mint[m][i]/12.); /* Fractional date in year */
 #endif              if ((y2>=dateprev1) && (y2<=dateprev2)) { /* Here is the main selection (fractional years) */
  system("wgnuplot ../gp37mgw/graph.plt");                if(agev[m][i]==0) agev[m][i]=iagemax+1;
                 if(agev[m][i]==1) agev[m][i]=iagemax+2;
 #ifdef windows                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); 
   while (z[0] != 'q') {                if (s[m][i]>0 && s[m][i]<=nlstate) { 
     chdir(pathcd);                  /*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]]);*/
     printf("\nType e to edit output files, c to start again, and q for exiting: ");                  prop[s[m][i]][(int)agev[m][i]] += weight[i];
     scanf("%s",z);                  prop[s[m][i]][iagemax+3] += weight[i]; 
     if (z[0] == 'c') system("./imach");                } 
     else if (z[0] == 'e') {              }
       chdir(path);            } /* end selection of waves */
       system("index.htm");          }
     }        }
     else if (z[0] == 'q') exit(0);        for(i=iagemin; i <= iagemax+3; i++){  
   }          for(jk=1,posprop=0; jk <=nlstate ; jk++) { 
 #endif            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=1e+5;
     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, k, cptj, cptj2, i2, j2;
     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, cptcode;
     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 **newm;
     double **dnewm,**doldm;
     int i, j, nhstepm, hstepm;
     int k, cptcode;
     double *xp;
     double *gp, *gm;
     double **gradg, **trgradg;
     double age,agelim;
     int theta;
     
     pstamp(ficresvpl);
     fprintf(ficresvpl,"# Standard deviation of period (stable) prevalences \n");
     fprintf(ficresvpl,"# Age");
     for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %1d-%1d",i,i);
     fprintf(ficresvpl,"\n");
   
     xp=vector(1,npar);
     dnewm=matrix(1,nlstate,1,npar);
     doldm=matrix(1,nlstate,1,nlstate);
     
     hstepm=1*YEARM; /* Every year of age */
     hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
     agelim = AGESUP;
     for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
       nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
       if (stepm >= YEARM) hstepm=1;
       nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
       gradg=matrix(1,npar,1,nlstate);
       gp=vector(1,nlstate);
       gm=vector(1,nlstate);
   
       for(theta=1; theta <=npar; theta++){
         for(i=1; i<=npar; i++){ /* Computes gradient */
           xp[i] = x[i] + (i==theta ?delti[theta]:0);
         }
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gp[i] = prlim[i][i];
       
         for(i=1; i<=npar; i++) /* Computes gradient */
           xp[i] = x[i] - (i==theta ?delti[theta]:0);
         prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);
         for(i=1;i<=nlstate;i++)
           gm[i] = prlim[i][i];
   
         for(i=1;i<=nlstate;i++)
           gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
       } /* End theta */
   
       trgradg =matrix(1,nlstate,1,npar);
   
       for(j=1; j<=nlstate;j++)
         for(theta=1; theta <=npar; theta++)
           trgradg[j][theta]=gradg[theta][j];
   
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] =0.;
       matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
       matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
       for(i=1;i<=nlstate;i++)
         varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
   
       fprintf(ficresvpl,"%.0f ",age );
       for(i=1; i<=nlstate;i++)
         fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
       fprintf(ficresvpl,"\n");
       free_vector(gp,1,nlstate);
       free_vector(gm,1,nlstate);
       free_matrix(gradg,1,npar,1,nlstate);
       free_matrix(trgradg,1,nlstate,1,npar);
     } /* End age */
   
     free_vector(xp,1,npar);
     free_matrix(doldm,1,nlstate,1,npar);
     free_matrix(dnewm,1,nlstate,1,nlstate);
   
   }
   
   /************ Variance of one-step probabilities  ******************/
   void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax, char strstart[])
   {
     int i, j=0,  i1, k1, l1, t, tj;
     int k2, l2, j1,  z1;
     int k=0,l, cptcode;
     int first=1, first1, 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,agelim, 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 from each state (1 to %d) to period (stable) prevalence in state %d <a href=\"%s%d_%d.png\">%s%d_%d.png</a><br> \
   <img src=\"%s%d_%d.png\">",nlstate, cpt, 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 m0,cpt=0,k1=0,i=0,k=0,j=0,jk=0,k2=0,k3=0,ij=0,l=0;
     int ng=0;
   /*   if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { */
   /*     printf("Problem with file %s",optionfilegnuplot); */
   /*     fprintf(ficlog,"Problem with file %s",optionfilegnuplot); */
   /*   } */
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
     m=pow(2,cptcoveff);
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
    /* 1eme*/
     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, c, cptcod, i, h, i1;
     int *popage;
     double agec; /* generic age */
     double agelim, ppij, yp,yp1,yp2,jprojmean,mprojmean,anprojmean;
     double *popeffectif,*popcount;
     double ***p3mat;
     double ***mobaverage;
     char fileresf[FILENAMELENGTH];
   
     agelim=AGESUP;
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
    
     strcpy(fileresf,"f"); 
     strcat(fileresf,fileres);
     if((ficresf=fopen(fileresf,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", fileresf);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", fileresf);
     }
     printf("Computing forecasting: result on file '%s' \n", fileresf);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", fileresf);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     if(estepm < stepm){
       printf ("Problem %d lower than %d\n",estepm, stepm);
     }
     else  hstepm=estepm;   
   
     hstepm=hstepm/stepm; 
     yp1=modf(dateintmean,&yp);/* extracts integral of datemean in yp  and
                                  fractional in yp1 */
     anprojmean=yp;
     yp2=modf((yp1*12),&yp);
     mprojmean=yp;
     yp1=modf((yp2*30.5),&yp);
     jprojmean=yp;
     if(jprojmean==0) jprojmean=1;
     if(mprojmean==0) jprojmean=1;
   
     i1=cptcoveff;
     if (cptcovn < 1){i1=1;}
     
     fprintf(ficresf,"# Mean day of interviews %.lf/%.lf/%.lf (%.2f) between %.2f and %.2f \n",jprojmean,mprojmean,anprojmean,dateintmean,dateprev1,dateprev2); 
     
     fprintf(ficresf,"#****** Routine prevforecast **\n");
   
   /*            if (h==(int)(YEARM*yearp)){ */
     for(cptcov=1, k=0;cptcov<=i1;cptcov++){
       for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficresf,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficresf," V%d=%d, hpijx=probability over h years, hp.jx is weighted by observed prev ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficresf,"******\n");
         fprintf(ficresf,"# Covariate valuofcovar yearproj age");
         for(j=1; j<=nlstate+ndeath;j++){ 
           for(i=1; i<=nlstate;i++)              
             fprintf(ficresf," p%d%d",i,j);
           fprintf(ficresf," p.%d",j);
         }
         for (yearp=0; yearp<=(anproj2-anproj1);yearp +=stepsize) { 
           fprintf(ficresf,"\n");
           fprintf(ficresf,"\n# Forecasting at date %.lf/%.lf/%.lf ",jproj1,mproj1,anproj1+yearp);   
   
           for (agec=fage; agec>=(ageminpar-1); agec--){ 
             nhstepm=(int) rint((agelim-agec)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agec,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h*hstepm/YEARM*stepm ==yearp) {
                 fprintf(ficresf,"\n");
                 for(j=1;j<=cptcoveff;j++) 
                   fprintf(ficresf,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
                 fprintf(ficresf,"%.f %.f ",anproj1+yearp,agec+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 ppij=0.;
                 for(i=1; i<=nlstate;i++) {
                   if (mobilav==1) 
                     ppij=ppij+p3mat[i][j][h]*mobaverage[(int)agec][i][cptcod];
                   else {
                     ppij=ppij+p3mat[i][j][h]*probs[(int)(agec)][i][cptcod];
                   }
                   if (h*hstepm/YEARM*stepm== yearp) {
                     fprintf(ficresf," %.3f", p3mat[i][j][h]);
                   }
                 } /* end i */
                 if (h*hstepm/YEARM*stepm==yearp) {
                   fprintf(ficresf," %.3f", ppij);
                 }
               }/* end j */
             } /* end h */
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           } /* end agec */
         } /* end yearp */
       } /* end cptcod */
     } /* end  cptcov */
          
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     fclose(ficresf);
   }
   
   /************** Forecasting *****not tested NB*************/
   populforecast(char fileres[], double anpyram,double mpyram,double jpyram,double ageminpar, double agemax,double dateprev1, double dateprev2, int mobilav, double agedeb, double fage, int popforecast, char popfile[], double anpyram1,double p[], int i2){
     
     int cpt, stepsize, hstepm, nhstepm, j,k,c, cptcod, i,h;
     int *popage;
     double calagedatem, agelim, kk1, kk2;
     double *popeffectif,*popcount;
     double ***p3mat,***tabpop,***tabpopprev;
     double ***mobaverage;
     char filerespop[FILENAMELENGTH];
   
     tabpop= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     tabpopprev= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     agelim=AGESUP;
     calagedatem=(anpyram+mpyram/12.+jpyram/365.-dateintmean)*YEARM;
     
     prevalence(probs, ageminpar, agemax, s, agev, nlstate, imx, Tvar, nbcode, ncodemax, mint, anint, dateprev1, dateprev2, firstpass, lastpass);
     
     
     strcpy(filerespop,"pop"); 
     strcat(filerespop,fileres);
     if((ficrespop=fopen(filerespop,"w"))==NULL) {
       printf("Problem with forecast resultfile: %s\n", filerespop);
       fprintf(ficlog,"Problem with forecast resultfile: %s\n", filerespop);
     }
     printf("Computing forecasting: result on file '%s' \n", filerespop);
     fprintf(ficlog,"Computing forecasting: result on file '%s' \n", filerespop);
   
     if (cptcoveff==0) ncodemax[cptcoveff]=1;
   
     if (mobilav!=0) {
       mobaverage= ma3x(1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
       if (movingaverage(probs, ageminpar, fage, mobaverage,mobilav)!=0){
         fprintf(ficlog," Error in movingaverage mobilav=%d\n",mobilav);
         printf(" Error in movingaverage mobilav=%d\n",mobilav);
       }
     }
   
     stepsize=(int) (stepm+YEARM-1)/YEARM;
     if (stepm<=12) stepsize=1;
     
     agelim=AGESUP;
     
     hstepm=1;
     hstepm=hstepm/stepm; 
     
     if (popforecast==1) {
       if((ficpop=fopen(popfile,"r"))==NULL) {
         printf("Problem with population file : %s\n",popfile);exit(0);
         fprintf(ficlog,"Problem with population file : %s\n",popfile);exit(0);
       } 
       popage=ivector(0,AGESUP);
       popeffectif=vector(0,AGESUP);
       popcount=vector(0,AGESUP);
       
       i=1;   
       while ((c=fscanf(ficpop,"%d %lf\n",&popage[i],&popcount[i])) != EOF) i=i+1;
      
       imx=i;
       for (i=1; i<imx;i++) popeffectif[popage[i]]=popcount[i];
     }
   
     for(cptcov=1,k=0;cptcov<=i2;cptcov++){
      for(cptcod=1;cptcod<=ncodemax[cptcoveff];cptcod++){
         k=k+1;
         fprintf(ficrespop,"\n#******");
         for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespop," V%d=%d ",Tvaraff[j],nbcode[Tvaraff[j]][codtab[k][j]]);
         }
         fprintf(ficrespop,"******\n");
         fprintf(ficrespop,"# Age");
         for(j=1; j<=nlstate+ndeath;j++) fprintf(ficrespop," P.%d",j);
         if (popforecast==1)  fprintf(ficrespop," [Population]");
         
         for (cpt=0; cpt<=0;cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
           
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficrespop,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   if (mobilav==1) 
                     kk1=kk1+p3mat[i][j][h]*mobaverage[(int)agedeb+1][i][cptcod];
                   else {
                     kk1=kk1+p3mat[i][j][h]*probs[(int)(agedeb+1)][i][cptcod];
                   }
                 }
                 if (h==(int)(calagedatem+12*cpt)){
                   tabpop[(int)(agedeb)][j][cptcod]=kk1;
                     /*fprintf(ficrespop," %.3f", kk1);
                       if (popforecast==1) fprintf(ficrespop," [%.f]", kk1*popeffectif[(int)agedeb+1]);*/
                 }
               }
               for(i=1; i<=nlstate;i++){
                 kk1=0.;
                   for(j=1; j<=nlstate;j++){
                     kk1= kk1+tabpop[(int)(agedeb)][j][cptcod]; 
                   }
                     tabpopprev[(int)(agedeb)][i][cptcod]=tabpop[(int)(agedeb)][i][cptcod]/kk1*popeffectif[(int)(agedeb+(calagedatem+12*cpt)*hstepm/YEARM*stepm-1)];
               }
   
               if (h==(int)(calagedatem+12*cpt)) for(j=1; j<=nlstate;j++) 
                 fprintf(ficrespop," %15.2f",tabpopprev[(int)(agedeb+1)][j][cptcod]);
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
    
     /******/
   
         for (cpt=1; cpt<=(anpyram1-anpyram);cpt++) { 
           fprintf(ficrespop,"\n\n# Forecasting at date %.lf/%.lf/%.lf ",jpyram,mpyram,anpyram+cpt);   
           for (agedeb=(fage-((int)calagedatem %12/12.)); agedeb>=(ageminpar-((int)calagedatem %12)/12.); agedeb--){ 
             nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); 
             nhstepm = nhstepm/hstepm; 
             
             p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
             oldm=oldms;savm=savms;
             hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm, k);  
             for (h=0; h<=nhstepm; h++){
               if (h==(int) (calagedatem+YEARM*cpt)) {
                 fprintf(ficresf,"\n %3.f ",agedeb+h*hstepm/YEARM*stepm);
               } 
               for(j=1; j<=nlstate+ndeath;j++) {
                 kk1=0.;kk2=0;
                 for(i=1; i<=nlstate;i++) {              
                   kk1=kk1+p3mat[i][j][h]*tabpopprev[(int)agedeb+1][i][cptcod];    
                 }
                 if (h==(int)(calagedatem+12*cpt)) fprintf(ficresf," %15.2f", kk1);        
               }
             }
             free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
           }
         }
      } 
     }
    
     if (mobilav!=0) free_ma3x(mobaverage,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
   
     if (popforecast==1) {
       free_ivector(popage,0,AGESUP);
       free_vector(popeffectif,0,AGESUP);
       free_vector(popcount,0,AGESUP);
     }
     free_ma3x(tabpop,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     free_ma3x(tabpopprev,1, AGESUP,1,NCOVMAX, 1,NCOVMAX);
     fclose(ficrespop);
   } /* End of popforecast */
   
   int fileappend(FILE *fichier, char *optionfich)
   {
     if((fichier=fopen(optionfich,"a"))==NULL) {
       printf("Problem with file: %s\n", optionfich);
       fprintf(ficlog,"Problem with file: %s\n", optionfich);
       return (0);
     }
     fflush(fichier);
     return (1);
   }
   
   
   /**************** function prwizard **********************/
   void prwizard(int ncovmodel, int nlstate, int ndeath,  char model[], FILE *ficparo)
   {
   
     /* Wizard to print covariance matrix template */
   
     char ca[32], cb[32], cc[32];
     int i,j, k, l, li, lj, lk, ll, jj, npar, itimes;
     int numlinepar;
   
     printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     fprintf(ficparo,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         /*ca[0]= k+'a'-1;ca[1]='\0';*/
         printf("%1d%1d",i,j);
         fprintf(ficparo,"%1d%1d",i,j);
         for(k=1; k<=ncovmodel;k++){
           /*        printf(" %lf",param[i][j][k]); */
           /*        fprintf(ficparo," %lf",param[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficparo,"# Scales (for hessian or gradient estimation)\n");
     npar= (nlstate+ndeath-1)*nlstate*ncovmodel; /* Number of parameters*/ 
     for(i=1; i <=nlstate; i++){
       jj=0;
       for(j=1; j <=nlstate+ndeath; j++){
         if(j==i) continue;
         jj++;
         fprintf(ficparo,"%1d%1d",i,j);
         printf("%1d%1d",i,j);
         fflush(stdout);
         for(k=1; k<=ncovmodel;k++){
           /*      printf(" %le",delti3[i][j][k]); */
           /*      fprintf(ficparo," %le",delti3[i][j][k]); */
           printf(" 0.");
           fprintf(ficparo," 0.");
         }
         numlinepar++;
         printf("\n");
         fprintf(ficparo,"\n");
       }
     }
     printf("# Covariance matrix\n");
   /* # 121 Var(a12)\n\ */
   /* # 122 Cov(b12,a12) Var(b12)\n\ */
   /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
   /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
   /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
   /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
   /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
   /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
     fflush(stdout);
     fprintf(ficparo,"# Covariance matrix\n");
     /* # 121 Var(a12)\n\ */
     /* # 122 Cov(b12,a12) Var(b12)\n\ */
     /* #   ...\n\ */
     /* # 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n" */
     
     for(itimes=1;itimes<=2;itimes++){
       jj=0;
       for(i=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if(j==i) continue;
           for(k=1; k<=ncovmodel;k++){
             jj++;
             ca[0]= k+'a'-1;ca[1]='\0';
             if(itimes==1){
               printf("#%1d%1d%d",i,j,k);
               fprintf(ficparo,"#%1d%1d%d",i,j,k);
             }else{
               printf("%1d%1d%d",i,j,k);
               fprintf(ficparo,"%1d%1d%d",i,j,k);
               /*  printf(" %.5le",matcov[i][j]); */
             }
             ll=0;
             for(li=1;li <=nlstate; li++){
               for(lj=1;lj <=nlstate+ndeath; lj++){
                 if(lj==li) continue;
                 for(lk=1;lk<=ncovmodel;lk++){
                   ll++;
                   if(ll<=jj){
                     cb[0]= lk +'a'-1;cb[1]='\0';
                     if(ll<jj){
                       if(itimes==1){
                         printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         fprintf(ficparo," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }else{
                       if(itimes==1){
                         printf(" Var(%s%1d%1d)",ca,i,j);
                         fprintf(ficparo," Var(%s%1d%1d)",ca,i,j);
                       }else{
                         printf(" 0.");
                         fprintf(ficparo," 0.");
                       }
                     }
                   }
                 } /* end lk */
               } /* end lj */
             } /* end li */
             printf("\n");
             fprintf(ficparo,"\n");
             numlinepar++;
           } /* end k*/
         } /*end j */
       } /* end i */
     } /* end itimes */
   
   } /* end of prwizard */
   /******************* Gompertz Likelihood ******************************/
   double gompertz(double x[])
   { 
     double A,B,L=0.0,sump=0.,num=0.;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
   
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agecens[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[1]/(x[2])*(exp(x[2]*(agedc[i]-agegomp))-exp(x[2]*(ageexmed[i]-agegomp)))
                +log(x[1]/YEARM)+x[2]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           L=L+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
    
     return -2*L*num/sump;
   }
   
   #ifdef GSL
   /******************* Gompertz_f Likelihood ******************************/
   double gompertz_f(const gsl_vector *v, void *params)
   { 
     double A,B,LL=0.0,sump=0.,num=0.;
     double *x= (double *) v->data;
     int i,n=0; /* n is the size of the sample */
   
     for (i=0;i<=imx-1 ; i++) {
       sump=sump+weight[i];
       /*    sump=sump+1;*/
       num=num+1;
     }
    
    
     /* for (i=0; i<=imx; i++) 
        if (wav[i]>0) printf("i=%d ageex=%lf agecens=%lf agedc=%lf cens=%d %d\n" ,i,ageexmed[i],agecens[i],agedc[i],cens[i],wav[i]);*/
     printf("x[0]=%lf x[1]=%lf\n",x[0],x[1]);
     for (i=1;i<=imx ; i++)
       {
         if (cens[i] == 1 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agecens[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)));
         
         if (cens[i] == 0 && wav[i]>1)
           A=-x[0]/(x[1])*(exp(x[1]*(agedc[i]-agegomp))-exp(x[1]*(ageexmed[i]-agegomp)))
                +log(x[0]/YEARM)+x[1]*(agedc[i]-agegomp)+log(YEARM);  
         
         /*if (wav[i] > 1 && agecens[i] > 15) {*/ /* ??? */
         if (wav[i] > 1 ) { /* ??? */
           LL=LL+A*weight[i];
           /*      printf("\ni=%d A=%f L=%lf x[1]=%lf x[2]=%lf ageex=%lf agecens=%lf cens=%d agedc=%lf weight=%lf\n",i,A,L,x[1],x[2],ageexmed[i]*12,agecens[i]*12,cens[i],agedc[i]*12,weight[i]);*/
         }
       }
   
    /*printf("x1=%2.9f x2=%2.9f x3=%2.9f L=%f\n",x[1],x[2],x[3],L);*/
     printf("x[0]=%lf x[1]=%lf -2*LL*num/sump=%lf\n",x[0],x[1],-2*LL*num/sump);
    
     return -2*LL*num/sump;
   }
   #endif
   
   /******************* Printing html file ***********/
   void printinghtmlmort(char fileres[], char title[], char datafile[], int firstpass, \
                     int lastpass, int stepm, int weightopt, char model[],\
                     int imx,  double p[],double **matcov,double agemortsup){
     int i,k;
   
     fprintf(fichtm,"<ul><li><h4>Result files </h4>\n Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):<br>");
     fprintf(fichtm,"  mu(age) =%lf*exp(%lf*(age-%d)) per year<br><br>",p[1],p[2],agegomp);
     for (i=1;i<=2;i++) 
       fprintf(fichtm," p[%d] = %lf [%f ; %f]<br>\n",i,p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
     fprintf(fichtm,"<br><br><img src=\"graphmort.png\">");
     fprintf(fichtm,"</ul>");
   
   fprintf(fichtm,"<ul><li><h4>Life table</h4>\n <br>");
   
    fprintf(fichtm,"\nAge   l<inf>x</inf>     q<inf>x</inf> d(x,x+1)    L<inf>x</inf>     T<inf>x</inf>     e<infx</inf><br>");
   
    for (k=agegomp;k<(agemortsup-2);k++) 
      fprintf(fichtm,"%d %.0lf %lf %.0lf %.0lf %.0lf %lf<br>\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
   
    
     fflush(fichtm);
   }
   
   /******************* Gnuplot file **************/
   void printinggnuplotmort(char fileres[], char optionfilefiname[], double ageminpar, double agemaxpar, double fage , char pathc[], double p[]){
   
     char dirfileres[132],optfileres[132];
     int m,cpt,k1,i,k,j,jk,k2,k3,ij,l;
     int ng;
   
   
     /*#ifdef windows */
     fprintf(ficgp,"cd \"%s\" \n",pathc);
       /*#endif */
   
   
     strcpy(dirfileres,optionfilefiname);
     strcpy(optfileres,"vpl");
     fprintf(ficgp,"set out \"graphmort.png\"\n "); 
     fprintf(ficgp,"set xlabel \"Age\"\n set ylabel \"Force of mortality (per year)\" \n "); 
     fprintf(ficgp, "set ter png small 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, j, n;
     int linei, month, year,iout;
     char line[MAXLINE], linetmp[MAXLINE];
     char stra[80], strb[80];
     char *stratrunc;
     int lstra;
   
   
     if((fic=fopen(datafile,"r"))==NULL)    {
       printf("Problem while opening datafile: %s\n", datafile);return 1;
       fprintf(ficlog,"Problem while opening datafile: %s\n", datafile);return 1;
     }
   
     i=1;
     linei=0;
     while ((fgets(line, MAXLINE, fic) != NULL) &&((i >= firstobs) && (i <=lastobs))) {
       linei=linei+1;
       for(j=strlen(line); j>=0;j--){  /* Untabifies line */
         if(line[j] == '\t')
           line[j] = ' ';
       }
       for(j=strlen(line)-1; (line[j]==' ')||(line[j]==10)||(line[j]==13);j--){
         ;
       };
       line[j+1]=0;  /* Trims blanks at end of line */
       if(line[0]=='#'){
         fprintf(ficlog,"Comment line\n%s\n",line);
         printf("Comment line\n%s\n",line);
         continue;
       }
       trimbb(linetmp,line); /* Trims multiple blanks in line */
       for (j=0; line[j]!='\0';j++){
         line[j]=linetmp[j];
       }
     
   
       for (j=maxwav;j>=1;j--){
         cutv(stra, strb, line, ' '); 
         if(strb[0]=='.') { /* Missing status */
           lval=-1;
         }else{
           errno=0;
           lval=strtol(strb,&endptr,10); 
         /*        if (errno == ERANGE && (lval == LONG_MAX || lval == LONG_MIN))*/
           if( strb[0]=='\0' || (*endptr != '\0')){
             printf("Error reading data around '%s' at line number %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 i1, 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);
   }
   
   
   /***********************************************/
   /**************** Main Program *****************/
   /***********************************************/
   
   int main(int argc, char *argv[])
   {
   #ifdef GSL
     const gsl_multimin_fminimizer_type *T;
     size_t iteri = 0, it;
     int rval = GSL_CONTINUE;
     int status = GSL_SUCCESS;
     double ssval;
   #endif
     int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
     int i,j, k, n=MAXN,iter,m,size=100,cptcode, cptcod;
     int linei, month, year,iout;
     int jj, ll, li, lj, lk, imk;
     int numlinepar=0; /* Current linenumber of parameter file */
     int itimes;
     int NDIM=2;
     int vpopbased=0;
   
     char ca[32], cb[32], cc[32];
     /*  FILE *fichtm; *//* Html File */
     /* FILE *ficgp;*/ /*Gnuplot File */
     struct stat info;
     double agedeb, agefin,hf;
     double ageminpar=1.e20,agemin=1.e20, agemaxpar=-1.e20, agemax=-1.e20;
   
     double fret;
     double **xi,tmp,delta;
   
     double dum; /* Dummy variable */
     double ***p3mat;
     double ***mobaverage;
     int *indx;
     char line[MAXLINE], linepar[MAXLINE];
     char path[MAXLINE],pathc[MAXLINE],pathcd[MAXLINE],pathtot[MAXLINE],model[MAXLINE];
     char pathr[MAXLINE], pathimach[MAXLINE]; 
     char **bp, *tok, *val; /* pathtot */
     int firstobs=1, lastobs=10;
     int sdeb, sfin; /* Status at beginning and end */
     int c,  h , cpt,l;
     int ju,jl, mi;
     int i1,j1, jk,aa,bb, stepsize, ij;
     int jnais,jdc,jint4,jint1,jint2,jint3,*tab; 
     int mobilavproj=0 , prevfcast=0 ; /* moving average of prev, If prevfcast=1 prevalence projection */
     int mobilav=0,popforecast=0;
     int hstepm, nhstepm;
     int agemortsup;
     float  sumlpop=0.;
     double jprev1=1, mprev1=1,anprev1=2000,jprev2=1, mprev2=1,anprev2=2000;
     double jpyram=1, mpyram=1,anpyram=2000,jpyram1=1, mpyram1=1,anpyram1=2000;
   
     double bage, fage, age, agelim, agebase;
     double ftolpl=FTOL;
     double **prlim;
     double ***param; /* Matrix of parameters */
     double  *p;
     double **matcov; /* Matrix of covariance */
     double ***delti3; /* Scale */
     double *delti; /* Scale */
     double ***eij, ***vareij;
     double **varpl; /* Variances of prevalence limits by age */
     double *epj, vepp;
     double kk1, kk2;
     double dateprev1, dateprev2,jproj1=1,mproj1=1,anproj1=2000,jproj2=1,mproj2=1,anproj2=2000;
     double **ximort;
     char *alph[]={"a","a","b","c","d","e"}, str[4]="1234";
     int *dcwave;
   
     char z[1]="c", occ;
   
     /*char  *strt;*/
     char strtend[80];
   
     long total_usecs;
    
   /*   setlocale (LC_ALL, ""); */
   /*   bindtextdomain (PACKAGE, LOCALEDIR); */
   /*   textdomain (PACKAGE); */
   /*   setlocale (LC_CTYPE, ""); */
   /*   setlocale (LC_MESSAGES, ""); */
   
     /*   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
     (void) gettimeofday(&start_time,&tzp);
     curr_time=start_time;
     tm = *localtime(&start_time.tv_sec);
     tmg = *gmtime(&start_time.tv_sec);
     strcpy(strstart,asctime(&tm));
   
   /*  printf("Localtime (at start)=%s",strstart); */
   /*  tp.tv_sec = tp.tv_sec +86400; */
   /*  tm = *localtime(&start_time.tv_sec); */
   /*   tmg.tm_year=tmg.tm_year +dsign*dyear; */
   /*   tmg.tm_mon=tmg.tm_mon +dsign*dmonth; */
   /*   tmg.tm_hour=tmg.tm_hour + 1; */
   /*   tp.tv_sec = mktime(&tmg); */
   /*   strt=asctime(&tmg); */
   /*   printf("Time(after) =%s",strstart);  */
   /*  (void) time (&time_value);
   *  printf("time=%d,t-=%d\n",time_value,time_value-86400);
   *  tm = *localtime(&time_value);
   *  strstart=asctime(&tm);
   *  printf("tim_value=%d,asctime=%s\n",time_value,strstart); 
   */
   
     nberr=0; /* Number of errors and warnings */
     nbwarn=0;
     getcwd(pathcd, size);
   
     printf("\n%s\n%s",version,fullversion);
     if(argc <=1){
       printf("\nEnter the parameter file name: ");
       fgets(pathr,FILENAMELENGTH,stdin);
       i=strlen(pathr);
       if(pathr[i-1]=='\n')
         pathr[i-1]='\0';
      for (tok = pathr; tok != NULL; ){
         printf("Pathr |%s|\n",pathr);
         while ((val = strsep(&tok, "\"" )) != NULL && *val == '\0');
         printf("val= |%s| pathr=%s\n",val,pathr);
         strcpy (pathtot, val);
         if(pathr[0] == '\0') break; /* Dirty */
       }
     }
     else{
       strcpy(pathtot,argv[1]);
     }
     /*if(getcwd(pathcd, MAXLINE)!= NULL)printf ("Error pathcd\n");*/
     /*cygwin_split_path(pathtot,path,optionfile);
       printf("pathtot=%s, path=%s, optionfile=%s\n",pathtot,path,optionfile);*/
     /* cutv(path,optionfile,pathtot,'\\');*/
   
     /* Split argv[0], imach program to get pathimach */
     printf("\nargv[0]=%s argv[1]=%s, \n",argv[0],argv[1]);
     split(argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
     printf("\nargv[0]=%s pathimach=%s, \noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",argv[0],pathimach,optionfile,optionfilext,optionfilefiname);
    /*   strcpy(pathimach,argv[0]); */
     /* Split argv[1]=pathtot, parameter file name to get path, optionfile, extension and name */
     split(pathtot,path,optionfile,optionfilext,optionfilefiname);
     printf("\npathtot=%s,\npath=%s,\noptionfile=%s \noptionfilext=%s \noptionfilefiname=%s\n",pathtot,path,optionfile,optionfilext,optionfilefiname);
     chdir(path); /* Can be a relative path */
     if(getcwd(pathcd,MAXLINE) > 0) /* So pathcd is the full path */
       printf("Current directory %s!\n",pathcd);
     strcpy(command,"mkdir ");
     strcat(command,optionfilefiname);
     if((outcmd=system(command)) != 0){
       printf("Problem creating directory or it already exists %s%s, err=%d\n",path,optionfilefiname,outcmd);
       /* fprintf(ficlog,"Problem creating directory %s%s\n",path,optionfilefiname); */
       /* fclose(ficlog); */
   /*     exit(1); */
     }
   /*   if((imk=mkdir(optionfilefiname))<0){ */
   /*     perror("mkdir"); */
   /*   } */
   
     /*-------- arguments in the command line --------*/
   
     /* Log file */
     strcat(filelog, optionfilefiname);
     strcat(filelog,".log");    /* */
     if((ficlog=fopen(filelog,"w"))==NULL)    {
       printf("Problem with logfile %s\n",filelog);
       goto end;
     }
     fprintf(ficlog,"Log filename:%s\n",filelog);
     fprintf(ficlog,"\n%s\n%s",version,fullversion);
     fprintf(ficlog,"\nEnter the parameter file name: \n");
     fprintf(ficlog,"pathimach=%s\npathtot=%s\n\
    path=%s \n\
    optionfile=%s\n\
    optionfilext=%s\n\
    optionfilefiname=%s\n",pathimach,pathtot,path,optionfile,optionfilext,optionfilefiname);
   
     printf("Local time (at start):%s",strstart);
     fprintf(ficlog,"Local time (at start): %s",strstart);
     fflush(ficlog);
   /*   (void) gettimeofday(&curr_time,&tzp); */
   /*   printf("Elapsed time %d\n", asc_diff_time(curr_time.tv_sec-start_time.tv_sec,tmpout)); */
   
     /* */
     strcpy(fileres,"r");
     strcat(fileres, optionfilefiname);
     strcat(fileres,".txt");    /* Other files have txt extension */
   
     /*---------arguments file --------*/
   
     if((ficpar=fopen(optionfile,"r"))==NULL)    {
       printf("Problem with optionfile '%s' 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");
   #elsedef
       printf("Powell\n");  fprintf(ficlog,"Powell\n");
   #endif
       strcpy(filerespow,"pow-mort"); 
       strcat(filerespow,fileres);
       if((ficrespow=fopen(filerespow,"w"))==NULL) {
         printf("Problem with resultfile: %s\n", filerespow);
         fprintf(ficlog,"Problem with resultfile: %s\n", filerespow);
       }
   #ifdef GSL
       fprintf(ficrespow,"# GSL optimization\n# iter -2*LL");
   #elsedef
       fprintf(ficrespow,"# Powell\n# iter -2*LL");
   #endif
       /*  for (i=1;i<=nlstate;i++)
           for(j=1;j<=nlstate+ndeath;j++)
           if(j!=i)fprintf(ficrespow," p%1d%1d",i,j);
       */
       fprintf(ficrespow,"\n");
   #ifdef GSL
       /* gsl starts here */ 
       T = gsl_multimin_fminimizer_nmsimplex;
       gsl_multimin_fminimizer *sfm = NULL;
       gsl_vector *ss, *x;
       gsl_multimin_function minex_func;
   
       /* Initial vertex size vector */
       ss = gsl_vector_alloc (NDIM);
       
       if (ss == NULL){
         GSL_ERROR_VAL ("failed to allocate space for ss", GSL_ENOMEM, 0);
       }
       /* Set all step sizes to 1 */
       gsl_vector_set_all (ss, 0.001);
   
       /* Starting point */
       
       x = gsl_vector_alloc (NDIM);
       
       if (x == NULL){
         gsl_vector_free(ss);
         GSL_ERROR_VAL ("failed to allocate space for x", GSL_ENOMEM, 0);
       }
     
       /* Initialize method and iterate */
       /*     p[1]=0.0268; p[NDIM]=0.083; */
   /*     gsl_vector_set(x, 0, 0.0268); */
   /*     gsl_vector_set(x, 1, 0.083); */
       gsl_vector_set(x, 0, p[1]);
       gsl_vector_set(x, 1, p[2]);
   
       minex_func.f = &gompertz_f;
       minex_func.n = NDIM;
       minex_func.params = (void *)&p; /* ??? */
       
       sfm = gsl_multimin_fminimizer_alloc (T, NDIM);
       gsl_multimin_fminimizer_set (sfm, &minex_func, x, ss);
       
       printf("Iterations beginning .....\n\n");
       printf("Iter. #    Intercept       Slope     -Log Likelihood     Simplex size\n");
   
       iteri=0;
       while (rval == GSL_CONTINUE){
         iteri++;
         status = gsl_multimin_fminimizer_iterate(sfm);
         
         if (status) printf("error: %s\n", gsl_strerror (status));
         fflush(0);
         
         if (status) 
           break;
         
         rval = gsl_multimin_test_size (gsl_multimin_fminimizer_size (sfm), 1e-6);
         ssval = gsl_multimin_fminimizer_size (sfm);
         
         if (rval == GSL_SUCCESS)
           printf ("converged to a local maximum at\n");
         
         printf("%5d ", iteri);
         for (it = 0; it < NDIM; it++){
           printf ("%10.5f ", gsl_vector_get (sfm->x, it));
         }
         printf("f() = %-10.5f ssize = %.7f\n", sfm->fval, ssval);
       }
       
       printf("\n\n Please note: Program should be run many times with varying starting points to detemine global maximum\n\n");
       
       gsl_vector_free(x); /* initial values */
       gsl_vector_free(ss); /* inital step size */
       for (it=0; it<NDIM; it++){
         p[it+1]=gsl_vector_get(sfm->x,it);
         fprintf(ficrespow," %.12lf", p[it]);
       }
       gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1)  */
   #endif
   #ifdef POWELL
        powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz);
   #endif  
       fclose(ficrespow);
       
       hesscov(matcov, p, NDIM, delti, 1e-4, gompertz); 
   
       for(i=1; i <=NDIM; i++)
         for(j=i+1;j<=NDIM;j++)
           matcov[i][j]=matcov[j][i];
       
       printf("\nCovariance matrix\n ");
       for(i=1; i <=NDIM; i++) {
         for(j=1;j<=NDIM;j++){ 
           printf("%f ",matcov[i][j]);
         }
         printf("\n ");
       }
       
       printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
       for (i=1;i<=NDIM;i++) 
         printf("%f [%f ; %f]\n",p[i],p[i]-2*sqrt(matcov[i][i]),p[i]+2*sqrt(matcov[i][i]));
   
       lsurv=vector(1,AGESUP);
       lpop=vector(1,AGESUP);
       tpop=vector(1,AGESUP);
       lsurv[agegomp]=100000;
       
       for (k=agegomp;k<=AGESUP;k++) {
         agemortsup=k;
         if (p[1]*exp(p[2]*(k-agegomp))>1) break;
       }
       
       for (k=agegomp;k<agemortsup;k++)
         lsurv[k+1]=lsurv[k]-lsurv[k]*(p[1]*exp(p[2]*(k-agegomp)));
       
       for (k=agegomp;k<agemortsup;k++){
         lpop[k]=(lsurv[k]+lsurv[k+1])/2.;
         sumlpop=sumlpop+lpop[k];
       }
       
       tpop[agegomp]=sumlpop;
       for (k=agegomp;k<(agemortsup-3);k++){
         /*  tpop[k+1]=2;*/
         tpop[k+1]=tpop[k]-lpop[k];
       }
       
       
       printf("\nAge   lx     qx    dx    Lx     Tx     e(x)\n");
       for (k=agegomp;k<(agemortsup-2);k++) 
         printf("%d %.0lf %lf %.0lf %.0lf %.0lf %lf\n",k,lsurv[k],p[1]*exp(p[2]*(k-agegomp)),(p[1]*exp(p[2]*(k-agegomp)))*lsurv[k],lpop[k],tpop[k],tpop[k]/lsurv[k]);
       
       
       replace_back_to_slash(pathc,pathcd); /* Even gnuplot wants a / */
       printinggnuplotmort(fileres, optionfilefiname,ageminpar,agemaxpar,fage, pathc,p);
       
       printinghtmlmort(fileres,title,datafile, firstpass, lastpass, \
                        stepm, weightopt,\
                        model,imx,p,matcov,agemortsup);
       
       free_vector(lsurv,1,AGESUP);
       free_vector(lpop,1,AGESUP);
       free_vector(tpop,1,AGESUP);
   #ifdef GSL
       free_ivector(cens,1,n);
       free_vector(agecens,1,n);
       free_ivector(dcwave,1,n);
       free_matrix(ximort,1,NDIM,1,NDIM);
   #endif
     } /* Endof if mle==-3 */
     
     else{ /* For mle >=1 */
       globpr=0;/* debug */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("First Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       globpr=1; /* to print the contributions */
       likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
       printf("Second Likeli=%12.6f ipmx=%ld sw=%12.6f",fretone,ipmx,sw);
       for (k=1; k<=npar;k++)
         printf(" %d %8.5f",k,p[k]);
       printf("\n");
       if(mle>=1){ /* Could be 1 or 2 */
         mlikeli(ficres,p, npar, ncovmodel, nlstate, ftol, func);
       }
       
       /*--------- results files --------------*/
       fprintf(ficres,"title=%s datafile=%s lastobs=%d firstpass=%d lastpass=%d\nftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle= 0 weight=%d\nmodel=%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate, ndeath, maxwav, weightopt,model);
       
       
       fprintf(ficres,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       printf("# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       fprintf(ficlog,"# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ...\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(k=1; k <=(nlstate+ndeath); k++){
           if (k != i) {
             printf("%d%d ",i,k);
             fprintf(ficlog,"%d%d ",i,k);
             fprintf(ficres,"%1d%1d ",i,k);
             for(j=1; j <=ncovmodel; j++){
               printf("%lf ",p[jk]);
               fprintf(ficlog,"%lf ",p[jk]);
               fprintf(ficres,"%lf ",p[jk]);
               jk++; 
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       if(mle!=0){
         /* Computing hessian and covariance matrix */
         ftolhess=ftol; /* Usually correct */
         hesscov(matcov, p, npar, delti, ftolhess, func);
       }
       fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
       printf("# Scales (for hessian or gradient estimation)\n");
       fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
       for(i=1,jk=1; i <=nlstate; i++){
         for(j=1; j <=nlstate+ndeath; j++){
           if (j!=i) {
             fprintf(ficres,"%1d%1d",i,j);
             printf("%1d%1d",i,j);
             fprintf(ficlog,"%1d%1d",i,j);
             for(k=1; k<=ncovmodel;k++){
               printf(" %.5e",delti[jk]);
               fprintf(ficlog," %.5e",delti[jk]);
               fprintf(ficres," %.5e",delti[jk]);
               jk++;
             }
             printf("\n");
             fprintf(ficlog,"\n");
             fprintf(ficres,"\n");
           }
         }
       }
       
       fprintf(ficres,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       if(mle>=1)
         printf("# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       fprintf(ficlog,"# Covariance matrix \n# 121 Var(a12)\n# 122 Cov(b12,a12) Var(b12)\n#   ...\n# 232 Cov(b23,a12)  Cov(b23,b12) ... Var (b23)\n");
       /* # 121 Var(a12)\n\ */
       /* # 122 Cov(b12,a12) Var(b12)\n\ */
       /* # 131 Cov(a13,a12) Cov(a13,b12, Var(a13)\n\ */
       /* # 132 Cov(b13,a12) Cov(b13,b12, Cov(b13,a13) Var(b13)\n\ */
       /* # 212 Cov(a21,a12) Cov(a21,b12, Cov(a21,a13) Cov(a21,b13) Var(a21)\n\ */
       /* # 212 Cov(b21,a12) Cov(b21,b12, Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21)\n\ */
       /* # 232 Cov(a23,a12) Cov(a23,b12, Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23)\n\ */
       /* # 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23)\n" */
       
       
       /* Just to have a covariance matrix which will be more understandable
          even is we still don't want to manage dictionary of variables
       */
       for(itimes=1;itimes<=2;itimes++){
         jj=0;
         for(i=1; i <=nlstate; i++){
           for(j=1; j <=nlstate+ndeath; j++){
             if(j==i) continue;
             for(k=1; k<=ncovmodel;k++){
               jj++;
               ca[0]= k+'a'-1;ca[1]='\0';
               if(itimes==1){
                 if(mle>=1)
                   printf("#%1d%1d%d",i,j,k);
                 fprintf(ficlog,"#%1d%1d%d",i,j,k);
                 fprintf(ficres,"#%1d%1d%d",i,j,k);
               }else{
                 if(mle>=1)
                   printf("%1d%1d%d",i,j,k);
                 fprintf(ficlog,"%1d%1d%d",i,j,k);
                 fprintf(ficres,"%1d%1d%d",i,j,k);
               }
               ll=0;
               for(li=1;li <=nlstate; li++){
                 for(lj=1;lj <=nlstate+ndeath; lj++){
                   if(lj==li) continue;
                   for(lk=1;lk<=ncovmodel;lk++){
                     ll++;
                     if(ll<=jj){
                       cb[0]= lk +'a'-1;cb[1]='\0';
                       if(ll<jj){
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficlog," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                           fprintf(ficres," Cov(%s%1d%1d,%s%1d%1d)",ca,i,j,cb, li,lj);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }else{
                         if(itimes==1){
                           if(mle>=1)
                             printf(" Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficlog," Var(%s%1d%1d)",ca,i,j);
                           fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                         }else{
                           if(mle>=1)
                             printf(" %.5e",matcov[jj][ll]); 
                           fprintf(ficlog," %.5e",matcov[jj][ll]); 
                           fprintf(ficres," %.5e",matcov[jj][ll]); 
                         }
                       }
                     }
                   } /* end lk */
                 } /* end lj */
               } /* end li */
               if(mle>=1)
                 printf("\n");
               fprintf(ficlog,"\n");
               fprintf(ficres,"\n");
               numlinepar++;
             } /* end k*/
           } /*end j */
         } /* end i */
       } /* end itimes */
       
       fflush(ficlog);
       fflush(ficres);
       
       while((c=getc(ficpar))=='#' && c!= EOF){
         ungetc(c,ficpar);
         fgets(line, MAXLINE, ficpar);
         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 */
             varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart);
             fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");
             if(vpopbased==1)
               fprintf(ficrest,"the age specific prevalence observed (cross-sectionally) in the population i.e cross-sectionally\n in each health state (popbased=1) (mobilav=%d)\n",mobilav);
             else
               fprintf(ficrest,"the age specific period (stable) prevalences in each health state \n");
             fprintf(ficrest,"# Age e.. (std) ");
             for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
             fprintf(ficrest,"\n");
   
             epj=vector(1,nlstate+1);
             for(age=bage; age <=fage ;age++){
               prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);
               if (vpopbased==1) {
                 if(mobilav ==0){
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=probs[(int)age][i][k];
                 }else{ /* mobilav */ 
                   for(i=1; i<=nlstate;i++)
                     prlim[i][i]=mobaverage[(int)age][i][k];
                 }
               }
           
               fprintf(ficrest," %4.0f",age);
               for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                 for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   epj[j] += prlim[i][i]*eij[i][j][(int)age];
                   /*  printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/
                 }
                 epj[nlstate+1] +=epj[j];
               }
   
               for(i=1, vepp=0.;i <=nlstate;i++)
                 for(j=1;j <=nlstate;j++)
                   vepp += vareij[i][j][(int)age];
               fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp));
               for(j=1;j <=nlstate;j++){
                 fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age]));
               }
               fprintf(ficrest,"\n");
             }
           }
           free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
           free_vector(epj,1,nlstate+1);
         /*}*/
       }
       free_vector(weight,1,n);
       free_imatrix(Tvard,1,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);
     tm = *localtime(&end_time.tv_sec);
     tmg = *gmtime(&end_time.tv_sec);
     strcpy(strtend,asctime(&tm));
     printf("Local time at start %s\nLocal time at end   %s",strstart, strtend); 
     fprintf(ficlog,"Local time at start %s\nLocal time at end   %s\n",strstart, strtend); 
     printf("Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
   
     printf("Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     fprintf(ficlog,"Total time used %s\n", asc_diff_time(end_time.tv_sec -start_time.tv_sec,tmpout));
     fprintf(ficlog,"Total time was %ld Sec.\n", end_time.tv_sec -start_time.tv_sec);
     /*  printf("Total time was %d uSec.\n", total_usecs);*/
   /*   if(fileappend(fichtm,optionfilehtm)){ */
     fprintf(fichtm,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtm);
     fprintf(fichtmcov,"<br>Local time at start %s<br>Local time at end   %s<br>\n</body></html>",strstart, strtend);
     fclose(fichtmcov);
     fclose(ficgp);
     fclose(ficlog);
     /*------ End -----------*/
   
   
      printf("Before Current directory %s!\n",pathcd);
      if(chdir(pathcd) != 0)
       printf("Can't move to directory %s!\n",path);
     if(getcwd(pathcd,MAXLINE) > 0)
       printf("Current directory %s!\n",pathcd);
     /*strcat(plotcmd,CHARSEPARATOR);*/
     sprintf(plotcmd,"gnuplot");
   #ifndef UNIX
     sprintf(plotcmd,"\"%sgnuplot.exe\"",pathimach);
   #endif
     if(!stat(plotcmd,&info)){
       printf("Error 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(" Successul, 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 OSX
         sprintf(pplotcmd, "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.1.2  
changed lines
  Added in v.1.155


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