--- imach096d/src/imach.c 2002/03/26 17:08:39 1.35 +++ imach096d/src/imach.c 2002/06/20 14:03:39 1.49 @@ -1,4 +1,4 @@ -/* $Id: imach.c,v 1.35 2002/03/26 17:08:39 lievre Exp $ +/* $Id: imach.c,v 1.49 2002/06/20 14:03:39 lievre Exp $ Interpolated Markov Chain Short summary of the programme: @@ -14,7 +14,7 @@ model. More health states you consider, more time is necessary to reach the Maximum Likelihood of the parameters involved in the model. The simplest model is the multinomial logistic model where pij is the - probabibility to be observed in state j at the second wave + probability to be observed in state j at the second wave conditional to be observed in state i at the first wave. Therefore the model is: log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex' is a covariate. If you want to have a more @@ -56,7 +56,7 @@ #include #define MAXLINE 256 -#define GNUPLOTPROGRAM "wgnuplot" +#define GNUPLOTPROGRAM "gnuplot" /*#define GNUPLOTPROGRAM "..\\gp37mgw\\wgnuplot"*/ #define FILENAMELENGTH 80 /*#define DEBUG*/ @@ -75,11 +75,16 @@ #define YEARM 12. /* Number of months per year */ #define AGESUP 130 #define AGEBASE 40 +#ifdef windows +#define DIRSEPARATOR '\\' +#else +#define DIRSEPARATOR '/' +#endif - +char version[80]="Imach version 0.8h, May 2002, INED-EUROREVES "; int erreur; /* Error number */ int nvar; -int cptcovn, cptcovage=0, cptcoveff=0,cptcov; +int cptcovn=0, cptcovage=0, cptcoveff=0,cptcov; int npar=NPARMAX; int nlstate=2; /* Number of live states */ int ndeath=1; /* Number of dead states */ @@ -96,13 +101,25 @@ double jmean; /* Mean space between 2 wa double **oldm, **newm, **savm; /* Working pointers to matrices */ double **oldms, **newms, **savms; /* Fixed working pointers to matrices */ FILE *fic,*ficpar, *ficparo,*ficres, *ficrespl, *ficrespij, *ficrest,*ficresf,*ficrespop; -FILE *ficgp,*ficresprob,*ficpop; +FILE *ficgp,*ficresprob,*ficpop, *ficresprobcov, *ficresprobcor; +FILE *fichtm; /* Html File */ FILE *ficreseij; - char filerese[FILENAMELENGTH]; - FILE *ficresvij; - char fileresv[FILENAMELENGTH]; - FILE *ficresvpl; - char fileresvpl[FILENAMELENGTH]; +char filerese[FILENAMELENGTH]; +FILE *ficresvij; +char fileresv[FILENAMELENGTH]; +FILE *ficresvpl; +char fileresvpl[FILENAMELENGTH]; +char title[MAXLINE]; +char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH], filerespl[FILENAMELENGTH]; +char optionfilext[10], optionfilefiname[FILENAMELENGTH], plotcmd[FILENAMELENGTH]; + +char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH], rfileres[FILENAMELENGTH]; + +char filerest[FILENAMELENGTH]; +char fileregp[FILENAMELENGTH]; +char popfile[FILENAMELENGTH]; + +char optionfilegnuplot[FILENAMELENGTH], optionfilehtm[FILENAMELENGTH]; #define NR_END 1 #define FREE_ARG char* @@ -136,6 +153,9 @@ int imx; int stepm; /* Stepm, step in month: minimum step interpolation*/ +int estepm; +/* Estepm, step in month to interpolate survival function in order to approximate Life Expectancy*/ + int m,nb; int *num, firstpass=0, lastpass=4,*cod, *ncodemax, *Tage; double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint; @@ -158,11 +178,7 @@ static int split( char *path, char *dirc l1 = strlen( path ); /* length of path */ if ( l1 == 0 ) return( GLOCK_ERROR_NOPATH ); -#ifdef windows - s = strrchr( path, '\\' ); /* find last / */ -#else - s = strrchr( path, '/' ); /* find last / */ -#endif + s = strrchr( path, DIRSEPARATOR ); /* find last / */ if ( s == NULL ) { /* no directory, so use current */ #if defined(__bsd__) /* get current working directory */ extern char *getwd( ); @@ -1327,10 +1343,10 @@ void prevalence(int agemin, float agemax j=cptcoveff; if (cptcovn<1) {j=1;ncodemax[1]=1;} - for(k1=1; k1<=j;k1++){ + for(k1=1; k1<=j;k1++){ for(i1=1; i1<=ncodemax[k1];i1++){ j1++; - + for (i=-1; i<=nlstate+ndeath; i++) for (jk=-1; jk<=nlstate+ndeath; jk++) for(m=agemin; m <= agemax+3; m++) @@ -1349,41 +1365,46 @@ void prevalence(int agemin, float agemax if ((k2>=dateprev1) && (k2<=dateprev2)) { if(agev[m][i]==0) agev[m][i]=agemax+1; if(agev[m][i]==1) agev[m][i]=agemax+2; - if (m0) + freq[s[m][i]][s[m+1][i]][(int)(agev[m][i]+1-((int)calagedate %12)/12.)] += weight[i]; + else + freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i]; + freq[s[m][i]][s[m+1][i]][(int)(agemax+3)] += weight[i]; + } } } } } - for(i=(int)agemin; i <= (int)agemax+3; i++){ - for(jk=1; jk <=nlstate ; jk++){ - for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++) - pp[jk] += freq[jk][m][i]; - } - for(jk=1; jk <=nlstate ; jk++){ - for(m=-1, pos=0; m <=0 ; m++) + for(i=(int)agemin; i <= (int)agemax+3; i++){ + for(jk=1; jk <=nlstate ; jk++){ + for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++) + pp[jk] += freq[jk][m][i]; + } + for(jk=1; jk <=nlstate ; jk++){ + for(m=-1, pos=0; m <=0 ; m++) pos += freq[jk][m][i]; } - for(jk=1; jk <=nlstate ; jk++){ - for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++) - pp[jk] += freq[jk][m][i]; - } - - for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk]; - - for(jk=1; jk <=nlstate ; jk++){ - if( i <= (int) agemax){ - if(pos>=1.e-5){ - probs[i][jk][j1]= pp[jk]/pos; - } - } - } - + for(jk=1; jk <=nlstate ; jk++){ + for(m=0, pp[jk]=0; m <=nlstate+ndeath; m++) + pp[jk] += freq[jk][m][i]; + } + + for(jk=1,pos=0; jk <=nlstate ; jk++) pos += pp[jk]; + + for(jk=1; jk <=nlstate ; jk++){ + if( i <= (int) agemax){ + if(pos>=1.e-5){ + probs[i][jk][j1]= pp[jk]/pos; + } + } } + + } } } - + free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3); free_vector(pp,1,nlstate); @@ -1500,7 +1521,7 @@ void tricode(int *Tvar, int **nbcode, in for (k=0; k<=19; k++) { if (Ndum[k] != 0) { nbcode[Tvar[j]][ij]=k; - /* printf("nbcodeaaaaaaaaaaa=%d Tvar[j]=%d ij=%d j=%d",nbcode[Tvar[j]][ij],Tvar[j],ij,j);*/ + ij++; } if (ij > ncodemax[j]) break; @@ -1528,35 +1549,59 @@ void tricode(int *Tvar, int **nbcode, in /*********** Health Expectancies ****************/ -void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij) +void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm, int ij, int estepm,double delti[],double **matcov ) + { /* Health expectancies */ - int i, j, nhstepm, hstepm, h, nstepm, k; + int i, j, nhstepm, hstepm, h, nstepm, k, cptj; double age, agelim, hf; - double ***p3mat; + double ***p3mat,***varhe; + double **dnewm,**doldm; + double *xp; + double **gp, **gm; + double ***gradg, ***trgradg; + int theta; + + varhe=ma3x(1,nlstate*2,1,nlstate*2,(int) bage, (int) fage); + xp=vector(1,npar); + dnewm=matrix(1,nlstate*2,1,npar); + doldm=matrix(1,nlstate*2,1,nlstate*2); fprintf(ficreseij,"# Health expectancies\n"); fprintf(ficreseij,"# Age"); for(i=1; i<=nlstate;i++) for(j=1; j<=nlstate;j++) - fprintf(ficreseij," %1d-%1d",i,j); + fprintf(ficreseij," %1d-%1d (SE)",i,j); fprintf(ficreseij,"\n"); - k=1; /* For example stepm=6 months */ - hstepm=k*YEARM; /* (a) Every k years of age (in months), for example every k=2 years 24 m */ - hstepm=stepm; /* or (b) We decided to compute the life expectancy with the smallest unit */ + 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 inbetween 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 k years */ + 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 k= 2 years, = 2/6 months = 4 */ + 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 */ @@ -1566,34 +1611,120 @@ void evsij(char fileres[], double ***eij /* 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); + gradg=ma3x(0,nhstepm,1,npar,1,nlstate*2); + gp=matrix(0,nhstepm,1,nlstate*2); + gm=matrix(0,nhstepm,1,nlstate*2); + /* Computed by stepm unit matrices, product of hstepm matrices, stored in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */ hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm, ij); + + hf=hstepm*stepm/YEARM; /* Duration of hstepm expressed in year unit. */ + + /* Computing Variances of health expectancies */ + + for(theta=1; theta <=npar; theta++){ + for(i=1; i<=npar; i++){ + xp[i] = x[i] + (i==theta ?delti[theta]:0); + } + hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij); + + cptj=0; + for(j=1; j<= nlstate; j++){ + for(i=1; i<=nlstate; i++){ + cptj=cptj+1; + for(h=0, gp[h][cptj]=0.; h<=nhstepm-1; h++){ + gp[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.; + } + } + } + + + for(i=1; i<=npar; i++) + xp[i] = x[i] - (i==theta ?delti[theta]:0); + hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij); + + cptj=0; + for(j=1; j<= nlstate; j++){ + for(i=1;i<=nlstate;i++){ + cptj=cptj+1; + for(h=0, gm[h][cptj]=0.; h<=nhstepm-1; h++){ + gm[h][cptj] = (p3mat[i][j][h]+p3mat[i][j][h+1])/2.; + } + } + } + for(j=1; j<= nlstate*2; j++) + for(h=0; h<=nhstepm-1; h++){ + gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta]; + } + } + +/* End theta */ + + trgradg =ma3x(0,nhstepm,1,nlstate*2,1,npar); + + for(h=0; h<=nhstepm-1; h++) + for(j=1; j<=nlstate*2;j++) + for(theta=1; theta <=npar; theta++) + trgradg[h][j][theta]=gradg[h][theta][j]; + + + for(i=1;i<=nlstate*2;i++) + for(j=1;j<=nlstate*2;j++) + varhe[i][j][(int)age] =0.; + + printf("%d|",(int)age);fflush(stdout); + for(h=0;h<=nhstepm-1;h++){ + for(k=0;k<=nhstepm-1;k++){ + matprod2(dnewm,trgradg[h],1,nlstate*2,1,npar,1,npar,matcov); + matprod2(doldm,dnewm,1,nlstate*2,1,npar,1,nlstate*2,gradg[k]); + for(i=1;i<=nlstate*2;i++) + for(j=1;j<=nlstate*2;j++) + varhe[i][j][(int)age] += doldm[i][j]*hf*hf; + } + } + /* 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]);*/ + +/* 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 ); + cptj=0; for(i=1; i<=nlstate;i++) for(j=1; j<=nlstate;j++){ - fprintf(ficreseij," %9.4f", eij[i][j][(int)age]); + cptj++; + fprintf(ficreseij," %9.4f (%.4f)", eij[i][j][(int)age], sqrt(varhe[cptj][cptj][(int)age]) ); } fprintf(ficreseij,"\n"); + + free_matrix(gm,0,nhstepm,1,nlstate*2); + free_matrix(gp,0,nhstepm,1,nlstate*2); + free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate*2); + free_ma3x(trgradg,0,nhstepm,1,nlstate*2,1,npar); free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm); } + printf("\n"); + + free_vector(xp,1,npar); + free_matrix(dnewm,1,nlstate*2,1,npar); + free_matrix(doldm,1,nlstate*2,1,nlstate*2); + free_ma3x(varhe,1,nlstate*2,1,nlstate*2,(int) bage, (int)fage); } /************ Variance ******************/ -void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij) +void varevsij(char fileres[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int ij, int estepm) { /* 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; - int i, j, nhstepm, hstepm, h, nstepm, kk; + int i, j, nhstepm, hstepm, h, nstepm ; int k, cptcode; double *xp; double **gp, **gm; @@ -1602,7 +1733,7 @@ void varevsij(char fileres[], double *** double age,agelim, hf; int theta; - fprintf(ficresvij,"# Covariances of life expectancies\n"); + fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n# (weighted average of eij where weights are the stable prevalence in health states i\n"); fprintf(ficresvij,"# Age"); for(i=1; i<=nlstate;i++) for(j=1; j<=nlstate;j++) @@ -1613,9 +1744,11 @@ void varevsij(char fileres[], double *** dnewm=matrix(1,nlstate,1,npar); doldm=matrix(1,nlstate,1,nlstate); - kk=1; /* For example stepm=6 months */ - hstepm=kk*YEARM; /* (a) Every k years of age (in months), for example every k=2 years 24 m */ - hstepm=stepm; /* or (b) We decided to compute the life expectancy with the smallest unit */ + 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. @@ -1627,7 +1760,7 @@ void varevsij(char fileres[], double *** 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 k= 2 years, = 2/6 months = 4 */ + 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 */ @@ -1735,7 +1868,7 @@ void varprevlim(char fileres[], double * double age,agelim; int theta; - fprintf(ficresvpl,"# Standard deviation of prevalences limit\n"); + fprintf(ficresvpl,"# Standard deviation of prevalence's limit\n"); fprintf(ficresvpl,"# Age"); for(i=1; i<=nlstate;i++) fprintf(ficresvpl," %1d-%1d",i,i); @@ -1804,145 +1937,314 @@ void varprevlim(char fileres[], double * } /************ Variance of one-step probabilities ******************/ -void varprob(char fileres[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij) +void varprob(char optionfilefiname[], double **matcov, double x[], double delti[], int nlstate, double bage, double fage, int ij, int *Tvar, int **nbcode, int *ncodemax) { - int i, j; - int k=0, cptcode; + int i, j=0, i1, k1, l1, t, tj; + int k2, l2, j1, z1; + int k=0,l, cptcode; + int first=1; + double cv12, mu1, mu2, lc1, lc2, v12, v21, v11, v22,v1,v2; double **dnewm,**doldm; double *xp; double *gp, *gm; double **gradg, **trgradg; + double **mu; double age,agelim, cov[NCOVMAX]; + 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); } - printf("Computing variance of one-step probabilities: result on file '%s' \n",fileresprob); - + strcpy(fileresprobcov,"probcov"); + strcat(fileresprobcov,fileres); + if((ficresprobcov=fopen(fileresprobcov,"w"))==NULL) { + printf("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); + } + printf("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); + printf("and correlation matrix of one-step probabilities: result on file '%s' \n",fileresprobcor); + + fprintf(ficresprob,"#One-step probabilities and stand. devi in ()\n"); + fprintf(ficresprob,"# Age"); + fprintf(ficresprobcov,"#One-step probabilities and covariance matrix\n"); + fprintf(ficresprobcov,"# Age"); + fprintf(ficresprobcor,"#One-step probabilities and correlation matrix\n"); + fprintf(ficresprobcov,"# 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+ndeath)*(nlstate+ndeath),1,npar); - doldm=matrix(1,(nlstate+ndeath)*(nlstate+ndeath),1,(nlstate+ndeath)*(nlstate+ndeath)); - - cov[1]=1; - for (age=bage; age<=fage; age ++){ - cov[2]=age; - gradg=matrix(1,npar,1,9); - trgradg=matrix(1,9,1,npar); - gp=vector(1,(nlstate+ndeath)*(nlstate+ndeath)); - gm=vector(1,(nlstate+ndeath)*(nlstate+ndeath)); - - for(theta=1; theta <=npar; theta++){ - for(i=1; i<=npar; i++) - xp[i] = x[i] + (i==theta ?delti[theta]:0); - - pmij(pmmij,cov,ncovmodel,xp,nlstate); - - k=0; - for(i=1; i<= (nlstate+ndeath); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - gp[k]=pmmij[i][j]; - } - } + 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; + if((ficgp=fopen(optionfilegnuplot,"a"))==NULL) { + printf("Problem with gnuplot file: %s\n", optionfilegnuplot); + exit(0); + } + else{ + fprintf(ficgp,"\n# Routine varprob"); + } + if((fichtm=fopen(optionfilehtm,"a"))==NULL) { + printf("Problem with html file: %s\n", optionfilehtm); + exit(0); + } + else{ + fprintf(fichtm,"\n

  • Computing matrix of variance-covariance of step probabilities

    • \n"); + fprintf(fichtm,"\nWe have drawn ellipsoids of confidence around the pij, pkl to understand the covariance between two incidences. They are expressed in year-1 in order to be less dependent of stepm.
    \n"); + fprintf(fichtm,"\n
    We have drawn x'cov-1x = 4 where x is the column vector (pij,pkl). It means that if pij and pkl where uncorrelated the (2X2) matrix would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis.
    When both incidences are correlated we diagonalised the inverse of the covariance matrix and made the appropriate rotation.
    \n"); - for(i=1; i<=npar; i++) - xp[i] = x[i] - (i==theta ?delti[theta]:0); - + } - pmij(pmmij,cov,ncovmodel,xp,nlstate); - k=0; - for(i=1; i<=(nlstate+ndeath); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - gm[k]=pmmij[i][j]; - } + + cov[1]=1; + tj=cptcoveff; + if (cptcovn<1) {tj=1;ncodemax[1]=1;} + j1=0; + for(t=1; t<=tj;t++){ + 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#"); + 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#"); + + 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#"); + + + fprintf(fichtm, "\n
    ********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]); + fprintf(fichtm, "**********\n
    "); + + fprintf(ficresprobcor, "\n#********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtab[j1][z1]]); + fprintf(ficgp, "**********\n#"); } + + 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]]]; + } + 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]]]; + + 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(theta=1; theta <=npar; theta++){ + for(i=1; i<=npar; i++) + xp[i] = x[i] + (i==theta ?delti[theta]: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]: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+ndeath)*(nlstate+ndeath); i++) - gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta]; - } - - for(j=1; j<=(nlstate+ndeath)*(nlstate+ndeath);j++) - for(theta=1; theta <=npar; theta++) - trgradg[j][theta]=gradg[theta][j]; - - matprod2(dnewm,trgradg,1,9,1,npar,1,npar,matcov); - matprod2(doldm,dnewm,1,9,1,npar,1,9,gradg); - - pmij(pmmij,cov,ncovmodel,x,nlstate); + for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) + gradg[theta][i]=(gp[i]-gm[i])/2./delti[theta]; + } - k=0; - for(i=1; i<=(nlstate+ndeath); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - gm[k]=pmmij[i][j]; + 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]; + } } - } - - /*printf("\n%d ",(int)age); - for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){ - + 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(ficresprob,"\n%d ",(int)age); - - for (i=1; i<=(nlstate+ndeath)*(nlstate+ndeath-1);i++){ - if (i== 2) fprintf(ficresprob,"%.3e %.3e ",gm[i],doldm[i][i]); -if (i== 4) fprintf(ficresprob,"%.3e %.3e ",gm[i],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=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++){ + 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 */ + /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/ + for (k1=1; k1<=(nlstate);k1++){ + for (l1=1; l1<=(nlstate+ndeath);l1++){ + if(l1==k1) continue; + i=(k1-1)*(nlstate+ndeath)+l1; + for (k2=1; k2<=(nlstate);k2++){ + for (l2=1; l2<=(nlstate+ndeath);l2++){ + if(l2==k2) continue; + j=(k2-1)*(nlstate+ndeath)+l2; + if(j<=i) 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; + /* Computing eigen value of matrix of covariance */ + lc1=(v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)); + lc2=(v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)); + printf("Var %.4e %.4e cov %.4e Eigen %.3e %.3e\n",v1,v2,cv12,lc1,lc2); + /* Eigen vectors */ + v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12)); + v21=sqrt(1.-v11*v11); + v12=-v21; + v22=v11; + /*printf(fignu*/ + /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */ + /* mu2+ v21*lc1*cost + v21*lc2*sin(t) */ + if(first==1){ + first=0; + fprintf(ficgp,"\nset parametric;set nolabel"); + fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k2,l2,k1,l1); + fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65"); + fprintf(fichtm,"\n
    Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year-1 :varpijgr%s%d%1d%1d-%1d%1d.png, ",k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1,optionfilefiname, j1,k2,l2,k1,l1); + fprintf(fichtm,"\n
    ",optionfilefiname, j1,k2,l2,k1,l1); + fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\"",optionfilefiname, j1,k2,l2,k1,l1); + fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1); + fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1); + 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)) t \"%d\"",\ + mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \ + mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age); + }else{ + first=0; + fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k2,l2,k1,l1); + fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu2,mu1); + 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)) t \"%d\"",\ + mu2,std,v21,sqrt(lc1),v21,sqrt(lc2), \ + mu1,std,v11,sqrt(lc1),v12,sqrt(lc2),(int) age); + }/* if first */ + } /* age mod 5 */ + } /* end loop age */ + fprintf(ficgp,"\nset out \"varpijgr%s%d%1d%1d-%1d%1d.png\";replot;",optionfilefiname, j1,k2,l2,k1,l1); + first=1; + } /*l12 */ + } /* k12 */ + } /*l1 */ + }/* k1 */ + } /* loop covariates */ + free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage); free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath)); free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath)); + free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage); free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar); free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar); + } + free_vector(xp,1,npar); + fclose(ficresprob); + fclose(ficresprobcov); + fclose(ficresprobcor); + fclose(ficgp); + fclose(fichtm); } - free_vector(xp,1,npar); -fclose(ficresprob); -} /******************* 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 optionfile[], \ - char optionfilehtm[],char rfileres[], char optionfilegnuplot[],\ - char version[], int popforecast ){ + 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; - FILE *fichtm; /*char optionfilehtm[FILENAMELENGTH];*/ - - strcpy(optionfilehtm,optionfile); - strcat(optionfilehtm,".htm"); - if((fichtm=fopen(optionfilehtm,"w"))==NULL) { + if((fichtm=fopen(optionfilehtm,"a"))==NULL) { printf("Problem with %s \n",optionfilehtm), exit(0); } - fprintf(fichtm," Imach, Version %s
    \n -Title=%s
    Datafile=%s Firstpass=%d Lastpass=%d Stepm=%d Weight=%d Model=%s
    \n -\n -Total number of observations=%d
    \n -Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf
    \n -
    -