Diff for /imach/src/imach.c between versions 1.202 and 1.203

version 1.202, 2015/09/22 19:45:16 version 1.203, 2015/09/30 17:45:14
Line 1 Line 1
 /* $Id$  /* $Id$
   $State$    $State$
   $Log$    $Log$
     Revision 1.203  2015/09/30 17:45:14  brouard
     Summary: looking at better estimation of the hessian
   
     Also a better criteria for convergence to the period prevalence And
     therefore adding the number of years needed to converge. (The
     prevalence in any alive state shold sum to one
   
   Revision 1.202  2015/09/22 19:45:16  brouard    Revision 1.202  2015/09/22 19:45:16  brouard
   Summary: Adding some overall graph on contribution to likelihood. Might change    Summary: Adding some overall graph on contribution to likelihood. Might change
   
Line 647 Line 654
   
 /* #define DEBUG */  /* #define DEBUG */
 /* #define DEBUGBRENT */  /* #define DEBUGBRENT */
 #define DEBUGLINMIN  /* #define DEBUGLINMIN */
   /* #define DEBUGHESS */
   #define DEBUGHESSIJ
   /* #define LINMINORIGINAL  /\* Don't use loop on scale in linmin (accepting nan)*\/ */
 #define POWELL /* Instead of NLOPT */  #define POWELL /* Instead of NLOPT */
 #define POWELLF1F3 /* Skip test */  #define POWELLF1F3 /* Skip test */
 /* #define POWELLORIGINAL /\* Don't use Directest to decide new direction but original Powell test *\/ */  /* #define POWELLORIGINAL /\* Don't use Directest to decide new direction but original Powell test *\/ */
Line 1602  void linmin(double p[], double xi[], int Line 1612  void linmin(double p[], double xi[], int
   double xx,xmin,bx,ax;     double xx,xmin,bx,ax; 
   double fx,fb,fa;    double fx,fb,fa;
   
   double scale=10., axs, xxs, xxss; /* Scale added for infinity */  #ifdef LINMINORIGINAL
    #else
     double scale=10., axs, xxs; /* Scale added for infinity */
   #endif
     
   ncom=n;     ncom=n; 
   pcom=vector(1,n);     pcom=vector(1,n); 
   xicom=vector(1,n);     xicom=vector(1,n); 
Line 1613  void linmin(double p[], double xi[], int Line 1626  void linmin(double p[], double xi[], int
     xicom[j]=xi[j]; /* Former scale xi[j] of currrent direction i */      xicom[j]=xi[j]; /* Former scale xi[j] of currrent direction i */
   }     } 
   
   /* axs=0.0; */  #ifdef LINMINORIGINAL
   /* xxss=1; /\* 1 and using scale *\/ */    xx=1.;
   xxs=1;  #else
   /* do{ */    axs=0.0;
     ax=0.;    xxs=1.;
     do{
     xx= xxs;      xx= xxs;
   #endif
       ax=0.;
     mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  /* Outputs: xtx[j]=pcom[j]+(*xx)*xicom[j]; fx=f(xtx[j]) */      mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim);  /* Outputs: xtx[j]=pcom[j]+(*xx)*xicom[j]; fx=f(xtx[j]) */
     /* brackets with inputs ax=0 and xx=1, but points, pcom=p, and directions values, xicom=xi, are sent via f1dim(x) */      /* brackets with inputs ax=0 and xx=1, but points, pcom=p, and directions values, xicom=xi, are sent via f1dim(x) */
     /* xt[x,j]=pcom[j]+x*xicom[j]  f(ax) = f(xt(a,j=1,n)) = f(p(j) + 0 * xi(j)) and  f(xx) = f(xt(x, j=1,n)) = f(p(j) + 1 * xi(j))   */      /* xt[x,j]=pcom[j]+x*xicom[j]  f(ax) = f(xt(a,j=1,n)) = f(p(j) + 0 * xi(j)) and  f(xx) = f(xt(x, j=1,n)) = f(p(j) + 1 * xi(j))   */
Line 1626  void linmin(double p[], double xi[], int Line 1642  void linmin(double p[], double xi[], int
     /* Given input ax=axs and xx=xxs, xx might be too far from ax to get a finite f(xx) */      /* Given input ax=axs and xx=xxs, xx might be too far from ax to get a finite f(xx) */
     /* Searches on line, outputs (ax, xx, bx) such that fx < min(fa and fb) */      /* Searches on line, outputs (ax, xx, bx) such that fx < min(fa and fb) */
     /* Find a bracket a,x,b in direction n=xi ie xicom, order may change. Scale is [0:xxs*xi[j]] et non plus  [0:xi[j]]*/      /* Find a bracket a,x,b in direction n=xi ie xicom, order may change. Scale is [0:xxs*xi[j]] et non plus  [0:xi[j]]*/
   /*   if (fx != fx){ */  #ifdef LINMINORIGINAL
   /*    xxs=xxs/scale; /\* Trying a smaller xx, closer to initial ax=0 *\/ */  #else
   /*    printf("\nLinmin NAN : input [axs=%lf:xxs=%lf], mnbrak outputs fx=%lf <(fb=%lf and fa=%lf) with xx=%lf in [ax=%lf:bx=%lf] \n",  axs, xxs, fx,fb, fa, xx, ax, bx); */      if (fx != fx){
   /*   } */          xxs=xxs/scale; /* Trying a smaller xx, closer to initial ax=0 */
   /* }while(fx != fx); */          printf("|");
           fprintf(ficlog,"|");
   #ifdef DEBUGLINMIN
           printf("\nLinmin NAN : input [axs=%lf:xxs=%lf], mnbrak outputs fx=%lf <(fb=%lf and fa=%lf) with xx=%lf in [ax=%lf:bx=%lf] \n",  axs, xxs, fx,fb, fa, xx, ax, bx);
   #endif
       }
     }while(fx != fx);
   #endif
     
 #ifdef DEBUGLINMIN  #ifdef DEBUGLINMIN
   printf("\nLinmin after mnbrak: ax=%12.7f xx=%12.7f bx=%12.7f fa=%12.2f fx=%12.2f fb=%12.2f\n",  ax,xx,bx,fa,fx,fb);    printf("\nLinmin after mnbrak: ax=%12.7f xx=%12.7f bx=%12.7f fa=%12.2f fx=%12.2f fb=%12.2f\n",  ax,xx,bx,fa,fx,fb);
   fprintf(ficlog,"\nLinmin after mnbrak: ax=%12.7f xx=%12.7f bx=%12.7f fa=%12.2f fx=%12.2f fb=%12.2f\n",  ax,xx,bx,fa,fx,fb);    fprintf(ficlog,"\nLinmin after mnbrak: ax=%12.7f xx=%12.7f bx=%12.7f fa=%12.2f fx=%12.2f fb=%12.2f\n",  ax,xx,bx,fa,fx,fb);
Line 1650  void linmin(double p[], double xi[], int Line 1673  void linmin(double p[], double xi[], int
   fprintf(ficlog,"linmin end ");    fprintf(ficlog,"linmin end ");
 #endif  #endif
   for (j=1;j<=n;j++) {     for (j=1;j<=n;j++) { 
     /* printf(" before xi[%d]=%12.8f", j,xi[j]); */  #ifdef LINMINORIGINAL
     xi[j] *= xmin; /* xi rescaled by xmin: if xmin=-1.237 and xi=(1,0,...,0) xi=(-1.237,0,...,0) */      xi[j] *= xmin; 
     /* if(xxs <1.0) */  #else
     /*   printf(" after xi[%d]=%12.8f, xmin=%12.8f, ax=%12.8f, xx=%12.8f, bx=%12.8f, xxs=%12.8f", j,xi[j], xmin, ax, xx, bx,xxs ); */  #ifdef DEBUGLINMIN
       if(xxs <1.0)
         printf(" before xi[%d]=%12.8f", j,xi[j]);
   #endif
       xi[j] *= xmin*xxs; /* xi rescaled by xmin and number of loops: if xmin=-1.237 and xi=(1,0,...,0) xi=(-1.237,0,...,0) */
   #ifdef DEBUGLINMIN
       if(xxs <1.0)
         printf(" after xi[%d]=%12.8f, xmin=%12.8f, ax=%12.8f, xx=%12.8f, bx=%12.8f, xxs=%12.8f", j,xi[j], xmin, ax, xx, bx,xxs );
   #endif
   #endif
     p[j] += xi[j]; /* Parameters values are updated accordingly */      p[j] += xi[j]; /* Parameters values are updated accordingly */
   }     } 
   /* printf("\n"); */  
 #ifdef DEBUGLINMIN  #ifdef DEBUGLINMIN
     printf("\n");
   printf("Comparing last *frec(xmin=%12.8f)=%12.8f from Brent and frec(0.)=%12.8f \n", xmin, *fret, (*func)(p));    printf("Comparing last *frec(xmin=%12.8f)=%12.8f from Brent and frec(0.)=%12.8f \n", xmin, *fret, (*func)(p));
   fprintf(ficlog,"Comparing last *frec(xmin=%12.8f)=%12.8f from Brent and frec(0.)=%12.8f \n", xmin, *fret, (*func)(p));    fprintf(ficlog,"Comparing last *frec(xmin=%12.8f)=%12.8f from Brent and frec(0.)=%12.8f \n", xmin, *fret, (*func)(p));
   for (j=1;j<=n;j++) {     for (j=1;j<=n;j++) { 
Line 1668  void linmin(double p[], double xi[], int Line 1700  void linmin(double p[], double xi[], int
       fprintf(ficlog,"\n");        fprintf(ficlog,"\n");
     }      }
   }    }
   #else
 #endif  #endif
   free_vector(xicom,1,n);     free_vector(xicom,1,n); 
   free_vector(pcom,1,n);     free_vector(pcom,1,n); 
Line 1745  void powell(double p[], double **xi, int Line 1778  void powell(double p[], double **xi, int
       for (j=1;j<=n;j++) xit[j]=xi[j][i]; /* Directions stored from previous iteration with previous scales */        for (j=1;j<=n;j++) xit[j]=xi[j][i]; /* Directions stored from previous iteration with previous scales */
       fptt=(*fret);         fptt=(*fret); 
 #ifdef DEBUG  #ifdef DEBUG
           printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);        printf("fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
           fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);        fprintf(ficlog, "fret=%lf, %lf, %lf \n", *fret, *fret, *fret);
 #endif  #endif
           printf("%d",i);fflush(stdout); /* print direction (parameter) i */        printf("%d",i);fflush(stdout); /* print direction (parameter) i */
       fprintf(ficlog,"%d",i);fflush(ficlog);        fprintf(ficlog,"%d",i);fflush(ficlog);
       linmin(p,xit,n,fret,func); /* Point p[n]. xit[n] has been loaded for direction i as input.*/        linmin(p,xit,n,fret,func); /* Point p[n]. xit[n] has been loaded for direction i as input.*/
                                     /* Outputs are fret(new point p) p is updated and xit rescaled */                                      /* Outputs are fret(new point p) p is updated and xit rescaled */
Line 1917  void powell(double p[], double **xi, int Line 1950  void powell(double p[], double **xi, int
   
 /**** Prevalence limit (stable or period prevalence)  ****************/  /**** Prevalence limit (stable or period prevalence)  ****************/
   
 double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int ij)  double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl, int *ncvyear, int ij)
 {  {
   /* Computes the prevalence limit in each live state at age x by left multiplying the unit    /* Computes the prevalence limit in each live state at age x by left multiplying the unit
      matrix by transitions matrix until convergence is reached */       matrix by transitions matrix until convergence is reached with precision ftolpl */
       
   int i, ii,j,k;    int i, ii,j,k;
   double min, max, maxmin, maxmax,sumnew=0.;    double min, max, maxmin, maxmax,sumnew=0.;
Line 1928  double **prevalim(double **prlim, int nl Line 1961  double **prevalim(double **prlim, int nl
   double **out, cov[NCOVMAX+1], **pmij();    double **out, cov[NCOVMAX+1], **pmij();
   double **newm;    double **newm;
   double agefin, delaymax=100 ; /* Max number of years to converge */    double agefin, delaymax=100 ; /* Max number of years to converge */
   long int ncvyear=0, ncvloop=0;    int ncvloop=0;
       
   for (ii=1;ii<=nlstate+ndeath;ii++)    for (ii=1;ii<=nlstate+ndeath;ii++)
     for (j=1;j<=nlstate+ndeath;j++){      for (j=1;j<=nlstate+ndeath;j++){
Line 1979  double **prevalim(double **prlim, int nl Line 2012  double **prevalim(double **prlim, int nl
         min=FMIN(min,prlim[i][j]);          min=FMIN(min,prlim[i][j]);
         /* printf(" age= %d prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d max=%f min=%f\n", (int)age, i, j, i, j, prlim[i][j],(int)agefin, max, min); */          /* printf(" age= %d prevalim i=%d, j=%d, prmlim[%d][%d]=%f, agefin=%d max=%f min=%f\n", (int)age, i, j, i, j, prlim[i][j],(int)agefin, max, min); */
       }        }
       maxmin=max-min;        maxmin=(max-min)/(max+min)*2;
       maxmax=FMAX(maxmax,maxmin);        maxmax=FMAX(maxmax,maxmin);
     } /* j loop */      } /* j loop */
       *ncvyear= (int)age- (int)agefin;
       /* printf("maxmax=%lf maxmin=%lf ncvloop=%ld, age=%d, agefin=%d ncvyear=%d \n", maxmax, maxmin, ncvloop, (int)age, (int)agefin, *ncvyear); */
     if(maxmax < ftolpl){      if(maxmax < ftolpl){
       /* printf("maxmax=%lf maxmin=%lf ncvloop=%ld, ncvyear=%d \n", maxmax, maxmin, ncvloop, (int)age-(int)agefin); */        /* printf("maxmax=%lf maxmin=%lf ncvloop=%ld, age=%d, agefin=%d ncvyear=%d \n", maxmax, maxmin, ncvloop, (int)age, (int)agefin, *ncvyear); */
       return prlim;        return prlim;
     }      }
   } /* age loop */    } /* age loop */
   printf("Warning: the stable prevalence did not converge with the required precision ftolpl=6*10^5*ftol=%g. \n\    printf("Warning: the stable prevalence at age %d did not converge with the required precision %g > ftolpl=%g. \n\
 Earliest age to start was %d-%d=%d, ncvloop=%ld, ncvyear=%d\n\  Earliest age to start was %d-%d=%d, ncvloop=%d, ncvyear=%d\n", (int)age, maxmax, ftolpl, (int)age, (int)delaymax, (int)agefin, ncvloop, *ncvyear);
 Try to lower 'ftol', for example from 1.e-8 to 6.e-9.\n", ftolpl, (int)age, (int)delaymax, (int)agefin, ncvloop, (int)age-(int)agefin);  /* Try to lower 'ftol', for example from 1.e-8 to 6.e-9.\n", ftolpl, (int)age, (int)delaymax, (int)agefin, ncvloop, (int)age-(int)agefin); */
   return prlim; /* should not reach here */    return prlim; /* should not reach here */
 }  }
   
Line 2694  void mlikeli(FILE *ficres,double p[], in Line 2729  void mlikeli(FILE *ficres,double p[], in
 #endif  #endif
   free_matrix(xi,1,npar,1,npar);    free_matrix(xi,1,npar,1,npar);
   fclose(ficrespow);    fclose(ficrespow);
   printf("#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));    printf("\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   fprintf(ficlog,"#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));    fprintf(ficlog,"\n#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   fprintf(ficres,"#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));    fprintf(ficres,"#Number of iterations & function calls = %d & %d, -2 Log likelihood = %.12f\n",iter, countcallfunc,func(p));
   
 }  }
   
 /**** Computes Hessian and covariance matrix ***/  /**** Computes Hessian and covariance matrix ***/
 void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))  void hesscov(double **matcov, double **hess, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
 {  {
   double  **a,**y,*x,pd;    double  **a,**y,*x,pd;
   double **hess;    /* double **hess; */
   int i, j;    int i, j;
   int *indx;    int *indx;
   
   double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);    double hessii(double p[], double delta, int theta, double delti[],double (*func)(double []),int npar);
   double hessij(double p[], double delti[], int i, int j,double (*func)(double []),int npar);    double hessij(double p[], double **hess, double delti[], int i, int j,double (*func)(double []),int npar);
   void lubksb(double **a, int npar, int *indx, double b[]) ;    void lubksb(double **a, int npar, int *indx, double b[]) ;
   void ludcmp(double **a, int npar, int *indx, double *d) ;    void ludcmp(double **a, int npar, int *indx, double *d) ;
   double gompertz(double p[]);    double gompertz(double p[]);
   hess=matrix(1,npar,1,npar);    /* hess=matrix(1,npar,1,npar); */
   
   printf("\nCalculation of the hessian matrix. Wait...\n");    printf("\nCalculation of the hessian matrix. Wait...\n");
   fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");    fprintf(ficlog,"\nCalculation of the hessian matrix. Wait...\n");
   for (i=1;i<=npar;i++){    for (i=1;i<=npar;i++){
     printf("%d",i);fflush(stdout);      printf("%d-",i);fflush(stdout);
     fprintf(ficlog,"%d",i);fflush(ficlog);      fprintf(ficlog,"%d-",i);fflush(ficlog);
         
      hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);       hess[i][i]=hessii(p,ftolhess,i,delti,func,npar);
           
Line 2730  void hesscov(double **matcov, double p[] Line 2765  void hesscov(double **matcov, double p[]
   for (i=1;i<=npar;i++) {    for (i=1;i<=npar;i++) {
     for (j=1;j<=npar;j++)  {      for (j=1;j<=npar;j++)  {
       if (j>i) {         if (j>i) { 
         printf(".%d%d",i,j);fflush(stdout);          printf(".%d-%d",i,j);fflush(stdout);
         fprintf(ficlog,".%d%d",i,j);fflush(ficlog);          fprintf(ficlog,".%d-%d",i,j);fflush(ficlog);
         hess[i][j]=hessij(p,delti,i,j,func,npar);          hess[i][j]=hessij(p,hess, delti,i,j,func,npar);
                   
         hess[j][i]=hess[i][j];              hess[j][i]=hess[i][j];    
         /*printf(" %lf ",hess[i][j]);*/          /*printf(" %lf ",hess[i][j]);*/
Line 2766  void hesscov(double **matcov, double p[] Line 2801  void hesscov(double **matcov, double p[]
   fprintf(ficlog,"\n#Hessian matrix#\n");    fprintf(ficlog,"\n#Hessian matrix#\n");
   for (i=1;i<=npar;i++) {     for (i=1;i<=npar;i++) { 
     for (j=1;j<=npar;j++) {       for (j=1;j<=npar;j++) { 
       printf("%.3e ",hess[i][j]);        printf("%.6e ",hess[i][j]);
       fprintf(ficlog,"%.3e ",hess[i][j]);        fprintf(ficlog,"%.6e ",hess[i][j]);
     }      }
     printf("\n");      printf("\n");
     fprintf(ficlog,"\n");      fprintf(ficlog,"\n");
   }    }
   
     /* printf("\n#Covariance matrix#\n"); */
     /* fprintf(ficlog,"\n#Covariance matrix#\n"); */
     /* for (i=1;i<=npar;i++) {  */
     /*   for (j=1;j<=npar;j++) {  */
     /*     printf("%.6e ",matcov[i][j]); */
     /*     fprintf(ficlog,"%.6e ",matcov[i][j]); */
     /*   } */
     /*   printf("\n"); */
     /*   fprintf(ficlog,"\n"); */
     /* } */
   
   /* Recompute Inverse */    /* Recompute Inverse */
   for (i=1;i<=npar;i++)    /* for (i=1;i<=npar;i++) */
     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];    /*   for (j=1;j<=npar;j++) a[i][j]=matcov[i][j]; */
   ludcmp(a,npar,indx,&pd);    /* ludcmp(a,npar,indx,&pd); */
   
     /*  printf("\n#Hessian matrix recomputed#\n"); */
   
     /* for (j=1;j<=npar;j++) { */
     /*   for (i=1;i<=npar;i++) x[i]=0; */
     /*   x[j]=1; */
     /*   lubksb(a,npar,indx,x); */
     /*   for (i=1;i<=npar;i++){  */
     /*     y[i][j]=x[i]; */
     /*     printf("%.3e ",y[i][j]); */
     /*     fprintf(ficlog,"%.3e ",y[i][j]); */
     /*   } */
     /*   printf("\n"); */
     /*   fprintf(ficlog,"\n"); */
     /* } */
   
     /* Verifying the inverse matrix */
   #ifdef DEBUGHESS
     y=matprod2(y,hess,1,npar,1,npar,1,npar,matcov);
   
   /*  printf("\n#Hessian matrix recomputed#\n");     printf("\n#Verification: multiplying the matrix of covariance by the Hessian matrix, should be unity:#\n");
      fprintf(ficlog,"\n#Verification: multiplying the matrix of covariance by the Hessian matrix. Should be unity:#\n");
   
   for (j=1;j<=npar;j++) {    for (j=1;j<=npar;j++) {
     for (i=1;i<=npar;i++) x[i]=0;  
     x[j]=1;  
     lubksb(a,npar,indx,x);  
     for (i=1;i<=npar;i++){       for (i=1;i<=npar;i++){ 
       y[i][j]=x[i];        printf("%.2f ",y[i][j]);
       printf("%.3e ",y[i][j]);        fprintf(ficlog,"%.2f ",y[i][j]);
       fprintf(ficlog,"%.3e ",y[i][j]);  
     }      }
     printf("\n");      printf("\n");
     fprintf(ficlog,"\n");      fprintf(ficlog,"\n");
   }    }
   */  #endif
   
   free_matrix(a,1,npar,1,npar);    free_matrix(a,1,npar,1,npar);
   free_matrix(y,1,npar,1,npar);    free_matrix(y,1,npar,1,npar);
   free_vector(x,1,npar);    free_vector(x,1,npar);
   free_ivector(indx,1,npar);    free_ivector(indx,1,npar);
   free_matrix(hess,1,npar,1,npar);    /* free_matrix(hess,1,npar,1,npar); */
   
   
 }  }
   
 /*************** hessian matrix ****************/  /*************** hessian matrix ****************/
 double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)  double hessii(double x[], double delta, int theta, double delti[], double (*func)(double []), int npar)
 {  { /* Around values of x, computes the function func and returns the scales delti and hessian */
   int i;    int i;
   int l=1, lmax=20;    int l=1, lmax=20;
   double k1,k2;    double k1,k2, res, fx;
   double p2[MAXPARM+1]; /* identical to x */    double p2[MAXPARM+1]; /* identical to x */
   double res;  
   double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;    double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4;
   double fx;  
   int k=0,kmax=10;    int k=0,kmax=10;
   double l1;    double l1;
   
Line 2828  double hessii(double x[], double delta, Line 2888  double hessii(double x[], double delta,
       p2[theta]=x[theta]-delt;        p2[theta]=x[theta]-delt;
       k2=func(p2)-fx;        k2=func(p2)-fx;
       /*res= (k1-2.0*fx+k2)/delt/delt; */        /*res= (k1-2.0*fx+k2)/delt/delt; */
       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */        res= (k1+k2)/delt/delt/2.; /* Divided by 2 because L and not 2*L */
               
 #ifdef DEBUGHESS  #ifdef DEBUGHESSII
       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);        printf("%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
       fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);        fprintf(ficlog,"%d %d k1=%.12e k2=%.12e xk1=%.12e xk2=%.12e delt=%.12e res=%.12e l=%d k=%d,fx=%.12e\n",theta,theta,k1,k2,x[theta]+delt,x[theta]-delt,delt,res, l, k,fx);
 #endif  #endif
Line 2844  double hessii(double x[], double delta, Line 2904  double hessii(double x[], double delta,
       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){         else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
         delts=delt;          delts=delt;
       }        }
     }      } /* End loop k */
   }    }
   delti[theta]=delts;    delti[theta]=delts;
   return res;     return res; 
       
 }  }
   
 double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar)  double hessij( double x[], double **hess, double delti[], int thetai,int thetaj,double (*func)(double []),int npar)
 {  {
   int i;    int i;
   int l=1, lmax=20;    int l=1, lmax=20;
   double k1,k2,k3,k4,res,fx;    double k1,k2,k3,k4,res,fx;
   double p2[MAXPARM+1];    double p2[MAXPARM+1];
   int k;    int k, kmax=1;
     double v1, v2, cv12, lc1, lc2;
     
   fx=func(x);    fx=func(x);
   for (k=1; k<=2; k++) {    for (k=1; k<=kmax; k=k+10) {
     for (i=1;i<=npar;i++) p2[i]=x[i];      for (i=1;i<=npar;i++) p2[i]=x[i];
     p2[thetai]=x[thetai]+delti[thetai]/k;      p2[thetai]=x[thetai]+delti[thetai]*k;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      p2[thetaj]=x[thetaj]+delti[thetaj]*k;
     k1=func(p2)-fx;      k1=func(p2)-fx;
       
     p2[thetai]=x[thetai]+delti[thetai]/k;      p2[thetai]=x[thetai]+delti[thetai]*k;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      p2[thetaj]=x[thetaj]-delti[thetaj]*k;
     k2=func(p2)-fx;      k2=func(p2)-fx;
       
     p2[thetai]=x[thetai]-delti[thetai]/k;      p2[thetai]=x[thetai]-delti[thetai]*k;
     p2[thetaj]=x[thetaj]+delti[thetaj]/k;      p2[thetaj]=x[thetaj]+delti[thetaj]*k;
     k3=func(p2)-fx;      k3=func(p2)-fx;
       
     p2[thetai]=x[thetai]-delti[thetai]/k;      p2[thetai]=x[thetai]-delti[thetai]*k;
     p2[thetaj]=x[thetaj]-delti[thetaj]/k;      p2[thetaj]=x[thetaj]-delti[thetaj]*k;
     k4=func(p2)-fx;      k4=func(p2)-fx;
     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */      res=(k1-k2-k3+k4)/4.0/delti[thetai]/k/delti[thetaj]/k/2.; /* Because of L not 2*L */
 #ifdef DEBUG      if(k1*k2*k3*k4 <0.){
     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);        kmax=kmax+10;
     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);        if(kmax >=10){
         printf("Warning: directions %d-%d, you are not estimating the Hessian at the exact maximum likelihood; increase ftol=%.2e\n",thetai,thetaj, ftol);
         fprintf(ficlog,"Warning: directions %d-%d, you are not estimating the Hessian at the exact maximum likelihood; increase ftol=%.2e\n",thetai,thetaj, ftol);
         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);
         }
       }
   #ifdef DEBUGHESSIJ
       v1=hess[thetai][thetai];
       v2=hess[thetaj][thetaj];
       cv12=res;
       /* Computing eigen value of Hessian matrix */
       lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
       if ((lc2 <0) || (lc1 <0) ){
         printf("Warning: sub Hessian matrix '%d%d' does not have positive eigen values \n",thetai,thetaj);
         fprintf(ficlog, "Warning: sub Hessian matrix '%d%d' does not have positive eigen values \n",thetai,thetaj);
         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);
       }
 #endif  #endif
   }    }
   return res;    return res;
 }  }
   
       /* Not done yet: Was supposed to fix if not exactly at the maximum */
   /* double hessij( double x[], double delti[], int thetai,int thetaj,double (*func)(double []),int npar) */
   /* { */
   /*   int i; */
   /*   int l=1, lmax=20; */
   /*   double k1,k2,k3,k4,res,fx; */
   /*   double p2[MAXPARM+1]; */
   /*   double delt=0.0001, delts, nkhi=10.,nkhif=1., khi=1.e-4; */
   /*   int k=0,kmax=10; */
   /*   double l1; */
     
   /*   fx=func(x); */
   /*   for(l=0 ; l <=lmax; l++){  /\* Enlarging the zone around the Maximum *\/ */
   /*     l1=pow(10,l); */
   /*     delts=delt; */
   /*     for(k=1 ; k <kmax; k=k+1){ */
   /*       delt = delti*(l1*k); */
   /*       for (i=1;i<=npar;i++) p2[i]=x[i]; */
   /*       p2[thetai]=x[thetai]+delti[thetai]/k; */
   /*       p2[thetaj]=x[thetaj]+delti[thetaj]/k; */
   /*       k1=func(p2)-fx; */
         
   /*       p2[thetai]=x[thetai]+delti[thetai]/k; */
   /*       p2[thetaj]=x[thetaj]-delti[thetaj]/k; */
   /*       k2=func(p2)-fx; */
         
   /*       p2[thetai]=x[thetai]-delti[thetai]/k; */
   /*       p2[thetaj]=x[thetaj]+delti[thetaj]/k; */
   /*       k3=func(p2)-fx; */
         
   /*       p2[thetai]=x[thetai]-delti[thetai]/k; */
   /*       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 *\/ */
   /* #ifdef DEBUGHESSIJ */
   /*       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); */
   /* #endif */
   /*       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)|| (k4 <khi/nkhi/2.)|| (k4 <khi/nkhi/2.)){ */
   /*      k=kmax; */
   /*       } */
   /*       else if((k1 >khi/nkhif) || (k2 >khi/nkhif) || (k4 >khi/nkhif) || (k4 >khi/nkhif)){ /\* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. *\/ */
   /*      k=kmax; l=lmax*10; */
   /*       } */
   /*       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){  */
   /*      delts=delt; */
   /*       } */
   /*     } /\* End loop k *\/ */
   /*   } */
   /*   delti[theta]=delts; */
   /*   return res;  */
   /* } */
   
   
 /************** Inverse of matrix **************/  /************** Inverse of matrix **************/
 void ludcmp(double **a, int n, int *indx, double *d)   void ludcmp(double **a, int n, int *indx, double *d) 
 {   { 
Line 3818  void cvevsij(double ***eij, double x[], Line 3952  void cvevsij(double ***eij, double x[],
 }  }
   
 /************ Variance ******************/  /************ 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[])   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 *ncvyear, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[])
 {  {
   /* Variance of health expectancies */    /* Variance of health expectancies */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
Line 3944  void varevsij(char optionfilefiname[], d Line 4078  void varevsij(char optionfilefiname[], d
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       }        }
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ncvyear,ij);
   
       if (popbased==1) {        if (popbased==1) {
         if(mobilav ==0){          if(mobilav ==0){
Line 3975  void varevsij(char optionfilefiname[], d Line 4109  void varevsij(char optionfilefiname[], d
       for(i=1; i<=npar; i++) /* Computes gradient x - delta */        for(i=1; i<=npar; i++) /* Computes gradient x - delta */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);          hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij);  
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ncvyear, ij);
     
       if (popbased==1) {        if (popbased==1) {
         if(mobilav ==0){          if(mobilav ==0){
Line 4050  void varevsij(char optionfilefiname[], d Line 4184  void varevsij(char optionfilefiname[], d
     /* end ppptj */      /* end ppptj */
     /*  x centered again */      /*  x centered again */
     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);        hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij);  
     prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ij);      prevalim(prlim,nlstate,x,age,oldm,savm,ftolpl,ncvyear,ij);
     
     if (popbased==1) {      if (popbased==1) {
       if(mobilav ==0){        if(mobilav ==0){
Line 4128  void varevsij(char optionfilefiname[], d Line 4262  void varevsij(char optionfilefiname[], d
 }  /* end varevsij */  }  /* end varevsij */
   
 /************ Variance of prevlim ******************/  /************ 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[])   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 *ncvyear, int ij, char strstart[])
 {  {
   /* Variance of prevalence limit */    /* Variance of prevalence limit */
   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/    /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double **savm,double ftolpl);*/
Line 4167  void varprevlim(char fileres[], double * Line 4301  void varprevlim(char fileres[], double *
       for(i=1; i<=npar; i++){ /* Computes gradient */        for(i=1; i<=npar; i++){ /* Computes gradient */
         xp[i] = x[i] + (i==theta ?delti[theta]:0);          xp[i] = x[i] + (i==theta ?delti[theta]:0);
       }        }
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ncvyear,ij);
       for(i=1;i<=nlstate;i++)        for(i=1;i<=nlstate;i++)
         gp[i] = prlim[i][i];          gp[i] = prlim[i][i];
           
       for(i=1; i<=npar; i++) /* Computes gradient */        for(i=1; i<=npar; i++) /* Computes gradient */
         xp[i] = x[i] - (i==theta ?delti[theta]:0);          xp[i] = x[i] - (i==theta ?delti[theta]:0);
       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ij);        prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl,ncvyear,ij);
       for(i=1;i<=nlstate;i++)        for(i=1;i<=nlstate;i++)
         gm[i] = prlim[i][i];          gm[i] = prlim[i][i];
   
Line 4631  divided by h: hPij/h : <a href=\"%s_%d-3 Line 4765  divided by h: hPij/h : <a href=\"%s_%d-3
  fprintf(fichtm,"\   fprintf(fichtm,"\
 \n<br><li><h4> <a name='secondorder'>Result files (second order: variances)</a></h4>\n\  \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> \   - Parameter file with estimated parameters and covariance matrix: <a href=\"%s\">%s</a> <br> \
  - 95%% confidence intervals and Wald tests of the estimated parameters are in the log file.<br> \   - 95%% confidence intervals and Wald tests of the estimated parameters are in the log file if optimization has been done (mle != 0).<br> \
 But because parameters are usually highly correlated (a higher incidence of disability \  But because parameters are usually highly correlated (a higher incidence of disability \
 and a higher incidence of recovery can give very close observed transition) it might \  and a higher incidence of recovery can give very close observed transition) it might \
 be very useful to look not only at linear confidence intervals estimated from the \  be very useful to look not only at linear confidence intervals estimated from the \
Line 4736  void printinggnuplot(char fileresu[], ch Line 4870  void printinggnuplot(char fileresu[], ch
     fprintf(ficgp,"\nset out \"%s.png\";",subdirf2(optionfilefiname,"ILK_"));      fprintf(ficgp,"\nset out \"%s.png\";",subdirf2(optionfilefiname,"ILK_"));
     fprintf(ficgp,"\nplot  \"%s\" u 2:(-$11):3 t \"All sample, all transitions\" with dots lc variable",subdirf(fileresilk));      fprintf(ficgp,"\nplot  \"%s\" u 2:(-$11):3 t \"All sample, all transitions\" with dots lc variable",subdirf(fileresilk));
     fprintf(ficgp,"\nreplot  \"%s\" u 2:($3 <= 3 ? -$11 : 1/0):3 t \"First 3 individuals\" with line lc variable", subdirf(fileresilk));      fprintf(ficgp,"\nreplot  \"%s\" u 2:($3 <= 3 ? -$11 : 1/0):3 t \"First 3 individuals\" with line lc variable", subdirf(fileresilk));
     fprintf(ficgp,"\nset out\n");      fprintf(ficgp,"\nset out;unset log\n");
     /* fprintf(ficgp,"\nset out \"%s.svg\"; replot; set out; # bug gnuplot",subdirf2(optionfilefiname,"ILK_")); */      /* fprintf(ficgp,"\nset out \"%s.svg\"; replot; set out; # bug gnuplot",subdirf2(optionfilefiname,"ILK_")); */
   
   strcpy(dirfileres,optionfilefiname);    strcpy(dirfileres,optionfilefiname);
Line 6317  void syscompilerinfo(int logged) Line 6451  void syscompilerinfo(int logged)
   
  }   }
   
  int prevalence_limit(double *p, double **prlim, double ageminpar, double agemaxpar, double ftolpl){   int prevalence_limit(double *p, double **prlim, double ageminpar, double agemaxpar, double ftolpl, int *ncvyear){
   /*--------------- Prevalence limit  (period or stable prevalence) --------------*/    /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
   int i, j, k, i1 ;    int i, j, k, i1 ;
   /* double ftolpl = 1.e-10; */    /* double ftolpl = 1.e-10; */
   double age, agebase, agelim;    double age, agebase, agelim;
     double tot;
   
   strcpy(filerespl,"PL_");    strcpy(filerespl,"PL_");
   strcat(filerespl,fileresu);    strcat(filerespl,fileresu);
Line 6332  void syscompilerinfo(int logged) Line 6467  void syscompilerinfo(int logged)
   printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);    printf("Computing period (stable) prevalence: result on file '%s' \n", filerespl);
   fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);    fprintf(ficlog,"Computing period (stable) prevalence: result on file '%s' \n", filerespl);
   pstamp(ficrespl);    pstamp(ficrespl);
   fprintf(ficrespl,"# Period (stable) prevalence \n");    fprintf(ficrespl,"# Period (stable) prevalence. Precision given by ftolpl=%g \n", ftolpl);
   fprintf(ficrespl,"#Age ");    fprintf(ficrespl,"#Age ");
   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);    for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
   fprintf(ficrespl,"\n");    fprintf(ficrespl,"\n");
Line 6367  void syscompilerinfo(int logged) Line 6502  void syscompilerinfo(int logged)
         for(j=1;j<=cptcoveff;j++) {          for(j=1;j<=cptcoveff;j++) {
           fprintf(ficrespl,"V%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtabm(k,j)]);            fprintf(ficrespl,"V%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtabm(k,j)]);
         }          }
         for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);          for(i=1; i<=nlstate;i++) fprintf(ficrespl,"  %d-%d   ",i,i);
         fprintf(ficrespl,"\n");          fprintf(ficrespl,"Total Years_to_converge\n");
                   
         for (age=agebase; age<=agelim; age++){          for (age=agebase; age<=agelim; age++){
         /* for (age=agebase; age<=agebase; age++){ */          /* for (age=agebase; age<=agebase; age++){ */
           prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k);            prevalim(prlim, nlstate, p, age, oldm, savm, ftolpl, ncvyear, k);
           fprintf(ficrespl,"%.0f ",age );            fprintf(ficrespl,"%.0f ",age );
           for(j=1;j<=cptcoveff;j++)            for(j=1;j<=cptcoveff;j++)
             fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtabm(k,j)]);              fprintf(ficrespl,"%d %d ",Tvaraff[j],nbcode[Tvaraff[j]][codtabm(k,j)]);
           for(i=1; i<=nlstate;i++)            tot=0.;
             for(i=1; i<=nlstate;i++){
               tot +=  prlim[i][i];
             fprintf(ficrespl," %.5f", prlim[i][i]);              fprintf(ficrespl," %.5f", prlim[i][i]);
           fprintf(ficrespl,"\n");            }
             fprintf(ficrespl," %.3f %d\n", tot, *ncvyear);
         } /* Age */          } /* Age */
         /* was end of cptcod */          /* was end of cptcod */
     } /* cptcov */      } /* cptcov */
Line 6471  int main(int argc, char *argv[]) Line 6609  int main(int argc, char *argv[])
 #endif  #endif
   int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);    int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav);
   int i,j, k, n=MAXN,iter=0,m,size=100, cptcod;    int i,j, k, n=MAXN,iter=0,m,size=100, cptcod;
     int ncvyearnp=0;
     int *ncvyear=&ncvyearnp; /* Number of years needed for the period prevalence to converge */
   int jj, ll, li, lj, lk;    int jj, ll, li, lj, lk;
   int numlinepar=0; /* Current linenumber of parameter file */    int numlinepar=0; /* Current linenumber of parameter file */
   int num_filled;    int num_filled;
Line 6519  int main(int argc, char *argv[]) Line 6658  int main(int argc, char *argv[])
   double ***param; /* Matrix of parameters */    double ***param; /* Matrix of parameters */
   double  *p;    double  *p;
   double **matcov; /* Matrix of covariance */    double **matcov; /* Matrix of covariance */
     double **hess; /* Hessian matrix */
   double ***delti3; /* Scale */    double ***delti3; /* Scale */
   double *delti; /* Scale */    double *delti; /* Scale */
   double ***eij, ***vareij;    double ***eij, ***vareij;
Line 6725  int main(int argc, char *argv[]) Line 6865  int main(int argc, char *argv[])
     }      }
     printf("ftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n",ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt);      printf("ftol=%e stepm=%d ncovcol=%d nlstate=%d ndeath=%d maxwav=%d mle=%d weight=%d\n",ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt);
   }    }
   ftolpl=6*ftol*1.e5; /* 6.e-3 make convergences in less than 80 loops for the prevalence limit */    /* ftolpl=6*ftol*1.e5; /\* 6.e-3 make convergences in less than 80 loops for the prevalence limit *\/ */
     ftolpl=6.e-3; /* 6.e-3 make convergences in less than 80 loops for the prevalence limit */
   /* Third parameter line */    /* Third parameter line */
   while(fgets(line, MAXLINE, ficpar)) {    while(fgets(line, MAXLINE, ficpar)) {
     /* If line starts with a # it is a comment */      /* If line starts with a # it is a comment */
Line 6755  int main(int argc, char *argv[]) Line 6896  int main(int argc, char *argv[])
       }        }
     }      }
     /* printf(" model=1+age%s modeltemp= %s, model=%s\n",model, modeltemp, model);fflush(stdout); */      /* printf(" model=1+age%s modeltemp= %s, model=%s\n",model, modeltemp, model);fflush(stdout); */
       printf("model=1+age+%s\n",model);fflush(stdout);
   }    }
   /* 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=1+age+%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model); */    /* 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=1+age+%s\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncovcol, &nlstate,&ndeath, &maxwav, &mle, &weightopt,model); */
   /* numlinepar=numlinepar+3; /\* In general *\/ */    /* numlinepar=numlinepar+3; /\* In general *\/ */
   /* 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=1+age+%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model); */    /* 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=1+age+%s\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncovcol, nlstate,ndeath, maxwav, mle, weightopt,model); */
   if(model[strlen(model)-1]=='.') /* Suppressing leading dot in the 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=1+age+%s.\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);
     model[strlen(model)-1]='\0';    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=1+age+%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=1+age%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=1+age%s.\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncovcol,nlstate,ndeath,maxwav, mle, weightopt,model);  
   fflush(ficlog);    fflush(ficlog);
   /* if(model[0]=='#'|| model[0]== '\0'){ */    /* if(model[0]=='#'|| model[0]== '\0'){ */
   if(model[0]=='#'){    if(model[0]=='#'){
Line 6827  int main(int argc, char *argv[]) Line 6967  int main(int argc, char *argv[])
     fprintf(ficlog," You chose mle=-3, look at file %s for a template of covariance matrix \n",filereso);      fprintf(ficlog," You chose mle=-3, look at file %s for a template of covariance matrix \n",filereso);
     param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);      param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncovmodel);
     matcov=matrix(1,npar,1,npar);      matcov=matrix(1,npar,1,npar);
       hess=matrix(1,npar,1,npar);
   }    }
   else{    else{
     /* Read guessed parameters */      /* Read guessed parameters */
Line 6935  run imach with mle=-1 to get a correct t Line 7076  run imach with mle=-1 to get a correct t
     ungetc(c,ficpar);      ungetc(c,ficpar);
       
     matcov=matrix(1,npar,1,npar);      matcov=matrix(1,npar,1,npar);
       hess=matrix(1,npar,1,npar);
     for(i=1; i <=npar; i++)      for(i=1; i <=npar; i++)
       for(j=1; j <=npar; j++) matcov[i][j]=0.;        for(j=1; j <=npar; j++) matcov[i][j]=0.;
               
Line 7402  Interval (in months) between two waves: Line 7544  Interval (in months) between two waves:
 #endif    #endif  
     fclose(ficrespow);      fclose(ficrespow);
           
     hesscov(matcov, p, NDIM, delti, 1e-4, gompertz);       hesscov(matcov, hess, p, NDIM, delti, 1e-4, gompertz); 
   
     for(i=1; i <=NDIM; i++)      for(i=1; i <=NDIM; i++)
       for(j=i+1;j<=NDIM;j++)        for(j=i+1;j<=NDIM;j++)
         matcov[i][j]=matcov[j][i];          matcov[i][j]=matcov[j][i];
           
     printf("\nCovariance matrix\n ");      printf("\nCovariance matrix\n ");
       fprintf(ficlog,"\nCovariance matrix\n ");
     for(i=1; i <=NDIM; i++) {      for(i=1; i <=NDIM; i++) {
       for(j=1;j<=NDIM;j++){         for(j=1;j<=NDIM;j++){ 
         printf("%f ",matcov[i][j]);          printf("%f ",matcov[i][j]);
           fprintf(ficlog,"%f ",matcov[i][j]);
       }        }
       printf("\n ");        printf("\n ");  fprintf(ficlog,"\n ");
     }      }
           
     printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);      printf("iter=%d MLE=%f Eq=%lf*exp(%lf*(age-%d))\n",iter,-gompertz(p),p[1],p[2],agegomp);
Line 7476  Please run with mle=-1 to get a correct Line 7620  Please run with mle=-1 to get a correct
 #endif  #endif
   } /* Endof if mle==-3 mortality only */    } /* Endof if mle==-3 mortality only */
   /* Standard maximisation */    /* Standard maximisation */
   else{ /* For mle >=1 */    else{ /* For mle !=- 3 */
     globpr=0;/* debug */      globpr=0;/* debug */
     /* Computes likelihood for initial parameters */      /* Computes likelihood for initial parameters */
     likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */      likelione(ficres, p, npar, nlstate, &globpr, &ipmx, &sw, &fretone, funcone); /* Prints the contributions to the likelihood */
Line 7519  Please run with mle=-1 to get a correct Line 7663  Please run with mle=-1 to get a correct
         }          }
       }        }
     }      }
     if(mle!=0){      if(mle != 0){
       /* Computing hessian and covariance matrix */        /* Computing hessian and covariance matrix only at a peak of the Likelihood, that is after optimization */
       ftolhess=ftol; /* Usually correct */        ftolhess=ftol; /* Usually correct */
       hesscov(matcov, p, npar, delti, ftolhess, func);        hesscov(matcov, hess, p, npar, delti, ftolhess, func);
     }        printf("Parameters and 95%% confidence intervals\n W is simply the result of the division of the parameter by the square root of covariance of the parameter.\n And Wald-based confidence intervals plus and minus 1.96 * W .\n But be careful that parameters are highly correlated because incidence of disability is highly correlated to incidence of recovery.\n It might be better to visualize the covariance matrix. See the page 'Matrix of variance-covariance of one-step probabilities' and its graphs.\n");
     printf("Parameters and 95%% confidence intervals\n W is simply the result of the division of the parameter by the square root of covariance of the parameter.\n And Wald-based confidence intervals plus and minus 1.96 * W .\n But be careful that parameters are highly correlated because incidence of disability is highly correlated to incidence of recovery.\n It might be better to visualize the covariance matrix. See the page 'Matrix of variance-covariance of one-step probabilities' and its graphs.\n");        fprintf(ficlog, "Parameters, Wald tests and Wald-based confidence intervals\n W is simply the result of the division of the parameter by the square root of covariance of the parameter.\n And Wald-based confidence intervals plus and minus 1.96 * W \n  It might be better to visualize the covariance matrix. See the page 'Matrix of variance-covariance of one-step probabilities' and its graphs.\n");
     fprintf(ficlog, "Parameters, Wald tests and Wald-based confidence intervals\n W is simply the result of the division of the parameter by the square root of covariance of the parameter.\n And Wald-based confidence intervals plus and minus 1.96 * W \n  It might be better to visualize the covariance matrix. See the page 'Matrix of variance-covariance of one-step probabilities' and its graphs.\n");        for(i=1,jk=1; i <=nlstate; i++){
     for(i=1,jk=1; i <=nlstate; i++){          for(k=1; k <=(nlstate+ndeath); k++){
       for(k=1; k <=(nlstate+ndeath); k++){            if (k != i) {
         if (k != i) {              printf("%d%d ",i,k);
           printf("%d%d ",i,k);              fprintf(ficlog,"%d%d ",i,k);
           fprintf(ficlog,"%d%d ",i,k);              for(j=1; j <=ncovmodel; j++){
           for(j=1; j <=ncovmodel; j++){                printf("%12.7f W=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-1.96*sqrt(matcov[jk][jk]),p[jk]+1.96*sqrt(matcov[jk][jk]));
             printf("%12.7f W=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-1.96*sqrt(matcov[jk][jk]),p[jk]+1.96*sqrt(matcov[jk][jk]));                fprintf(ficlog,"%12.7f W=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-1.96*sqrt(matcov[jk][jk]),p[jk]+1.96*sqrt(matcov[jk][jk]));
             fprintf(ficlog,"%12.7f W=%8.3f CI=[%12.7f ; %12.7f] ",p[jk], p[jk]/sqrt(matcov[jk][jk]), p[jk]-1.96*sqrt(matcov[jk][jk]),p[jk]+1.96*sqrt(matcov[jk][jk]));                jk++; 
             jk++;               }
               printf("\n");
               fprintf(ficlog,"\n");
           }            }
           printf("\n");  
           fprintf(ficlog,"\n");  
         }          }
       }        }
     }      } /* end of hesscov and Wald tests */
   
       /*  */
     fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");      fprintf(ficres,"# Scales (for hessian or gradient estimation)\n");
     printf("# Scales (for hessian or gradient estimation)\n");      printf("# Scales (for hessian or gradient estimation)\n");
     fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");      fprintf(ficlog,"# Scales (for hessian or gradient estimation)\n");
Line 7565  Please run with mle=-1 to get a correct Line 7710  Please run with mle=-1 to get a correct
     }      }
           
     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");      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)      if(mle >= 1) /* To big for the screen */
       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");        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");      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\ */      /* # 121 Var(a12)\n\ */
Line 7628  Please run with mle=-1 to get a correct Line 7773  Please run with mle=-1 to get a correct
                         fprintf(ficres," Var(%s%1d%1d)",ca,i,j);                          fprintf(ficres," Var(%s%1d%1d)",ca,i,j);
                       }else{                        }else{
                         if(mle>=1)                          if(mle>=1)
                           printf(" %.5e",matcov[jj][ll]);                             printf(" %.7e",matcov[jj][ll]); 
                         fprintf(ficlog," %.5e",matcov[jj][ll]);                           fprintf(ficlog," %.7e",matcov[jj][ll]); 
                         fprintf(ficres," %.5e",matcov[jj][ll]);                           fprintf(ficres," %.7e",matcov[jj][ll]); 
                       }                        }
                     }                      }
                   }                    }
Line 7758  Please run with mle=-1 to get a correct Line 7903  Please run with mle=-1 to get a correct
     /*--------------- Prevalence limit  (period or stable prevalence) --------------*/      /*--------------- Prevalence limit  (period or stable prevalence) --------------*/
     /*#include "prevlim.h"*/  /* Use ficrespl, ficlog */      /*#include "prevlim.h"*/  /* Use ficrespl, ficlog */
     prlim=matrix(1,nlstate,1,nlstate);      prlim=matrix(1,nlstate,1,nlstate);
     prevalence_limit(p, prlim,  ageminpar, agemaxpar, ftolpl);      prevalence_limit(p, prlim,  ageminpar, agemaxpar, ftolpl, ncvyear);
     fclose(ficrespl);      fclose(ficrespl);
   
 #ifdef FREEEXIT2  #ifdef FREEEXIT2
Line 7920  Please run with mle=-1 to get a correct Line 8065  Please run with mle=-1 to get a correct
         for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/          for(vpopbased=0; vpopbased <= popbased; vpopbased++){ /* Done for vpopbased=0 and vpopbased=1 if popbased==1*/
           oldm=oldms;savm=savms; /* ZZ Segmentation fault */            oldm=oldms;savm=savms; /* ZZ Segmentation fault */
           cptcod= 0; /* To be deleted */            cptcod= 0; /* To be deleted */
           varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart); /* cptcod not initialized Intel */            varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl, ncvyear, k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart); /* cptcod not initialized Intel */
           fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each health state\n#  (weighted average of eij where weights are ");            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)            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);              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);
Line 7932  Please run with mle=-1 to get a correct Line 8077  Please run with mle=-1 to get a correct
           /* printf("Which p?\n"); for(i=1;i<=npar;i++)printf("p[i=%d]=%lf,",i,p[i]);printf("\n"); */            /* printf("Which p?\n"); for(i=1;i<=npar;i++)printf("p[i=%d]=%lf,",i,p[i]);printf("\n"); */
           epj=vector(1,nlstate+1);            epj=vector(1,nlstate+1);
           for(age=bage; age <=fage ;age++){            for(age=bage; age <=fage ;age++){
             prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl,k); /*ZZ Is it the correct prevalim */              prevalim(prlim, nlstate, p, age, oldm, savm, ftolpl, ncvyear, k); /*ZZ Is it the correct prevalim */
             if (vpopbased==1) {              if (vpopbased==1) {
               if(mobilav ==0){                if(mobilav ==0){
                 for(i=1; i<=nlstate;i++)                  for(i=1; i<=nlstate;i++)
Line 8004  Please run with mle=-1 to get a correct Line 8149  Please run with mle=-1 to get a correct
               
         varpl=matrix(1,nlstate,(int) bage, (int) fage);          varpl=matrix(1,nlstate,(int) bage, (int) fage);
         oldm=oldms;savm=savms;          oldm=oldms;savm=savms;
         varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl,k,strstart);          varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl, ncvyear, k, strstart);
         free_matrix(varpl,1,nlstate,(int) bage, (int)fage);          free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
       /*}*/        /*}*/
     }      }
Line 8023  Please run with mle=-1 to get a correct Line 8168  Please run with mle=-1 to get a correct
     free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);      free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
     free_matrix(covar,0,NCOVMAX,1,n);      free_matrix(covar,0,NCOVMAX,1,n);
     free_matrix(matcov,1,npar,1,npar);      free_matrix(matcov,1,npar,1,npar);
       free_matrix(hess,1,npar,1,npar);
     /*free_vector(delti,1,npar);*/      /*free_vector(delti,1,npar);*/
     free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel);       free_ma3x(delti3,1,nlstate,1, nlstate+ndeath-1,1,ncovmodel); 
     free_matrix(agev,1,maxwav,1,imx);      free_matrix(agev,1,maxwav,1,imx);

Removed from v.1.202  
changed lines
  Added in v.1.203


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