Annotation of imach096d/src/imach.c, revision 1.1.1.1

1.1       brouard     1:     
                      2: /*********************** Imach **************************************        
                      3:   This program computes Healthy Life Expectancies from cross-longitudinal 
                      4:   data. Cross-longitudinal consist in a first survey ("cross") where 
                      5:   individuals from different ages are interviewed on their health status
                      6:   or degree of  disability. At least a second wave of interviews 
                      7:   ("longitudinal") should  measure each new individual health status. 
                      8:   Health expectancies are computed from the transistions observed between 
                      9:   waves and are computed for each degree of severity of disability (number
                     10:   of life states). More degrees you consider, more time is necessary to
                     11:   reach the Maximum Likekilhood of the parameters involved in the model.
                     12:   The simplest model is the multinomial logistic model where pij is
                     13:   the probabibility to be observed in state j at the second wave conditional
                     14:   to be observed in state i at the first wave. Therefore the model is:
                     15:   log(pij/pii)= aij + bij*age+ cij*sex + etc , where 'age' is age and 'sex' 
                     16:   is a covariate. If you want to have a more complex model than "constant and
                     17:   age", you should modify the program where the markup 
                     18:     *Covariates have to be included here again* invites you to do it.
                     19:   More covariates you add, less is the speed of the convergence.
                     20: 
                     21:   The advantage that this computer programme claims, comes from that if the 
                     22:   delay between waves is not identical for each individual, or if some 
                     23:   individual missed an interview, the information is not rounded or lost, but
                     24:   taken into account using an interpolation or extrapolation.
                     25:   hPijx is the probability to be
                     26:   observed in state i at age x+h conditional to the observed state i at age 
                     27:   x. The delay 'h' can be split into an exact number (nh*stepm) of 
                     28:   unobserved intermediate  states. This elementary transition (by month or 
                     29:   quarter trimester, semester or year) is model as a multinomial logistic. 
                     30:   The hPx matrix is simply the matrix product of nh*stepm elementary matrices
                     31:   and the contribution of each individual to the likelihood is simply hPijx.
                     32: 
                     33:   Also this programme outputs the covariance matrix of the parameters but also
                     34:   of the life expectancies. It also computes the prevalence limits. 
                     35:   
                     36:   Authors: Nicolas Brouard (brouard@ined.fr) and Agnès Lièvre (lievre@ined.fr).
                     37:            Institut national d'études démographiques, Paris.
                     38:   This software have been partly granted by Euro-REVES, a concerted action
                     39:   from the European Union.
                     40:   It is copyrighted identically to a GNU software product, ie programme and
                     41:   software can be distributed freely for non commercial use. Latest version
                     42:   can be accessed at http://euroreves.ined.fr/imach .
                     43:   **********************************************************************/
                     44:  
                     45: #include <math.h>
                     46: #include <stdio.h>
                     47: #include <stdlib.h>
                     48: #include <unistd.h>
                     49: 
                     50: #define MAXLINE 256
                     51: #define FILENAMELENGTH 80
                     52: /*#define DEBUG*/
                     53: /*#define win*/
                     54: 
                     55: #define MAXPARM 30 /* Maximum number of parameters for the optimization */
                     56: #define NPARMAX 64 /* (nlstate+ndeath-1)*nlstate*ncov */
                     57: 
                     58: #define NINTERVMAX 8
                     59: #define NLSTATEMAX 8 /* Maximum number of live states (for func) */
                     60: #define NDEATHMAX 8 /* Maximum number of dead states (for func) */
                     61: #define NCOVMAX 8 /* Maximum number of covariates */
                     62: #define MAXN 20000
                     63: #define YEARM 12. /* Number of months per year */
                     64: #define AGESUP 130
                     65: #define AGEBASE 40
                     66: 
                     67: 
                     68: int nvar;
                     69: 
                     70: int npar=NPARMAX;
                     71: int nlstate=2; /* Number of live states */
                     72: int ndeath=1; /* Number of dead states */
                     73: int ncov;     /* Total number of covariables including constant a12*1 +b12*x ncov=2 */
                     74: 
                     75: int *wav; /* Number of waves for this individuual 0 is possible */
                     76: int maxwav; /* Maxim number of waves */
                     77: int mle, weightopt;
                     78: int **mw; /* mw[mi][i] is number of the mi wave for this individual */
                     79: int **dh; /* dh[mi][i] is number of steps between mi,mi+1 for this individual */
                     80: double **oldm, **newm, **savm; /* Working pointers to matrices */
                     81: double **oldms, **newms, **savms; /* Fixed working pointers to matrices */
                     82: FILE *fic,*ficpar, *ficparo,*ficres,  *ficrespl, *ficrespij, *ficrest;
                     83: FILE *ficgp, *fichtm;
                     84: 
                     85: #define NR_END 1
                     86: #define FREE_ARG char*
                     87: #define FTOL 1.0e-10
                     88: 
                     89: #define NRANSI 
                     90: #define ITMAX 200 
                     91: 
                     92: #define TOL 2.0e-4 
                     93: 
                     94: #define CGOLD 0.3819660 
                     95: #define ZEPS 1.0e-10 
                     96: #define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d); 
                     97: 
                     98: #define GOLD 1.618034 
                     99: #define GLIMIT 100.0 
                    100: #define TINY 1.0e-20 
                    101: 
                    102: static double maxarg1,maxarg2;
                    103: #define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)>(maxarg2)? (maxarg1):(maxarg2))
                    104: #define FMIN(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1)<(maxarg2)? (maxarg1):(maxarg2))
                    105:  
                    106: #define SIGN(a,b) ((b)>0.0 ? fabs(a) : -fabs(a))
                    107: #define rint(a) floor(a+0.5)
                    108: 
                    109: static double sqrarg;
                    110: #define SQR(a) ((sqrarg=(a)) == 0.0 ? 0.0 :sqrarg*sqrarg)
                    111: #define SWAP(a,b) {temp=(a);(a)=(b);(b)=temp;} 
                    112: 
                    113: int imx; 
                    114: int stepm;
                    115: /* Stepm, step in month: minimum step interpolation*/
                    116: 
                    117: int m,nb;
                    118: int *num, firstpass=0, lastpass=2,*cod;
                    119: double **agev,*moisnais, *annais, *moisdc, *andc,**mint, **anint;
                    120: double **pmmij;
                    121: 
                    122: double *weight;
                    123: int **s; /* Status */
                    124: double *agedc, **covar, idx;
                    125: 
                    126: 
                    127: double ftol=FTOL; /* Tolerance for computing Max Likelihood */
                    128: double ftolhess; /* Tolerance for computing hessian */
                    129: 
                    130: 
                    131: /******************************************/
                    132: 
                    133: void replace(char *s, char*t)
                    134: {
                    135:   int i;
                    136:   int lg=20;
                    137:   i=0;
                    138:   lg=strlen(t);
                    139:   for(i=0; i<= lg; i++) {
                    140:     (s[i] = t[i]);
                    141:     if (t[i]== '\\') s[i]='/';
                    142:   }
                    143: }
                    144: void cut(char *u,char *v, char*t)
                    145: {
                    146:   int i,lg,j,p;
                    147:   i=0;
                    148:   for(j=0; j<=strlen(t); j++) {
                    149:     if(t[j]=='\\') p=j;
                    150:   }
                    151: 
                    152:   lg=strlen(t);
                    153:   for(j=0; j<p; j++) {
                    154:     (u[j] = t[j]);
                    155:     u[p]='\0';
                    156:   }
                    157: 
                    158:   for(j=0; j<= lg; j++) {
                    159:     if (j>=(p+1))(v[j-p-1] = t[j]);
                    160:   }
                    161: }
                    162: 
                    163: /********************** nrerror ********************/
                    164: 
                    165: void nrerror(char error_text[])
                    166: {
                    167:   fprintf(stderr,"ERREUR ...\n");
                    168:   fprintf(stderr,"%s\n",error_text);
                    169:   exit(1);
                    170: }
                    171: /*********************** vector *******************/
                    172: double *vector(int nl, int nh)
                    173: {
                    174:   double *v;
                    175:   v=(double *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(double)));
                    176:   if (!v) nrerror("allocation failure in vector");
                    177:   return v-nl+NR_END;
                    178: }
                    179: 
                    180: /************************ free vector ******************/
                    181: void free_vector(double*v, int nl, int nh)
                    182: {
                    183:   free((FREE_ARG)(v+nl-NR_END));
                    184: }
                    185: 
                    186: /************************ivector *******************************/
                    187: int *ivector(long nl,long nh)
                    188: {
                    189:   int *v;
                    190:   v=(int *) malloc((size_t)((nh-nl+1+NR_END)*sizeof(int)));
                    191:   if (!v) nrerror("allocation failure in ivector");
                    192:   return v-nl+NR_END;
                    193: }
                    194: 
                    195: /******************free ivector **************************/
                    196: void free_ivector(int *v, long nl, long nh)
                    197: {
                    198:   free((FREE_ARG)(v+nl-NR_END));
                    199: }
                    200: 
                    201: /******************* imatrix *******************************/
                    202: int **imatrix(long nrl, long nrh, long ncl, long nch) 
                    203:      /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */ 
                    204: { 
                    205:   long i, nrow=nrh-nrl+1,ncol=nch-ncl+1; 
                    206:   int **m; 
                    207:   
                    208:   /* allocate pointers to rows */ 
                    209:   m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*))); 
                    210:   if (!m) nrerror("allocation failure 1 in matrix()"); 
                    211:   m += NR_END; 
                    212:   m -= nrl; 
                    213:   
                    214:   
                    215:   /* allocate rows and set pointers to them */ 
                    216:   m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int))); 
                    217:   if (!m[nrl]) nrerror("allocation failure 2 in matrix()"); 
                    218:   m[nrl] += NR_END; 
                    219:   m[nrl] -= ncl; 
                    220:   
                    221:   for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol; 
                    222:   
                    223:   /* return pointer to array of pointers to rows */ 
                    224:   return m; 
                    225: } 
                    226: 
                    227: /****************** free_imatrix *************************/
                    228: void free_imatrix(m,nrl,nrh,ncl,nch)
                    229:       int **m;
                    230:       long nch,ncl,nrh,nrl; 
                    231:      /* free an int matrix allocated by imatrix() */ 
                    232: { 
                    233:   free((FREE_ARG) (m[nrl]+ncl-NR_END)); 
                    234:   free((FREE_ARG) (m+nrl-NR_END)); 
                    235: } 
                    236: 
                    237: /******************* matrix *******************************/
                    238: double **matrix(long nrl, long nrh, long ncl, long nch)
                    239: {
                    240:   long i, nrow=nrh-nrl+1, ncol=nch-ncl+1;
                    241:   double **m;
                    242: 
                    243:   m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
                    244:   if (!m) nrerror("allocation failure 1 in matrix()");
                    245:   m += NR_END;
                    246:   m -= nrl;
                    247: 
                    248:   m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
                    249:   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
                    250:   m[nrl] += NR_END;
                    251:   m[nrl] -= ncl;
                    252: 
                    253:   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
                    254:   return m;
                    255: }
                    256: 
                    257: /*************************free matrix ************************/
                    258: void free_matrix(double **m, long nrl, long nrh, long ncl, long nch)
                    259: {
                    260:   free((FREE_ARG)(m[nrl]+ncl-NR_END));
                    261:   free((FREE_ARG)(m+nrl-NR_END));
                    262: }
                    263: 
                    264: /******************* ma3x *******************************/
                    265: double ***ma3x(long nrl, long nrh, long ncl, long nch, long nll, long nlh)
                    266: {
                    267:   long i, j, nrow=nrh-nrl+1, ncol=nch-ncl+1, nlay=nlh-nll+1;
                    268:   double ***m;
                    269: 
                    270:   m=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
                    271:   if (!m) nrerror("allocation failure 1 in matrix()");
                    272:   m += NR_END;
                    273:   m -= nrl;
                    274: 
                    275:   m[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
                    276:   if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
                    277:   m[nrl] += NR_END;
                    278:   m[nrl] -= ncl;
                    279: 
                    280:   for (i=nrl+1; i<=nrh; i++) m[i]=m[i-1]+ncol;
                    281: 
                    282:   m[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*nlay+NR_END)*sizeof(double)));
                    283:   if (!m[nrl][ncl]) nrerror("allocation failure 3 in matrix()");
                    284:   m[nrl][ncl] += NR_END;
                    285:   m[nrl][ncl] -= nll;
                    286:   for (j=ncl+1; j<=nch; j++) 
                    287:     m[nrl][j]=m[nrl][j-1]+nlay;
                    288:   
                    289:   for (i=nrl+1; i<=nrh; i++) {
                    290:     m[i][ncl]=m[i-1l][ncl]+ncol*nlay;
                    291:     for (j=ncl+1; j<=nch; j++) 
                    292:       m[i][j]=m[i][j-1]+nlay;
                    293:   }
                    294:   return m;
                    295: }
                    296: 
                    297: /*************************free ma3x ************************/
                    298: void free_ma3x(double ***m, long nrl, long nrh, long ncl, long nch,long nll, long nlh)
                    299: {
                    300:   free((FREE_ARG)(m[nrl][ncl]+ nll-NR_END));
                    301:   free((FREE_ARG)(m[nrl]+ncl-NR_END));
                    302:   free((FREE_ARG)(m+nrl-NR_END));
                    303: }
                    304: 
                    305: /***************** f1dim *************************/
                    306: extern int ncom; 
                    307: extern double *pcom,*xicom;
                    308: extern double (*nrfunc)(double []); 
                    309:  
                    310: double f1dim(double x) 
                    311: { 
                    312:   int j; 
                    313:   double f;
                    314:   double *xt; 
                    315:  
                    316:   xt=vector(1,ncom); 
                    317:   for (j=1;j<=ncom;j++) xt[j]=pcom[j]+x*xicom[j]; 
                    318:   f=(*nrfunc)(xt); 
                    319:   free_vector(xt,1,ncom); 
                    320:   return f; 
                    321: } 
                    322: 
                    323: /*****************brent *************************/
                    324: double brent(double ax, double bx, double cx, double (*f)(double), double tol,         double *xmin) 
                    325: { 
                    326:   int iter; 
                    327:   double a,b,d,etemp;
                    328:   double fu,fv,fw,fx;
                    329:   double ftemp;
                    330:   double p,q,r,tol1,tol2,u,v,w,x,xm; 
                    331:   double e=0.0; 
                    332:  
                    333:   a=(ax < cx ? ax : cx); 
                    334:   b=(ax > cx ? ax : cx); 
                    335:   x=w=v=bx; 
                    336:   fw=fv=fx=(*f)(x); 
                    337:   for (iter=1;iter<=ITMAX;iter++) { 
                    338:     xm=0.5*(a+b); 
                    339:     tol2=2.0*(tol1=tol*fabs(x)+ZEPS); 
                    340:     /*         if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret)))*/
                    341:     printf(".");fflush(stdout);
                    342: #ifdef DEBUG
                    343:     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);
                    344:     /*         if ((fabs(x-xm) <= (tol2-0.5*(b-a)))||(2.0*fabs(fu-ftemp) <= ftol*1.e-2*(fabs(fu)+fabs(ftemp)))) { */
                    345: #endif
                    346:     if (fabs(x-xm) <= (tol2-0.5*(b-a))){ 
                    347:       *xmin=x; 
                    348:       return fx; 
                    349:     } 
                    350:     ftemp=fu;
                    351:     if (fabs(e) > tol1) { 
                    352:       r=(x-w)*(fx-fv); 
                    353:       q=(x-v)*(fx-fw); 
                    354:       p=(x-v)*q-(x-w)*r; 
                    355:       q=2.0*(q-r); 
                    356:       if (q > 0.0) p = -p; 
                    357:       q=fabs(q); 
                    358:       etemp=e; 
                    359:       e=d; 
                    360:       if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x)) 
                    361:        d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
                    362:       else { 
                    363:        d=p/q; 
                    364:        u=x+d; 
                    365:        if (u-a < tol2 || b-u < tol2) 
                    366:          d=SIGN(tol1,xm-x); 
                    367:       } 
                    368:     } else { 
                    369:       d=CGOLD*(e=(x >= xm ? a-x : b-x)); 
                    370:     } 
                    371:     u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d)); 
                    372:     fu=(*f)(u); 
                    373:     if (fu <= fx) { 
                    374:       if (u >= x) a=x; else b=x; 
                    375:       SHFT(v,w,x,u) 
                    376:        SHFT(fv,fw,fx,fu) 
                    377:        } else { 
                    378:          if (u < x) a=u; else b=u; 
                    379:          if (fu <= fw || w == x) { 
                    380:            v=w; 
                    381:            w=u; 
                    382:            fv=fw; 
                    383:            fw=fu; 
                    384:          } else if (fu <= fv || v == x || v == w) { 
                    385:            v=u; 
                    386:            fv=fu; 
                    387:          } 
                    388:        } 
                    389:   } 
                    390:   nrerror("Too many iterations in brent"); 
                    391:   *xmin=x; 
                    392:   return fx; 
                    393: } 
                    394: 
                    395: /****************** mnbrak ***********************/
                    396: 
                    397: void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, double *fc, 
                    398:            double (*func)(double)) 
                    399: { 
                    400:   double ulim,u,r,q, dum;
                    401:   double fu; 
                    402:  
                    403:   *fa=(*func)(*ax); 
                    404:   *fb=(*func)(*bx); 
                    405:   if (*fb > *fa) { 
                    406:     SHFT(dum,*ax,*bx,dum) 
                    407:       SHFT(dum,*fb,*fa,dum) 
                    408:       } 
                    409:   *cx=(*bx)+GOLD*(*bx-*ax); 
                    410:   *fc=(*func)(*cx); 
                    411:   while (*fb > *fc) { 
                    412:     r=(*bx-*ax)*(*fb-*fc); 
                    413:     q=(*bx-*cx)*(*fb-*fa); 
                    414:     u=(*bx)-((*bx-*cx)*q-(*bx-*ax)*r)/ 
                    415:       (2.0*SIGN(FMAX(fabs(q-r),TINY),q-r)); 
                    416:     ulim=(*bx)+GLIMIT*(*cx-*bx); 
                    417:     if ((*bx-u)*(u-*cx) > 0.0) { 
                    418:       fu=(*func)(u); 
                    419:     } else if ((*cx-u)*(u-ulim) > 0.0) { 
                    420:       fu=(*func)(u); 
                    421:       if (fu < *fc) { 
                    422:        SHFT(*bx,*cx,u,*cx+GOLD*(*cx-*bx)) 
                    423:          SHFT(*fb,*fc,fu,(*func)(u)) 
                    424:          } 
                    425:     } else if ((u-ulim)*(ulim-*cx) >= 0.0) { 
                    426:       u=ulim; 
                    427:       fu=(*func)(u); 
                    428:     } else { 
                    429:       u=(*cx)+GOLD*(*cx-*bx); 
                    430:       fu=(*func)(u); 
                    431:     } 
                    432:     SHFT(*ax,*bx,*cx,u) 
                    433:       SHFT(*fa,*fb,*fc,fu) 
                    434:       } 
                    435: } 
                    436: 
                    437: /*************** linmin ************************/
                    438: 
                    439: int ncom; 
                    440: double *pcom,*xicom;
                    441: double (*nrfunc)(double []); 
                    442:  
                    443: void linmin(double p[], double xi[], int n, double *fret,double (*func)(double [])) 
                    444: { 
                    445:   double brent(double ax, double bx, double cx, 
                    446:               double (*f)(double), double tol, double *xmin); 
                    447:   double f1dim(double x); 
                    448:   void mnbrak(double *ax, double *bx, double *cx, double *fa, double *fb, 
                    449:              double *fc, double (*func)(double)); 
                    450:   int j; 
                    451:   double xx,xmin,bx,ax; 
                    452:   double fx,fb,fa;
                    453:  
                    454:   ncom=n; 
                    455:   pcom=vector(1,n); 
                    456:   xicom=vector(1,n); 
                    457:   nrfunc=func; 
                    458:   for (j=1;j<=n;j++) { 
                    459:     pcom[j]=p[j]; 
                    460:     xicom[j]=xi[j]; 
                    461:   } 
                    462:   ax=0.0; 
                    463:   xx=1.0; 
                    464:   mnbrak(&ax,&xx,&bx,&fa,&fx,&fb,f1dim); 
                    465:   *fret=brent(ax,xx,bx,f1dim,TOL,&xmin); 
                    466: #ifdef DEBUG
                    467:   printf("retour brent fret=%.12e xmin=%.12e\n",*fret,xmin);
                    468: #endif
                    469:   for (j=1;j<=n;j++) { 
                    470:     xi[j] *= xmin; 
                    471:     p[j] += xi[j]; 
                    472:   } 
                    473:   free_vector(xicom,1,n); 
                    474:   free_vector(pcom,1,n); 
                    475: } 
                    476: 
                    477: /*************** powell ************************/
                    478: void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret, 
                    479:            double (*func)(double [])) 
                    480: 
                    481: { 
                    482: 
                    483: 
                    484:   void linmin(double p[], double xi[], int n, double *fret, 
                    485:              double (*func)(double [])); 
                    486:   int i,ibig,j; 
                    487:   double del,t,*pt,*ptt,*xit;
                    488:   double fp,fptt;
                    489:   double *xits;
                    490:   pt=vector(1,n); 
                    491:   ptt=vector(1,n); 
                    492:   xit=vector(1,n); 
                    493:   xits=vector(1,n); 
                    494:   *fret=(*func)(p); 
                    495:   for (j=1;j<=n;j++) pt[j]=p[j]; 
                    496:   for (*iter=1;;++(*iter)) { 
                    497:     fp=(*fret); 
                    498:     ibig=0; 
                    499:     del=0.0; 
                    500:     printf("\nPowell iter=%d -2*LL=%.12f",*iter,*fret);
                    501:     for (i=1;i<=n;i++) 
                    502:       printf(" %d %.12f",i, p[i]);
                    503:     printf("\n");
                    504:     for (i=1;i<=n;i++) { 
                    505:       for (j=1;j<=n;j++) xit[j]=xi[j][i]; 
                    506:       fptt=(*fret); 
                    507: #ifdef DEBUG
                    508:       printf("fret=%lf \n",*fret);
                    509: #endif
                    510:       printf("%d",i);fflush(stdout);
                    511:       linmin(p,xit,n,fret,func); 
                    512:       if (fabs(fptt-(*fret)) > del) { 
                    513:        del=fabs(fptt-(*fret)); 
                    514:        ibig=i; 
                    515:       } 
                    516: #ifdef DEBUG
                    517:       printf("%d %.12e",i,(*fret));
                    518:       for (j=1;j<=n;j++) {
                    519:        xits[j]=FMAX(fabs(p[j]-pt[j]),1.e-5);
                    520:        printf(" x(%d)=%.12e",j,xit[j]);
                    521:       }
                    522:       for(j=1;j<=n;j++) 
                    523:        printf(" p=%.12e",p[j]);
                    524:       printf("\n");
                    525: #endif
                    526:     } 
                    527:     if (2.0*fabs(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))) {
                    528: #ifdef DEBUG
                    529:       int k[2],l;
                    530:       k[0]=1;
                    531:       k[1]=-1;
                    532:       printf("Max: %.12e",(*func)(p));
                    533:       for (j=1;j<=n;j++) 
                    534:        printf(" %.12e",p[j]);
                    535:       printf("\n");
                    536:       for(l=0;l<=1;l++) {
                    537:        for (j=1;j<=n;j++) {
                    538:          ptt[j]=p[j]+(p[j]-pt[j])*k[l];
                    539:          printf("l=%d j=%d ptt=%.12e, xits=%.12e, p=%.12e, xit=%.12e", l,j,ptt[j],xits[j],p[j],xit[j]);
                    540:        }
                    541:        printf("func(ptt)=%.12e, deriv=%.12e\n",(*func)(ptt),(ptt[j]-p[j])/((*func)(ptt)-(*func)(p)));
                    542:       }
                    543: #endif
                    544: 
                    545: 
                    546:       free_vector(xit,1,n); 
                    547:       free_vector(xits,1,n); 
                    548:       free_vector(ptt,1,n); 
                    549:       free_vector(pt,1,n); 
                    550:       return; 
                    551:     } 
                    552:     if (*iter == ITMAX) nrerror("powell exceeding maximum iterations."); 
                    553:     for (j=1;j<=n;j++) { 
                    554:       ptt[j]=2.0*p[j]-pt[j]; 
                    555:       xit[j]=p[j]-pt[j]; 
                    556:       pt[j]=p[j]; 
                    557:     } 
                    558:     fptt=(*func)(ptt); 
                    559:     if (fptt < fp) { 
                    560:       t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt); 
                    561:       if (t < 0.0) { 
                    562:        linmin(p,xit,n,fret,func); 
                    563:        for (j=1;j<=n;j++) { 
                    564:          xi[j][ibig]=xi[j][n]; 
                    565:          xi[j][n]=xit[j]; 
                    566:        }
                    567: #ifdef DEBUG
                    568:        printf("Direction changed  last moved %d in place of ibig=%d, new last is the average:\n",n,ibig);
                    569:        for(j=1;j<=n;j++)
                    570:          printf(" %.12e",xit[j]);
                    571:        printf("\n");
                    572: #endif
                    573:       } 
                    574:     } 
                    575:   } 
                    576: } 
                    577: 
                    578: /**** Prevalence limit ****************/
                    579: 
                    580: double **prevalim(double **prlim, int nlstate, double x[], double age, double **oldm, double **savm, double ftolpl)
                    581: {
                    582:   /* Computes the prevalence limit in each live state at age x by left multiplying the unit
                    583:      matrix by transitions matrix until convergence is reached */
                    584: 
                    585:   int i, ii,j,k;
                    586:   double min, max, maxmin, maxmax,sumnew=0.;
                    587:   double **matprod2();
                    588:   double **out, cov[NCOVMAX], **pmij();
                    589:   double **newm;
                    590:   double agefin, delaymax=50 ; /* Max number of years to converge */
                    591: 
                    592:   for (ii=1;ii<=nlstate+ndeath;ii++)
                    593:     for (j=1;j<=nlstate+ndeath;j++){
                    594:       oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                    595:     }
                    596:   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
                    597:   for(agefin=age-stepm/YEARM; agefin>=age-delaymax; agefin=agefin-stepm/YEARM){
                    598:     newm=savm;
                    599:     /* Covariates have to be included here again */
                    600:     cov[1]=1.;
                    601:     cov[2]=agefin;
                    602:     out=matprod2(newm, pmij(pmmij,cov,ncov,x,nlstate),1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, oldm);
                    603: /*    printf("age=%f agefin=%f po=%f pn=%f\n",age,agefin,oldm[1][1],newm[1][1]);*/
                    604:     
                    605:     savm=oldm;
                    606:     oldm=newm;
                    607:     maxmax=0.;
                    608:     for(j=1;j<=nlstate;j++){
                    609:       min=1.;
                    610:       max=0.;
                    611:       for(i=1; i<=nlstate; i++) {
                    612:        sumnew=0;
                    613:        for(k=1; k<=ndeath; k++) sumnew+=newm[i][nlstate+k];
                    614:        prlim[i][j]= newm[i][j]/(1-sumnew);
                    615:        max=FMAX(max,prlim[i][j]);
                    616:        min=FMIN(min,prlim[i][j]);
                    617:       }
                    618:       maxmin=max-min;
                    619:       maxmax=FMAX(maxmax,maxmin);
                    620:     }
                    621:     if(maxmax < ftolpl){
                    622:       return prlim;
                    623:     }
                    624:   }
                    625: }
                    626: 
                    627: /*************** transition probabilities **********/ 
                    628: 
                    629: double **pmij(double **ps, double *cov, int ncov, double *x, int nlstate )
                    630: {
                    631:   double s1, s2;
                    632:   /*double t34;*/
                    633:   int i,j,j1, nc, ii, jj;
                    634: 
                    635:     for(i=1; i<= nlstate; i++){
                    636:     for(j=1; j<i;j++){
                    637:       for (nc=1, s2=0.;nc <=ncov; nc++){
                    638:        /*s2 += param[i][j][nc]*cov[nc];*/
                    639:        s2 += x[(i-1)*nlstate*ncov+(j-1)*ncov+nc+(i-1)*(ndeath-1)*ncov]*cov[nc];
                    640:        /*printf("Int j<i s1=%.17e, s2=%.17e\n",s1,s2);*/
                    641:       }
                    642:       ps[i][j]=s2;
                    643:       /*printf("s1=%.17e, s2=%.17e\n",s1,s2);*/
                    644:     }
                    645:     for(j=i+1; j<=nlstate+ndeath;j++){
                    646:       for (nc=1, s2=0.;nc <=ncov; nc++){
                    647:        s2 += x[(i-1)*nlstate*ncov+(j-2)*ncov+nc+(i-1)*(ndeath-1)*ncov]*cov[nc];
                    648:        /*printf("Int j>i s1=%.17e, s2=%.17e %lx %lx\n",s1,s2,s1,s2);*/
                    649:       }
                    650:       ps[i][j]=s2;
                    651:     }
                    652:   }
                    653:   for(i=1; i<= nlstate; i++){
                    654:      s1=0;
                    655:     for(j=1; j<i; j++)
                    656:       s1+=exp(ps[i][j]);
                    657:     for(j=i+1; j<=nlstate+ndeath; j++)
                    658:       s1+=exp(ps[i][j]);
                    659:     ps[i][i]=1./(s1+1.);
                    660:     for(j=1; j<i; j++)
                    661:       ps[i][j]= exp(ps[i][j])*ps[i][i];
                    662:     for(j=i+1; j<=nlstate+ndeath; j++)
                    663:       ps[i][j]= exp(ps[i][j])*ps[i][i];
                    664:     /* ps[i][nlstate+1]=1.-s1- ps[i][i];*/ /* Sum should be 1 */
                    665:   } /* end i */
                    666: 
                    667:   for(ii=nlstate+1; ii<= nlstate+ndeath; ii++){
                    668:     for(jj=1; jj<= nlstate+ndeath; jj++){
                    669:       ps[ii][jj]=0;
                    670:       ps[ii][ii]=1;
                    671:     }
                    672:   }
                    673: 
                    674:   /*   for(ii=1; ii<= nlstate+ndeath; ii++){
                    675:     for(jj=1; jj<= nlstate+ndeath; jj++){
                    676:      printf("%lf ",ps[ii][jj]);
                    677:    }
                    678:     printf("\n ");
                    679:     }
                    680:     printf("\n ");printf("%lf ",cov[2]);*/
                    681: /*
                    682:   for(i=1; i<= npar; i++) printf("%f ",x[i]);
                    683:   goto end;*/
                    684:     return ps;
                    685: }
                    686: 
                    687: /**************** Product of 2 matrices ******************/
                    688: 
                    689: double **matprod2(double **out, double **in,long nrl, long nrh, long ncl, long nch, long ncolol, long ncoloh, double **b)
                    690: {
                    691:   /* Computes the matric product of in(1,nrh-nrl+1)(1,nch-ncl+1) times
                    692:      b(1,nch-ncl+1)(1,ncoloh-ncolol+1) into out(...) */
                    693:   /* in, b, out are matrice of pointers which should have been initialized 
                    694:      before: only the contents of out is modified. The function returns
                    695:      a pointer to pointers identical to out */
                    696:   long i, j, k;
                    697:   for(i=nrl; i<= nrh; i++)
                    698:     for(k=ncolol; k<=ncoloh; k++)
                    699:       for(j=ncl,out[i][k]=0.; j<=nch; j++)
                    700:        out[i][k] +=in[i][j]*b[j][k];
                    701: 
                    702:   return out;
                    703: }
                    704: 
                    705: 
                    706: /************* Higher Matrix Product ***************/
                    707: 
                    708: double ***hpxij(double ***po, int nhstepm, double age, int hstepm, double *x, int nlstate, int stepm, double **oldm, double **savm )
                    709: {
                    710:   /* Computes the transition matrix starting at age 'age' over 'nhstepm*hstepm*stepm' month 
                    711:      duration (i.e. until
                    712:      age (in years)  age+nhstepm*stepm/12) by multiplying nhstepm*hstepm matrices. 
                    713:      Output is stored in matrix po[i][j][h] for h every 'hstepm' step 
                    714:      (typically every 2 years instead of every month which is too big).
                    715:      Model is determined by parameters x and covariates have to be 
                    716:      included manually here. 
                    717: 
                    718:      */
                    719: 
                    720:   int i, j, d, h;
                    721:   double **out, cov[NCOVMAX];
                    722:   double **newm;
                    723: 
                    724:   /* Hstepm could be zero and should return the unit matrix */
                    725:   for (i=1;i<=nlstate+ndeath;i++)
                    726:     for (j=1;j<=nlstate+ndeath;j++){
                    727:       oldm[i][j]=(i==j ? 1.0 : 0.0);
                    728:       po[i][j][0]=(i==j ? 1.0 : 0.0);
                    729:     }
                    730:   /* Even if hstepm = 1, at least one multiplication by the unit matrix */
                    731:   for(h=1; h <=nhstepm; h++){
                    732:     for(d=1; d <=hstepm; d++){
                    733:       newm=savm;
                    734:       /* Covariates have to be included here again */
                    735:       cov[1]=1.;
                    736:       cov[2]=age+((h-1)*hstepm + (d-1))*stepm/YEARM;
                    737:       /*printf("h=%d d=%d age=%f cov=%f\n",h,d,age,cov[2]);*/
                    738:       out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,1,nlstate+ndeath, 
                    739:                   pmij(pmmij,cov,ncov,x,nlstate));
                    740:       savm=oldm;
                    741:       oldm=newm;
                    742:     }
                    743:     for(i=1; i<=nlstate+ndeath; i++)
                    744:       for(j=1;j<=nlstate+ndeath;j++) {
                    745:        po[i][j][h]=newm[i][j];
                    746:        /*printf("i=%d j=%d h=%d po[i][j][h]=%f ",i,j,h,po[i][j][h]);
                    747:         */
                    748:       }
                    749:   } /* end h */
                    750:   return po;
                    751: }
                    752: 
                    753: 
                    754: /*************** log-likelihood *************/
                    755: double func( double *x)
                    756: {
                    757:   int i, ii, j, k, mi, d;
                    758:   double l, ll[NLSTATEMAX], cov[NCOVMAX];
                    759:   double **out;
                    760:   double sw; /* Sum of weights */
                    761:   double lli; /* Individual log likelihood */
                    762:   long ipmx;
                    763:   /*extern weight */
                    764:   /* We are differentiating ll according to initial status */
                    765:   /*  for (i=1;i<=npar;i++) printf("%f ", x[i]);*/
                    766:   /*for(i=1;i<imx;i++) 
                    767: printf(" %d\n",s[4][i]);
                    768:   */
                    769: 
                    770:   for(k=1; k<=nlstate; k++) ll[k]=0.;
                    771:   for (i=1,ipmx=0, sw=0.; i<=imx; i++){
                    772:        for(mi=1; mi<= wav[i]-1; mi++){
                    773:       for (ii=1;ii<=nlstate+ndeath;ii++)
                    774:        for (j=1;j<=nlstate+ndeath;j++) oldm[ii][j]=(ii==j ? 1.0 : 0.0);
                    775:             for(d=0; d<dh[mi][i]; d++){
                    776:        newm=savm;
                    777:          cov[1]=1.;
                    778:          cov[2]=agev[mw[mi][i]][i]+d*stepm/YEARM;
                    779:            out=matprod2(newm,oldm,1,nlstate+ndeath,1,nlstate+ndeath,
                    780:                       1,nlstate+ndeath,pmij(pmmij,cov,ncov,x,nlstate));
                    781:          savm=oldm;
                    782:          oldm=newm;
                    783: 
                    784: 
                    785:       } /* end mult */
                    786:    
                    787:       lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);
                    788:       /* printf(" %f ",out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]);*/
                    789:       ipmx +=1;
                    790:       sw += weight[i];
                    791:       ll[s[mw[mi][i]][i]] += 2*weight[i]*lli;
                    792:     } /* end of wave */
                    793:   } /* end of individual */
                    794: 
                    795:   for(k=1,l=0.; k<=nlstate; k++) l += ll[k];
                    796:   /* printf("l1=%f l2=%f ",ll[1],ll[2]); */
                    797:   l= l*ipmx/sw; /* To get the same order of magnitude as if weight=1 for every body */
                    798:   return -l;
                    799: }
                    800: 
                    801: 
                    802: /*********** Maximum Likelihood Estimation ***************/
                    803: 
                    804: void mlikeli(FILE *ficres,double p[], int npar, int ncov, int nlstate, double ftol, double (*func)(double []))
                    805: {
                    806:   int i,j, iter;
                    807:   double **xi,*delti;
                    808:   double fret;
                    809:   xi=matrix(1,npar,1,npar);
                    810:   for (i=1;i<=npar;i++)
                    811:     for (j=1;j<=npar;j++)
                    812:       xi[i][j]=(i==j ? 1.0 : 0.0);
                    813:   printf("Powell\n");
                    814:   powell(p,xi,npar,ftol,&iter,&fret,func);
                    815: 
                    816:    printf("\n#Number of iterations = %d, -2 Log likelihood = %.12f\n",iter,func(p));
                    817:   fprintf(ficres,"#Number of iterations = %d, -2 Log likelihood = %.12f ",iter,func(p));
                    818: 
                    819: }
                    820: 
                    821: /**** Computes Hessian and covariance matrix ***/
                    822: void hesscov(double **matcov, double p[], int npar, double delti[], double ftolhess, double (*func)(double []))
                    823: {
                    824:   double  **a,**y,*x,pd;
                    825:   double **hess;
                    826:   int i, j,jk;
                    827:   int *indx;
                    828: 
                    829:   double hessii(double p[], double delta, int theta, double delti[]);
                    830:   double hessij(double p[], double delti[], int i, int j);
                    831:   void lubksb(double **a, int npar, int *indx, double b[]) ;
                    832:   void ludcmp(double **a, int npar, int *indx, double *d) ;
                    833: 
                    834: 
                    835:   hess=matrix(1,npar,1,npar);
                    836: 
                    837:   printf("\nCalculation of the hessian matrix. Wait...\n");
                    838:   for (i=1;i<=npar;i++){
                    839:     printf("%d",i);fflush(stdout);
                    840:     hess[i][i]=hessii(p,ftolhess,i,delti);
                    841:     /*printf(" %f ",p[i]);*/
                    842:   }
                    843: 
                    844:   for (i=1;i<=npar;i++) {
                    845:     for (j=1;j<=npar;j++)  {
                    846:       if (j>i) { 
                    847:        printf(".%d%d",i,j);fflush(stdout);
                    848:        hess[i][j]=hessij(p,delti,i,j);
                    849:        hess[j][i]=hess[i][j];
                    850:       }
                    851:     }
                    852:   }
                    853:   printf("\n");
                    854: 
                    855:   printf("\nInverting the hessian to get the covariance matrix. Wait...\n");
                    856:   
                    857:   a=matrix(1,npar,1,npar);
                    858:   y=matrix(1,npar,1,npar);
                    859:   x=vector(1,npar);
                    860:   indx=ivector(1,npar);
                    861:   for (i=1;i<=npar;i++)
                    862:     for (j=1;j<=npar;j++) a[i][j]=hess[i][j];
                    863:   ludcmp(a,npar,indx,&pd);
                    864: 
                    865:   for (j=1;j<=npar;j++) {
                    866:     for (i=1;i<=npar;i++) x[i]=0;
                    867:     x[j]=1;
                    868:     lubksb(a,npar,indx,x);
                    869:     for (i=1;i<=npar;i++){ 
                    870:       matcov[i][j]=x[i];
                    871:     }
                    872:   }
                    873: 
                    874:   printf("\n#Hessian matrix#\n");
                    875:   for (i=1;i<=npar;i++) { 
                    876:     for (j=1;j<=npar;j++) { 
                    877:       printf("%.3e ",hess[i][j]);
                    878:     }
                    879:     printf("\n");
                    880:   }
                    881: 
                    882:   /* Recompute Inverse */
                    883:   for (i=1;i<=npar;i++)
                    884:     for (j=1;j<=npar;j++) a[i][j]=matcov[i][j];
                    885:   ludcmp(a,npar,indx,&pd);
                    886: 
                    887:   /*  printf("\n#Hessian matrix recomputed#\n");
                    888: 
                    889:   for (j=1;j<=npar;j++) {
                    890:     for (i=1;i<=npar;i++) x[i]=0;
                    891:     x[j]=1;
                    892:     lubksb(a,npar,indx,x);
                    893:     for (i=1;i<=npar;i++){ 
                    894:       y[i][j]=x[i];
                    895:       printf("%.3e ",y[i][j]);
                    896:     }
                    897:     printf("\n");
                    898:   }
                    899:   */
                    900: 
                    901:   free_matrix(a,1,npar,1,npar);
                    902:   free_matrix(y,1,npar,1,npar);
                    903:   free_vector(x,1,npar);
                    904:   free_ivector(indx,1,npar);
                    905:   free_matrix(hess,1,npar,1,npar);
                    906: 
                    907: 
                    908: }
                    909: 
                    910: /*************** hessian matrix ****************/
                    911: double hessii( double x[], double delta, int theta, double delti[])
                    912: {
                    913:   int i;
                    914:   int l=1, lmax=20;
                    915:   double k1,k2;
                    916:   double p2[NPARMAX+1];
                    917:   double res;
                    918:   double delt, delts, nkhi=10.,nkhif=1., khi=1.e-4;
                    919:   double fx;
                    920:   int k=0,kmax=10;
                    921:   double l1;
                    922: 
                    923:   fx=func(x);
                    924:   for (i=1;i<=npar;i++) p2[i]=x[i];
                    925:   for(l=0 ; l <=lmax; l++){
                    926:     l1=pow(10,l);
                    927:     delts=delt;
                    928:     for(k=1 ; k <kmax; k=k+1){
                    929:       delt = delta*(l1*k);
                    930:       p2[theta]=x[theta] +delt;
                    931:       k1=func(p2)-fx;
                    932:       p2[theta]=x[theta]-delt;
                    933:       k2=func(p2)-fx;
                    934:       /*res= (k1-2.0*fx+k2)/delt/delt; */
                    935:       res= (k1+k2)/delt/delt/2.; /* Divided by because L and not 2*L */
                    936:       
                    937: #ifdef DEBUG
                    938:       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);
                    939: #endif
                    940:       /*if(fabs(k1-2.0*fx+k2) <1.e-13){ */
                    941:       if((k1 <khi/nkhi/2.) || (k2 <khi/nkhi/2.)){
                    942:        k=kmax;
                    943:       }
                    944:       else if((k1 >khi/nkhif) || (k2 >khi/nkhif)){ /* Keeps lastvalue before 3.84/2 KHI2 5% 1d.f. */
                    945:        k=kmax; l=lmax*10.;
                    946:       }
                    947:       else if((k1 >khi/nkhi) || (k2 >khi/nkhi)){ 
                    948:        delts=delt;
                    949:       }
                    950:     }
                    951:   }
                    952:   delti[theta]=delts;
                    953:   return res;
                    954:   
                    955: }
                    956: 
                    957: double hessij( double x[], double delti[], int thetai,int thetaj)
                    958: {
                    959:   int i;
                    960:   int l=1, l1, lmax=20;
                    961:   double k1,k2,k3,k4,res,fx;
                    962:   double p2[NPARMAX+1];
                    963:   int k;
                    964: 
                    965:   fx=func(x);
                    966:   for (k=1; k<=2; k++) {
                    967:     for (i=1;i<=npar;i++) p2[i]=x[i];
                    968:     p2[thetai]=x[thetai]+delti[thetai]/k;
                    969:     p2[thetaj]=x[thetaj]+delti[thetaj]/k;
                    970:     k1=func(p2)-fx;
                    971:   
                    972:     p2[thetai]=x[thetai]+delti[thetai]/k;
                    973:     p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                    974:     k2=func(p2)-fx;
                    975:   
                    976:     p2[thetai]=x[thetai]-delti[thetai]/k;
                    977:     p2[thetaj]=x[thetaj]+delti[thetaj]/k;
                    978:     k3=func(p2)-fx;
                    979:   
                    980:     p2[thetai]=x[thetai]-delti[thetai]/k;
                    981:     p2[thetaj]=x[thetaj]-delti[thetaj]/k;
                    982:     k4=func(p2)-fx;
                    983:     res=(k1-k2-k3+k4)/4.0/delti[thetai]*k/delti[thetaj]*k/2.; /* Because of L not 2*L */
                    984: #ifdef DEBUG
                    985:     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);
                    986: #endif
                    987:   }
                    988:   return res;
                    989: }
                    990: 
                    991: /************** Inverse of matrix **************/
                    992: void ludcmp(double **a, int n, int *indx, double *d) 
                    993: { 
                    994:   int i,imax,j,k; 
                    995:   double big,dum,sum,temp; 
                    996:   double *vv; 
                    997:  
                    998:   vv=vector(1,n); 
                    999:   *d=1.0; 
                   1000:   for (i=1;i<=n;i++) { 
                   1001:     big=0.0; 
                   1002:     for (j=1;j<=n;j++) 
                   1003:       if ((temp=fabs(a[i][j])) > big) big=temp; 
                   1004:     if (big == 0.0) nrerror("Singular matrix in routine ludcmp"); 
                   1005:     vv[i]=1.0/big; 
                   1006:   } 
                   1007:   for (j=1;j<=n;j++) { 
                   1008:     for (i=1;i<j;i++) { 
                   1009:       sum=a[i][j]; 
                   1010:       for (k=1;k<i;k++) sum -= a[i][k]*a[k][j]; 
                   1011:       a[i][j]=sum; 
                   1012:     } 
                   1013:     big=0.0; 
                   1014:     for (i=j;i<=n;i++) { 
                   1015:       sum=a[i][j]; 
                   1016:       for (k=1;k<j;k++) 
                   1017:        sum -= a[i][k]*a[k][j]; 
                   1018:       a[i][j]=sum; 
                   1019:       if ( (dum=vv[i]*fabs(sum)) >= big) { 
                   1020:        big=dum; 
                   1021:        imax=i; 
                   1022:       } 
                   1023:     } 
                   1024:     if (j != imax) { 
                   1025:       for (k=1;k<=n;k++) { 
                   1026:        dum=a[imax][k]; 
                   1027:        a[imax][k]=a[j][k]; 
                   1028:        a[j][k]=dum; 
                   1029:       } 
                   1030:       *d = -(*d); 
                   1031:       vv[imax]=vv[j]; 
                   1032:     } 
                   1033:     indx[j]=imax; 
                   1034:     if (a[j][j] == 0.0) a[j][j]=TINY; 
                   1035:     if (j != n) { 
                   1036:       dum=1.0/(a[j][j]); 
                   1037:       for (i=j+1;i<=n;i++) a[i][j] *= dum; 
                   1038:     } 
                   1039:   } 
                   1040:   free_vector(vv,1,n);  /* Doesn't work */
                   1041: ;
                   1042: } 
                   1043: 
                   1044: void lubksb(double **a, int n, int *indx, double b[]) 
                   1045: { 
                   1046:   int i,ii=0,ip,j; 
                   1047:   double sum; 
                   1048:  
                   1049:   for (i=1;i<=n;i++) { 
                   1050:     ip=indx[i]; 
                   1051:     sum=b[ip]; 
                   1052:     b[ip]=b[i]; 
                   1053:     if (ii) 
                   1054:       for (j=ii;j<=i-1;j++) sum -= a[i][j]*b[j]; 
                   1055:     else if (sum) ii=i; 
                   1056:     b[i]=sum; 
                   1057:   } 
                   1058:   for (i=n;i>=1;i--) { 
                   1059:     sum=b[i]; 
                   1060:     for (j=i+1;j<=n;j++) sum -= a[i][j]*b[j]; 
                   1061:     b[i]=sum/a[i][i]; 
                   1062:   } 
                   1063: } 
                   1064: 
                   1065: /************ Frequencies ********************/
                   1066: void  freqsummary(char fileres[], int agemin, int agemax, int **s, double **agev, int nlstate, int imx)
                   1067: {  /* Some frequencies */
                   1068:  
                   1069:   int i, m, jk;
                   1070:   double ***freq; /* Frequencies */
                   1071:   double *pp;
                   1072:   double pos;
                   1073:   FILE *ficresp;
                   1074:   char fileresp[FILENAMELENGTH];
                   1075: 
                   1076:   pp=vector(1,nlstate);
                   1077: 
                   1078:   strcpy(fileresp,"p");
                   1079:   strcat(fileresp,fileres);
                   1080:   if((ficresp=fopen(fileresp,"w"))==NULL) {
                   1081:     printf("Problem with prevalence resultfile: %s\n", fileresp);
                   1082:     exit(0);
                   1083:   }
                   1084: 
                   1085:   freq= ma3x(-1,nlstate+ndeath,-1,nlstate+ndeath,agemin,agemax+3);
                   1086:   for (i=-1; i<=nlstate+ndeath; i++)  
                   1087:     for (jk=-1; jk<=nlstate+ndeath; jk++)  
                   1088:       for(m=agemin; m <= agemax+3; m++)
                   1089:        freq[i][jk][m]=0;
                   1090: 
                   1091:   for (i=1; i<=imx; i++)  {
                   1092:     for(m=firstpass; m<= lastpass-1; m++){
                   1093:       if(agev[m][i]==0) agev[m][i]=agemax+1;
                   1094:       if(agev[m][i]==1) agev[m][i]=agemax+2;
                   1095:        freq[s[m][i]][s[m+1][i]][(int)agev[m][i]] += weight[i];
                   1096:        freq[s[m][i]][s[m+1][i]][(int) agemax+3] += weight[i];
                   1097:     }
                   1098:   }
                   1099: 
                   1100:   fprintf(ficresp, "#");
                   1101:   for(i=1; i<=nlstate;i++) 
                   1102:     fprintf(ficresp, " Age Prev(%d) N(%d) N",i,i);
                   1103: fprintf(ficresp, "\n");
                   1104: 
                   1105:   for(i=(int)agemin; i <= (int)agemax+3; i++){
                   1106:     if(i==(int)agemax+3)
                   1107:       printf("Total");
                   1108:     else
                   1109:       printf("Age %d", i);
                   1110:     for(jk=1; jk <=nlstate ; jk++){
                   1111:       for(m=-1, pp[jk]=0; m <=nlstate+ndeath ; m++)
                   1112:        pp[jk] += freq[jk][m][i];
                   1113:     }
                   1114:     for(jk=1; jk <=nlstate ; jk++){
                   1115:       for(m=-1, pos=0; m <=0 ; m++)
                   1116:        pos += freq[jk][m][i];
                   1117:       if(pp[jk]>=1.e-10)
                   1118:        printf(" %d.=%.0f loss[%d]=%.1f%%",jk,pp[jk],jk,100*pos/pp[jk]);
                   1119:       else
                   1120:         printf(" %d.=%.0f loss[%d]=NaNQ%%",jk,pp[jk],jk);
                   1121:     }
                   1122:     for(jk=1; jk <=nlstate ; jk++){
                   1123:       for(m=1, pp[jk]=0; m <=nlstate+ndeath; m++)
                   1124:        pp[jk] += freq[jk][m][i];
                   1125:     }
                   1126:     for(jk=1,pos=0; jk <=nlstate ; jk++)
                   1127:       pos += pp[jk];
                   1128:     for(jk=1; jk <=nlstate ; jk++){
                   1129:       if(pos>=1.e-5)
                   1130:        printf(" %d.=%.0f prev[%d]=%.1f%%",jk,pp[jk],jk,100*pp[jk]/pos);
                   1131:       else
                   1132:        printf(" %d.=%.0f prev[%d]=NaNQ%%",jk,pp[jk],jk);
                   1133:       if( i <= (int) agemax){
                   1134:        if(pos>=1.e-5)
                   1135:          fprintf(ficresp," %d %.5f %.0f %.0f",i,pp[jk]/pos, pp[jk],pos);
                   1136:       else
                   1137:          fprintf(ficresp," %d NaNq %.0f %.0f",i,pp[jk],pos);
                   1138:       }
                   1139:     }
                   1140:     for(jk=-1; jk <=nlstate+ndeath; jk++)
                   1141:       for(m=-1; m <=nlstate+ndeath; m++)
                   1142:        if(freq[jk][m][i] !=0 ) printf(" %d%d=%.0f",jk,m,freq[jk][m][i]);
                   1143:     if(i <= (int) agemax)
                   1144:       fprintf(ficresp,"\n");
                   1145:     printf("\n");
                   1146:   }
                   1147: 
                   1148:   fclose(ficresp);
                   1149:   free_ma3x(freq,-1,nlstate+ndeath,-1,nlstate+ndeath,(int) agemin,(int) agemax+3);
                   1150:   free_vector(pp,1,nlstate);
                   1151: 
                   1152: }  /* End of Freq */
                   1153: 
                   1154: /************* Waves Concatenation ***************/
                   1155: 
                   1156: void  concatwav(int wav[], int **dh, int **mw, int **s, double *agedc, double **agev, int  firstpass, int lastpass, int imx, int nlstate, int stepm)
                   1157: {
                   1158:   /* Concatenates waves: wav[i] is the number of effective (useful waves) of individual i.
                   1159:      Death is a valid wave (if date is known).
                   1160:      mw[mi][i] is the mi (mi=1 to wav[i])  effective wave of individual i
                   1161:      dh[m][i] of dh[mw[mi][i][i] is the delay between two effective waves m=mw[mi][i]
                   1162:      and mw[mi+1][i]. dh depends on stepm.
                   1163:      */
                   1164: 
                   1165:   int i, mi, m;
                   1166:   int j, k=0,jk, ju, jl,jmin=1e+5, jmax=-1;
                   1167: float sum=0.;
                   1168: 
                   1169:   for(i=1; i<=imx; i++){
                   1170:     mi=0;
                   1171:     m=firstpass;
                   1172:     while(s[m][i] <= nlstate){
                   1173:       if(s[m][i]>=1)
                   1174:        mw[++mi][i]=m;
                   1175:       if(m >=lastpass)
                   1176:        break;
                   1177:       else
                   1178:        m++;
                   1179:     }/* end while */
                   1180:     if (s[m][i] > nlstate){
                   1181:       mi++;    /* Death is another wave */
                   1182:       /* if(mi==0)  never been interviewed correctly before death */
                   1183:         /* Only death is a correct wave */
                   1184:       mw[mi][i]=m;
                   1185:     }
                   1186: 
                   1187:     wav[i]=mi;
                   1188:     if(mi==0)
                   1189:       printf("Warning, no any valid information for:%d line=%d\n",num[i],i);
                   1190:   }
                   1191: 
                   1192:   for(i=1; i<=imx; i++){
                   1193:     for(mi=1; mi<wav[i];mi++){
                   1194:       if (stepm <=0)
                   1195:        dh[mi][i]=1;
                   1196:       else{
                   1197:        if (s[mw[mi+1][i]][i] > nlstate) {
                   1198:          j= rint(agedc[i]*12-agev[mw[mi][i]][i]*12); 
                   1199:          if(j=0) j=1;  /* Survives at least one month after exam */
                   1200:        }
                   1201:        else{
                   1202:          j= rint( (agev[mw[mi+1][i]][i]*12 - agev[mw[mi][i]][i]*12));
                   1203:          k=k+1;
                   1204:          if (j >= jmax) jmax=j;
                   1205:          else if (j <= jmin)jmin=j;
                   1206:          sum=sum+j;
                   1207:        }
                   1208:        jk= j/stepm;
                   1209:        jl= j -jk*stepm;
                   1210:        ju= j -(jk+1)*stepm;
                   1211:        if(jl <= -ju)
                   1212:          dh[mi][i]=jk;
                   1213:        else
                   1214:          dh[mi][i]=jk+1;
                   1215:        if(dh[mi][i]==0)
                   1216:          dh[mi][i]=1; /* At least one step */
                   1217:       }
                   1218:     }
                   1219:   }
                   1220:   printf("Delay (in months) between two waves Min=%d Max=%d Mean=%f\n\n ",jmin, jmax,sum/k);
                   1221: }
                   1222: 
                   1223: /*********** Health Expectancies ****************/
                   1224: 
                   1225: void evsij(char fileres[], double ***eij, double x[], int nlstate, int stepm, int bage, int fage, double **oldm, double **savm)
                   1226: {
                   1227:   /* Health expectancies */
                   1228:   int i, j, nhstepm, hstepm, h;
                   1229:   double age, agelim,hf;
                   1230:   double ***p3mat;
                   1231: 
                   1232:   FILE  *ficreseij;
                   1233:   char filerese[FILENAMELENGTH];
                   1234: 
                   1235:   strcpy(filerese,"e");
                   1236:   strcat(filerese,fileres);
                   1237:   if((ficreseij=fopen(filerese,"w"))==NULL) {
                   1238:     printf("Problem with Health Exp. resultfile: %s\n", filerese); exit(0);
                   1239:   }
                   1240:   printf("Computing Health Expectancies: result on file '%s' \n", filerese);
                   1241: 
                   1242:   fprintf(ficreseij,"# Health expectancies\n");
                   1243:   fprintf(ficreseij,"# Age");
                   1244:   for(i=1; i<=nlstate;i++)
                   1245:     for(j=1; j<=nlstate;j++)
                   1246:       fprintf(ficreseij," %1d-%1d",i,j);
                   1247:   fprintf(ficreseij,"\n");
                   1248: 
                   1249:   hstepm=1*YEARM; /*  Every j years of age (in month) */
                   1250:   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
                   1251: 
                   1252:   agelim=AGESUP;
                   1253:   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
                   1254:     /* nhstepm age range expressed in number of stepm */
                   1255:     nhstepm=(int) rint((agelim-age)*YEARM/stepm); 
                   1256:     /* Typically if 20 years = 20*12/6=40 stepm */ 
                   1257:     if (stepm >= YEARM) hstepm=1;
                   1258:     nhstepm = nhstepm/hstepm;/* Expressed in hstepm, typically 40/4=10 */
                   1259:     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   1260:     /* Computed by stepm unit matrices, product of hstepm matrices, stored
                   1261:        in an array of nhstepm length: nhstepm=10, hstepm=4, stepm=6 months */
                   1262:     hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm, savm);  
                   1263: 
                   1264: 
                   1265:     for(i=1; i<=nlstate;i++)
                   1266:       for(j=1; j<=nlstate;j++)
                   1267:        for (h=0, eij[i][j][(int)age]=0; h<=nhstepm; h++){
                   1268:          eij[i][j][(int)age] +=p3mat[i][j][h];
                   1269:        }
                   1270:     
                   1271:     hf=1;
                   1272:     if (stepm >= YEARM) hf=stepm/YEARM;
                   1273:     fprintf(ficreseij,"%.0f",age );
                   1274:     for(i=1; i<=nlstate;i++)
                   1275:       for(j=1; j<=nlstate;j++){
                   1276:        fprintf(ficreseij," %.4f", hf*eij[i][j][(int)age]);
                   1277:       }
                   1278:     fprintf(ficreseij,"\n");
                   1279:     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   1280:   }
                   1281:   fclose(ficreseij);
                   1282: }
                   1283: 
                   1284: /************ Variance ******************/
                   1285: 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)
                   1286: {
                   1287:   /* Variance of health expectancies */
                   1288:   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
                   1289:   double **newm;
                   1290:   double **dnewm,**doldm;
                   1291:   int i, j, nhstepm, hstepm, h;
                   1292:   int k;
                   1293:   FILE  *ficresvij;
                   1294:   char fileresv[FILENAMELENGTH];
                   1295:   double *xp;
                   1296:   double **gp, **gm;
                   1297:   double ***gradg, ***trgradg;
                   1298:   double ***p3mat;
                   1299:   double age,agelim;
                   1300:   int theta;
                   1301: 
                   1302:   strcpy(fileresv,"v");
                   1303:   strcat(fileresv,fileres);
                   1304:   if((ficresvij=fopen(fileresv,"w"))==NULL) {
                   1305:     printf("Problem with variance resultfile: %s\n", fileresv);exit(0);
                   1306:   }
                   1307:   printf("Computing Variance-covariance of DFLEs: file '%s' \n", fileresv);
                   1308: 
                   1309: 
                   1310:   fprintf(ficresvij,"# Covariances of life expectancies\n");
                   1311:   fprintf(ficresvij,"# Age");
                   1312:   for(i=1; i<=nlstate;i++)
                   1313:     for(j=1; j<=nlstate;j++)
                   1314:       fprintf(ficresvij," Cov(e%1d, e%1d)",i,j);
                   1315:   fprintf(ficresvij,"\n");
                   1316: 
                   1317:   xp=vector(1,npar);
                   1318:   dnewm=matrix(1,nlstate,1,npar);
                   1319:   doldm=matrix(1,nlstate,1,nlstate);
                   1320:   
                   1321:   hstepm=1*YEARM; /* Every year of age */
                   1322:   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
                   1323:   agelim = AGESUP;
                   1324:   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
                   1325:     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
                   1326:     if (stepm >= YEARM) hstepm=1;
                   1327:     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
                   1328:     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   1329:     gradg=ma3x(0,nhstepm,1,npar,1,nlstate);
                   1330:     gp=matrix(0,nhstepm,1,nlstate);
                   1331:     gm=matrix(0,nhstepm,1,nlstate);
                   1332: 
                   1333:     for(theta=1; theta <=npar; theta++){
                   1334:       for(i=1; i<=npar; i++){ /* Computes gradient */
                   1335:        xp[i] = x[i] + (i==theta ?delti[theta]:0);
                   1336:       }
                   1337:       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);  
                   1338:       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);
                   1339:       for(j=1; j<= nlstate; j++){
                   1340:        for(h=0; h<=nhstepm; h++){
                   1341:          for(i=1, gp[h][j]=0.;i<=nlstate;i++)
                   1342:            gp[h][j] += prlim[i][i]*p3mat[i][j][h];
                   1343:        }
                   1344:       }
                   1345:     
                   1346:       for(i=1; i<=npar; i++) /* Computes gradient */
                   1347:        xp[i] = x[i] - (i==theta ?delti[theta]:0);
                   1348:       hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm);  
                   1349:       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);
                   1350:       for(j=1; j<= nlstate; j++){
                   1351:        for(h=0; h<=nhstepm; h++){
                   1352:          for(i=1, gm[h][j]=0.;i<=nlstate;i++)
                   1353:            gm[h][j] += prlim[i][i]*p3mat[i][j][h];
                   1354:        }
                   1355:       }
                   1356:       for(j=1; j<= nlstate; j++)
                   1357:        for(h=0; h<=nhstepm; h++){
                   1358:          gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta];
                   1359:        }
                   1360:     } /* End theta */
                   1361: 
                   1362:     trgradg =ma3x(0,nhstepm,1,nlstate,1,npar);
                   1363: 
                   1364:     for(h=0; h<=nhstepm; h++)
                   1365:       for(j=1; j<=nlstate;j++)
                   1366:        for(theta=1; theta <=npar; theta++)
                   1367:          trgradg[h][j][theta]=gradg[h][theta][j];
                   1368: 
                   1369:     for(i=1;i<=nlstate;i++)
                   1370:       for(j=1;j<=nlstate;j++)
                   1371:        vareij[i][j][(int)age] =0.;
                   1372:     for(h=0;h<=nhstepm;h++){
                   1373:       for(k=0;k<=nhstepm;k++){
                   1374:        matprod2(dnewm,trgradg[h],1,nlstate,1,npar,1,npar,matcov);
                   1375:        matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]);
                   1376:        for(i=1;i<=nlstate;i++)
                   1377:          for(j=1;j<=nlstate;j++)
                   1378:            vareij[i][j][(int)age] += doldm[i][j];
                   1379:       }
                   1380:     }
                   1381:     h=1;
                   1382:     if (stepm >= YEARM) h=stepm/YEARM;
                   1383:     fprintf(ficresvij,"%.0f ",age );
                   1384:     for(i=1; i<=nlstate;i++)
                   1385:       for(j=1; j<=nlstate;j++){
                   1386:        fprintf(ficresvij," %.4f", h*vareij[i][j][(int)age]);
                   1387:       }
                   1388:     fprintf(ficresvij,"\n");
                   1389:     free_matrix(gp,0,nhstepm,1,nlstate);
                   1390:     free_matrix(gm,0,nhstepm,1,nlstate);
                   1391:     free_ma3x(gradg,0,nhstepm,1,npar,1,nlstate);
                   1392:     free_ma3x(trgradg,0,nhstepm,1,nlstate,1,npar);
                   1393:     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   1394:   } /* End age */
                   1395:   fclose(ficresvij);
                   1396:   free_vector(xp,1,npar);
                   1397:   free_matrix(doldm,1,nlstate,1,npar);
                   1398:   free_matrix(dnewm,1,nlstate,1,nlstate);
                   1399: 
                   1400: }
                   1401: 
                   1402: /************ Variance of prevlim ******************/
                   1403: 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)
                   1404: {
                   1405:   /* Variance of health expectancies */
                   1406:   /*  double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl);*/
                   1407:   double **newm;
                   1408:   double **dnewm,**doldm;
                   1409:   int i, j, nhstepm, hstepm;
                   1410:   int k;
                   1411:   FILE  *ficresvpl;
                   1412:   char fileresvpl[FILENAMELENGTH];
                   1413:   double *xp;
                   1414:   double *gp, *gm;
                   1415:   double **gradg, **trgradg;
                   1416:   double age,agelim;
                   1417:   int theta;
                   1418: 
                   1419:   strcpy(fileresvpl,"vpl");
                   1420:   strcat(fileresvpl,fileres);
                   1421:   if((ficresvpl=fopen(fileresvpl,"w"))==NULL) {
                   1422:     printf("Problem with variance prev lim resultfile: %s\n", fileresvpl);
                   1423:     exit(0);
                   1424:   }
                   1425:   printf("Computing Variance-covariance of Prevalence limit: file '%s' \n", fileresvpl);
                   1426: 
                   1427: 
                   1428:   fprintf(ficresvpl,"# Standard deviation of prevalences limit\n");
                   1429:   fprintf(ficresvpl,"# Age");
                   1430:   for(i=1; i<=nlstate;i++)
                   1431:       fprintf(ficresvpl," %1d-%1d",i,i);
                   1432:   fprintf(ficresvpl,"\n");
                   1433: 
                   1434:   xp=vector(1,npar);
                   1435:   dnewm=matrix(1,nlstate,1,npar);
                   1436:   doldm=matrix(1,nlstate,1,nlstate);
                   1437:   
                   1438:   hstepm=1*YEARM; /* Every year of age */
                   1439:   hstepm=hstepm/stepm; /* Typically in stepm units, if j= 2 years, = 2/6 months = 4 */ 
                   1440:   agelim = AGESUP;
                   1441:   for (age=bage; age<=fage; age ++){ /* If stepm=6 months */
                   1442:     nhstepm=(int) rint((agelim-age)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
                   1443:     if (stepm >= YEARM) hstepm=1;
                   1444:     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
                   1445:     gradg=matrix(1,npar,1,nlstate);
                   1446:     gp=vector(1,nlstate);
                   1447:     gm=vector(1,nlstate);
                   1448: 
                   1449:     for(theta=1; theta <=npar; theta++){
                   1450:       for(i=1; i<=npar; i++){ /* Computes gradient */
                   1451:        xp[i] = x[i] + (i==theta ?delti[theta]:0);
                   1452:       }
                   1453:       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);
                   1454:       for(i=1;i<=nlstate;i++)
                   1455:        gp[i] = prlim[i][i];
                   1456:     
                   1457:       for(i=1; i<=npar; i++) /* Computes gradient */
                   1458:        xp[i] = x[i] - (i==theta ?delti[theta]:0);
                   1459:       prevalim(prlim,nlstate,xp,age,oldm,savm,ftolpl);
                   1460:       for(i=1;i<=nlstate;i++)
                   1461:        gm[i] = prlim[i][i];
                   1462: 
                   1463:       for(i=1;i<=nlstate;i++)
                   1464:        gradg[theta][i]= (gp[i]-gm[i])/2./delti[theta];
                   1465:     } /* End theta */
                   1466: 
                   1467:     trgradg =matrix(1,nlstate,1,npar);
                   1468: 
                   1469:     for(j=1; j<=nlstate;j++)
                   1470:       for(theta=1; theta <=npar; theta++)
                   1471:        trgradg[j][theta]=gradg[theta][j];
                   1472: 
                   1473:     for(i=1;i<=nlstate;i++)
                   1474:       varpl[i][(int)age] =0.;
                   1475:     matprod2(dnewm,trgradg,1,nlstate,1,npar,1,npar,matcov);
                   1476:     matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg);
                   1477:     for(i=1;i<=nlstate;i++)
                   1478:       varpl[i][(int)age] = doldm[i][i]; /* Covariances are useless */
                   1479: 
                   1480:     fprintf(ficresvpl,"%.0f ",age );
                   1481:     for(i=1; i<=nlstate;i++)
                   1482:       fprintf(ficresvpl," %.5f (%.5f)",prlim[i][i],sqrt(varpl[i][(int)age]));
                   1483:     fprintf(ficresvpl,"\n");
                   1484:     free_vector(gp,1,nlstate);
                   1485:     free_vector(gm,1,nlstate);
                   1486:     free_matrix(gradg,1,npar,1,nlstate);
                   1487:     free_matrix(trgradg,1,nlstate,1,npar);
                   1488:   } /* End age */
                   1489:   fclose(ficresvpl);
                   1490:   free_vector(xp,1,npar);
                   1491:   free_matrix(doldm,1,nlstate,1,npar);
                   1492:   free_matrix(dnewm,1,nlstate,1,nlstate);
                   1493: 
                   1494: }
                   1495: 
                   1496: 
                   1497: 
                   1498: /***********************************************/
                   1499: /**************** Main Program *****************/
                   1500: /***********************************************/
                   1501: 
                   1502: /*int main(int argc, char *argv[])*/
                   1503: int main()
                   1504: {
                   1505: 
                   1506:   int i,j, k, n=MAXN,iter,m,size;
                   1507:   double agedeb, agefin,hf;
                   1508:   double agemin=1.e20, agemax=-1.e20;
                   1509: 
                   1510:   double fret;
                   1511:   double **xi,tmp,delta;
                   1512: 
                   1513:   double dum; /* Dummy variable */
                   1514:   double ***p3mat;
                   1515:   int *indx;
                   1516:   char line[MAXLINE], linepar[MAXLINE];
                   1517:   char title[MAXLINE];
                   1518:   char optionfile[FILENAMELENGTH], datafile[FILENAMELENGTH],  filerespl[FILENAMELENGTH];
                   1519:   char fileres[FILENAMELENGTH], filerespij[FILENAMELENGTH], filereso[FILENAMELENGTH];
                   1520:   char filerest[FILENAMELENGTH];
                   1521:   char fileregp[FILENAMELENGTH];
                   1522:   char path[80],pathc[80],pathcd[80],pathtot[80];
                   1523:   int firstobs=1, lastobs=10;
                   1524:   int sdeb, sfin; /* Status at beginning and end */
                   1525:   int c,  h , cpt,l;
                   1526:   int ju,jl, mi;
                   1527:   int i1,j1, k1,jk,aa,bb, stepsize;
                   1528:   int jnais,jdc,jint4,jint1,jint2,jint3,**outcome,**adl,*tab;
                   1529:   
                   1530:   int hstepm, nhstepm;
                   1531:   double bage, fage, age, agelim, agebase;
                   1532:   double ftolpl=FTOL;
                   1533:   double **prlim;
                   1534:   double *severity;
                   1535:   double ***param; /* Matrix of parameters */
                   1536:   double  *p;
                   1537:   double **matcov; /* Matrix of covariance */
                   1538:   double ***delti3; /* Scale */
                   1539:   double *delti; /* Scale */
                   1540:   double ***eij, ***vareij;
                   1541:   double **varpl; /* Variances of prevalence limits by age */
                   1542:   double *epj, vepp;
                   1543:   char version[80]="Imach version 0.64, May 2000, INED-EUROREVES ";
                   1544:   char *alph[]={"a","a","b","c","d","e"}, str[4];
                   1545:   char z[1]="c";
                   1546: #include <sys/time.h>
                   1547: #include <time.h>
                   1548: 
                   1549:   /* long total_usecs;
                   1550:   struct timeval start_time, end_time;
                   1551:   
                   1552:   gettimeofday(&start_time, (struct timezone*)0); */ /* at first time */
                   1553: 
                   1554: 
                   1555:   printf("\nIMACH, Version 0.64");
                   1556:   printf("\nEnter the parameter file name: ");
                   1557: #define windows 1
                   1558: #ifdef windows
                   1559:   scanf("%s",pathtot);
                   1560:   getcwd(pathcd, size);
                   1561:   cut(path,optionfile,pathtot);
                   1562:   chdir(path);
                   1563:   replace(pathc,path);
                   1564: #endif
                   1565: #ifdef unix
                   1566:   scanf("%s",optionfile);
                   1567: #endif
                   1568: 
                   1569: /*-------- arguments in the command line --------*/
                   1570: 
                   1571:   strcpy(fileres,"r");
                   1572:   strcat(fileres, optionfile);
                   1573: 
                   1574:   /*---------arguments file --------*/
                   1575: 
                   1576:   if((ficpar=fopen(optionfile,"r"))==NULL)    {
                   1577:     printf("Problem with optionfile %s\n",optionfile);
                   1578:     goto end;
                   1579:   }
                   1580: 
                   1581:   strcpy(filereso,"o");
                   1582:   strcat(filereso,fileres);
                   1583:   if((ficparo=fopen(filereso,"w"))==NULL) {
                   1584:     printf("Problem with Output resultfile: %s\n", filereso);goto end;
                   1585:   }
                   1586: 
                   1587: /*--------- index.htm --------*/
                   1588: 
                   1589:   if((fichtm=fopen("index.htm","w"))==NULL)    {
                   1590:     printf("Problem with index.htm \n");goto end;
                   1591:   }
                   1592: 
                   1593:  fprintf(fichtm,"<body><ul><li>Outputs files<br><br>\n
                   1594:         - Observed prevalence in each state: <a href=\"p%s\">p%s</a> <br>\n
                   1595: - Estimated parameters and the covariance matrix: <a href=\"%s\">%s</a> <br>
                   1596:         - Stationary prevalence in each state: <a href=\"pl%s\">pl%s</a> <br>
                   1597:         - Transition probabilities: <a href=\"pij%s\">pij%s</a><br>
                   1598:         - Copy of the parameter file: <a href=\"o%s\">o%s</a><br>
                   1599:         - Life expectancies by age and initial health status: <a href=\"e%s\">e%s</a> <br>
                   1600:         - Variances of life expectancies by age and initial health status: <a href=\"v%s\">v%s</a><br>
                   1601:         - Health expectancies with their variances: <a href=\"t%s\">t%s</a> <br>
                   1602:         - 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);
                   1603: 
                   1604:  fprintf(fichtm," <li>Graphs<br> <br>");
                   1605:  
                   1606: for(cpt=1; cpt<nlstate;cpt++)
                   1607:    fprintf(fichtm,"- Prevalence of disability: p%s1.gif<br>
                   1608: <img src=\"p%s1.gif\"><br>",strtok(optionfile, "."),strtok(optionfile, "."),cpt);
                   1609:  for(cpt=1; cpt<=nlstate;cpt++)
                   1610:      fprintf(fichtm,"- Observed and stationary  prevalence (with confident
                   1611: interval) in state (%d): v%s%d.gif <br>
                   1612: <img src=\"v%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);
                   1613:  
                   1614:  for(cpt=1; cpt<=nlstate;cpt++)
                   1615:      fprintf(fichtm,"- Health life expectancies by age and initial health state (%d): exp%s%d.gif <br>
                   1616: <img src=\"ex%s%d.gif\"><br>",cpt,strtok(optionfile, "."),cpt,strtok(optionfile, "."),cpt);
                   1617:    
                   1618:  fprintf(fichtm,"- Total life expectancy by age and
                   1619:         health expectancies in states (1) and (2): e%s.gif<br>
                   1620:        <img src=\"e%s.gif\"></li> </ul></body>",strtok(optionfile, "."),strtok(optionfile, "."));
                   1621: 
                   1622: 
                   1623: fclose(fichtm);
                   1624: 
                   1625:   /* Reads comments: lines beginning with '#' */
                   1626:   while((c=getc(ficpar))=='#' && c!= EOF){
                   1627:     ungetc(c,ficpar);
                   1628:     fgets(line, MAXLINE, ficpar);
                   1629:     puts(line);
                   1630:     fputs(line,ficparo);
                   1631:   }
                   1632:   ungetc(c,ficpar);
                   1633: 
                   1634:   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\n",title, datafile, &lastobs, &firstpass,&lastpass,&ftol, &stepm, &ncov, &nlstate,&ndeath, &maxwav, &mle, &weightopt);
                   1635:   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\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate,ndeath, maxwav, mle, weightopt);
                   1636:   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\n", title, datafile, lastobs, firstpass,lastpass,ftol,stepm,ncov,nlstate,ndeath,maxwav, mle, weightopt);
                   1637:   
                   1638:   nvar=ncov-1; /* Suppressing age as a basic covariate */
                   1639:   
                   1640:   /* Read guess parameters */
                   1641:   /* Reads comments: lines beginning with '#' */
                   1642:   while((c=getc(ficpar))=='#' && c!= EOF){
                   1643:     ungetc(c,ficpar);
                   1644:     fgets(line, MAXLINE, ficpar);
                   1645:     puts(line);
                   1646:     fputs(line,ficparo);
                   1647:   }
                   1648:   ungetc(c,ficpar);
                   1649:   
                   1650:   param= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);
                   1651:     for(i=1; i <=nlstate; i++)
                   1652:     for(j=1; j <=nlstate+ndeath-1; j++){
                   1653:       fscanf(ficpar,"%1d%1d",&i1,&j1);
                   1654:       fprintf(ficparo,"%1d%1d",i1,j1);
                   1655:       printf("%1d%1d",i,j);
                   1656:       for(k=1; k<=ncov;k++){
                   1657:        fscanf(ficpar," %lf",&param[i][j][k]);
                   1658:        printf(" %lf",param[i][j][k]);
                   1659:        fprintf(ficparo," %lf",param[i][j][k]);
                   1660:       }
                   1661:       fscanf(ficpar,"\n");
                   1662:       printf("\n");
                   1663:       fprintf(ficparo,"\n");
                   1664:     }
                   1665:   
                   1666:   npar= (nlstate+ndeath-1)*nlstate*ncov;
                   1667:   p=param[1][1];
                   1668:   
                   1669:   /* Reads comments: lines beginning with '#' */
                   1670:   while((c=getc(ficpar))=='#' && c!= EOF){
                   1671:     ungetc(c,ficpar);
                   1672:     fgets(line, MAXLINE, ficpar);
                   1673:     puts(line);
                   1674:     fputs(line,ficparo);
                   1675:   }
                   1676:   ungetc(c,ficpar);
                   1677: 
                   1678:   delti3= ma3x(1,nlstate,1,nlstate+ndeath-1,1,ncov);
                   1679:   delti=vector(1,npar); /* Scale of each paramater (output from hesscov) */
                   1680:   for(i=1; i <=nlstate; i++){
                   1681:     for(j=1; j <=nlstate+ndeath-1; j++){
                   1682:       fscanf(ficpar,"%1d%1d",&i1,&j1);
                   1683:       printf("%1d%1d",i,j);
                   1684:       fprintf(ficparo,"%1d%1d",i1,j1);
                   1685:       for(k=1; k<=ncov;k++){
                   1686:        fscanf(ficpar,"%le",&delti3[i][j][k]);
                   1687:        printf(" %le",delti3[i][j][k]);
                   1688:        fprintf(ficparo," %le",delti3[i][j][k]);
                   1689:       }
                   1690:       fscanf(ficpar,"\n");
                   1691:       printf("\n");
                   1692:       fprintf(ficparo,"\n");
                   1693:     }
                   1694:   }
                   1695:   delti=delti3[1][1];
                   1696:   
                   1697:   /* Reads comments: lines beginning with '#' */
                   1698:   while((c=getc(ficpar))=='#' && c!= EOF){
                   1699:     ungetc(c,ficpar);
                   1700:     fgets(line, MAXLINE, ficpar);
                   1701:     puts(line);
                   1702:     fputs(line,ficparo);
                   1703:   }
                   1704:   ungetc(c,ficpar);
                   1705:   
                   1706:   matcov=matrix(1,npar,1,npar);
                   1707:   for(i=1; i <=npar; i++){
                   1708:     fscanf(ficpar,"%s",&str);
                   1709:     printf("%s",str);
                   1710:     fprintf(ficparo,"%s",str);
                   1711:     for(j=1; j <=i; j++){
                   1712:       fscanf(ficpar," %le",&matcov[i][j]);
                   1713:       printf(" %.5le",matcov[i][j]);
                   1714:       fprintf(ficparo," %.5le",matcov[i][j]);
                   1715:     }
                   1716:     fscanf(ficpar,"\n");
                   1717:     printf("\n");
                   1718:     fprintf(ficparo,"\n");
                   1719:   }
                   1720:   for(i=1; i <=npar; i++)
                   1721:     for(j=i+1;j<=npar;j++)
                   1722:       matcov[i][j]=matcov[j][i];
                   1723:    
                   1724:   printf("\n");
                   1725:   
                   1726:   
                   1727:   if(mle==1){
                   1728:     /*-------- data file ----------*/
                   1729:     if((ficres =fopen(fileres,"w"))==NULL) {
                   1730:       printf("Problem with resultfile: %s\n", fileres);goto end;
                   1731:     }
                   1732:     fprintf(ficres,"#%s\n",version);
                   1733:     
                   1734:     if((fic=fopen(datafile,"r"))==NULL)    {
                   1735:       printf("Problem with datafile: %s\n", datafile);goto end;
                   1736:     }
                   1737:     
                   1738:     n= lastobs;
                   1739:     severity = vector(1,maxwav);
                   1740:     outcome=imatrix(1,maxwav+1,1,n);
                   1741:     num=ivector(1,n);
                   1742:     moisnais=vector(1,n);
                   1743:     annais=vector(1,n);
                   1744:     moisdc=vector(1,n);
                   1745:     andc=vector(1,n);
                   1746:     agedc=vector(1,n);
                   1747:     cod=ivector(1,n);
                   1748:     weight=vector(1,n);
                   1749:     for(i=1;i<=n;i++) weight[i]=1.0; /* Equal weights, 1 by default */
                   1750:     mint=matrix(1,maxwav,1,n);
                   1751:     anint=matrix(1,maxwav,1,n);
                   1752:     covar=matrix(1,NCOVMAX,1,n);
                   1753:     s=imatrix(1,maxwav+1,1,n);
                   1754:     adl=imatrix(1,maxwav+1,1,n);    
                   1755:     tab=ivector(1,NCOVMAX);
                   1756:     i=1; 
                   1757:     while (fgets(line, MAXLINE, fic) != NULL)    {
                   1758:       if ((i >= firstobs) && (i <lastobs)) {
                   1759: sscanf(line,"%d %lf %lf %lf %lf/%lf %lf/%lf %lf/%lf %d %lf/%lf %d %lf/%lf %d %lf/%lf %d", &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]);
                   1760:        i=i+1;
                   1761:       }
                   1762:     } 
                   1763:   imx=i-1; /* Number of individuals */
                   1764: 
                   1765:     fclose(fic);
                   1766: 
                   1767:     if (weightopt != 1) { /* Maximisation without weights*/
                   1768:       for(i=1;i<=n;i++) weight[i]=1.0;
                   1769:     }
                   1770:     /*-calculation of age at interview from date of interview and age at death -*/
                   1771:     agev=matrix(1,maxwav,1,imx);
                   1772:     
                   1773:     for (i=1; i<=imx; i++)  {
                   1774:       agedc[i]=(moisdc[i]/12.+andc[i])-(moisnais[i]/12.+annais[i]);
                   1775:       for(m=1; (m<= maxwav); m++){
                   1776:        if(s[m][i] >0){
                   1777:          if (s[m][i] == nlstate+1) {
                   1778:            if(agedc[i]>0)
                   1779:              agev[m][i]=agedc[i];
                   1780:            else{
                   1781:              printf("Warning negative age at death: %d line:%d\n",num[i],i);
                   1782:              agev[m][i]=-1;
                   1783:            }
                   1784:          }
                   1785:          else if(s[m][i] !=9){ /* Should no more exist */
                   1786:            agev[m][i]=(mint[m][i]/12.+1./24.+anint[m][i])-(moisnais[i]/12.+1./24.+annais[i]);
                   1787:            if(mint[m][i]==99 || anint[m][i]==9999)
                   1788:              agev[m][i]=1;
                   1789:            else if(agev[m][i] <agemin){ 
                   1790:              agemin=agev[m][i];
                   1791:              /*printf(" Min anint[%d][%d]=%.2f annais[%d]=%.2f, agemin=%.2f\n",m,i,anint[m][i], i,annais[i], agemin);*/
                   1792:            }
                   1793:            else if(agev[m][i] >agemax){
                   1794:              agemax=agev[m][i];
                   1795:             /* printf(" anint[%d][%d]=%.0f annais[%d]=%.0f, agemax=%.0f\n",m,i,anint[m][i], i,annais[i], agemax);*/
                   1796:            }
                   1797:            /*agev[m][i]=anint[m][i]-annais[i];*/
                   1798:            /*   agev[m][i] = age[i]+2*m;*/
                   1799:          }
                   1800:          else { /* =9 */
                   1801:            agev[m][i]=1;
                   1802:            s[m][i]=-1;
                   1803:          }
                   1804:        }
                   1805:        else /*= 0 Unknown */
                   1806:          agev[m][i]=1;
                   1807:       }
                   1808:     
                   1809:     }
                   1810:     for (i=1; i<=imx; i++)  {
                   1811:       for(m=1; (m<= maxwav); m++){
                   1812:        if (s[m][i] > (nlstate+ndeath)) {
                   1813:          printf("Error: Wrong value in nlstate or ndeath\n");  
                   1814:          goto end;
                   1815:        }
                   1816:       }
                   1817:     }
                   1818: 
                   1819: printf("Total number of individuals= %d, Agemin = %.2f, Agemax= %.2f\n\n", imx, agemin, agemax);
                   1820: 
                   1821:     free_vector(severity,1,maxwav);
                   1822:     free_imatrix(outcome,1,maxwav+1,1,n);
                   1823:     free_vector(moisnais,1,n);
                   1824:     free_vector(annais,1,n);
                   1825:     free_matrix(mint,1,maxwav,1,n);
                   1826:     free_matrix(anint,1,maxwav,1,n);
                   1827:     free_vector(moisdc,1,n);
                   1828:     free_vector(andc,1,n);
                   1829: 
                   1830:    
                   1831:     wav=ivector(1,imx);
                   1832:     dh=imatrix(1,lastpass-firstpass+1,1,imx);
                   1833:     mw=imatrix(1,lastpass-firstpass+1,1,imx);
                   1834:    
                   1835:     /* Concatenates waves */
                   1836:       concatwav(wav, dh, mw, s, agedc, agev,  firstpass, lastpass, imx, nlstate, stepm);
                   1837:     
                   1838:    /* Calculates basic frequencies. Computes observed prevalence at single age
                   1839:        and prints on file fileres'p'. */
                   1840:       freqsummary(fileres, agemin, agemax, s, agev, nlstate, imx); 
                   1841: 
                   1842:     pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   1843:     oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   1844:     newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   1845:     savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   1846:     oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
                   1847:     
                   1848:     /* For Powell, parameters are in a vector p[] starting at p[1]
                   1849:        so we point p on param[1][1] so that p[1] maps on param[1][1][1] */
                   1850:     p=param[1][1]; /* *(*(*(param +1)+1)+0) */
                   1851:     
                   1852:     mlikeli(ficres,p, npar, ncov, nlstate, ftol, func);
                   1853: 
                   1854:     
                   1855:     /*--------- results files --------------*/
                   1856:     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\n", title, datafile, lastobs, firstpass,lastpass,ftol, stepm, ncov, nlstate, ndeath, maxwav, mle,weightopt);
                   1857:     
                   1858:    jk=1;
                   1859:    fprintf(ficres,"# Parameters\n");
                   1860:    printf("# Parameters\n");
                   1861:    for(i=1,jk=1; i <=nlstate; i++){
                   1862:      for(k=1; k <=(nlstate+ndeath); k++){
                   1863:        if (k != i) 
                   1864:         {
                   1865:           printf("%d%d ",i,k);
                   1866:           fprintf(ficres,"%1d%1d ",i,k);
                   1867:           for(j=1; j <=ncov; j++){
                   1868:             printf("%f ",p[jk]);
                   1869:             fprintf(ficres,"%f ",p[jk]);
                   1870:             jk++; 
                   1871:           }
                   1872:           printf("\n");
                   1873:           fprintf(ficres,"\n");
                   1874:         }
                   1875:      }
                   1876:    }
                   1877: 
                   1878:     /* Computing hessian and covariance matrix */
                   1879:     ftolhess=ftol; /* Usually correct */
                   1880:     hesscov(matcov, p, npar, delti, ftolhess, func);
                   1881:     fprintf(ficres,"# Scales\n");
                   1882:     printf("# Scales\n");
                   1883:      for(i=1,jk=1; i <=nlstate; i++){
                   1884:       for(j=1; j <=nlstate+ndeath; j++){
                   1885:        if (j!=i) {
                   1886:          fprintf(ficres,"%1d%1d",i,j);
                   1887:          printf("%1d%1d",i,j);
                   1888:          for(k=1; k<=ncov;k++){
                   1889:            printf(" %.5e",delti[jk]);
                   1890:            fprintf(ficres," %.5e",delti[jk]);
                   1891:            jk++;
                   1892:          }
                   1893:          printf("\n");
                   1894:          fprintf(ficres,"\n");
                   1895:        }
                   1896:       }
                   1897:       }
                   1898:     
                   1899:     k=1;
                   1900:     fprintf(ficres,"# Covariance\n");
                   1901:     printf("# Covariance\n");
                   1902:     for(i=1;i<=npar;i++){
                   1903:       /*  if (k>nlstate) k=1;
                   1904:       i1=(i-1)/(ncov*nlstate)+1; 
                   1905:       fprintf(ficres,"%s%d%d",alph[k],i1,tab[i]);
                   1906:       printf("%s%d%d",alph[k],i1,tab[i]);*/
                   1907:       fprintf(ficres,"%3d",i);
                   1908:       printf("%3d",i);
                   1909:       for(j=1; j<=i;j++){
                   1910:        fprintf(ficres," %.5e",matcov[i][j]);
                   1911:        printf(" %.5e",matcov[i][j]);
                   1912:       }
                   1913:       fprintf(ficres,"\n");
                   1914:       printf("\n");
                   1915:       k++;
                   1916:     }
                   1917:     
                   1918:     while((c=getc(ficpar))=='#' && c!= EOF){
                   1919:       ungetc(c,ficpar);
                   1920:       fgets(line, MAXLINE, ficpar);
                   1921:       puts(line);
                   1922:       fputs(line,ficparo);
                   1923:     }
                   1924:     ungetc(c,ficpar);
                   1925:   
                   1926:     fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);
                   1927:     
                   1928:     if (fage <= 2) {
                   1929:       bage = agemin;
                   1930:       fage = agemax;
                   1931:     }
                   1932: 
                   1933:     fprintf(ficres,"# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood).\n");
                   1934:     fprintf(ficres,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);
                   1935: /*------------ gnuplot -------------*/
                   1936: chdir(pathcd);
                   1937:   if((ficgp=fopen("graph.gp","w"))==NULL) {
                   1938:     printf("Problem with file graph.gp");goto end;
                   1939:   }
                   1940: #ifdef windows
                   1941:   fprintf(ficgp,"cd \"%s\" \n",pathc);
                   1942: #endif
                   1943:    /* 1eme*/
                   1944: 
                   1945:   for (cpt=1; cpt<= nlstate ; cpt ++) {
                   1946: #ifdef windows
                   1947:     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"vpl%s\" u 1:%d \"\%%lf",agemin,fage,fileres,cpt*2);
                   1948: #endif
                   1949: #ifdef unix
                   1950: fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nplot [%.f:%.f] \"vpl%s\" u 1:%d \"\%%lf",agemin,fage,fileres,cpt*2);
                   1951: #endif
                   1952:     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");
                   1953:     fprintf(ficgp,"\" t\"Stationary prevalence\" w l 0,\"vpl%s\" u 1:($%d+2*$%d) \"\%%lf",fileres,2*cpt,cpt*2+1);
                   1954:     for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)");
                   1955:   fprintf(ficgp,"\" t\"95\%% CI\" w l 1,\"vpl%s\" u 1:($%d-2*$%d) \"\%%lf",fileres,2*cpt,2*cpt+1); 
                   1956:      for (i=1; i<= nlstate ; i ++) fprintf(ficgp," \%%lf (\%%lf)"); 
                   1957:      fprintf(ficgp,"\" t\"\" w l 1,\"p%s\" u 1:($%d) t\"Observed prevalence \" w l 2",fileres,2+4*(cpt-1));
                   1958: #ifdef unix
                   1959: fprintf(ficgp,"\nset ter gif small size 400,300");
                   1960: #endif
                   1961: fprintf(ficgp,"\nset out \"v%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);
                   1962:  
                   1963:   }
                   1964:   /*2 eme*/
                   1965:  
                   1966:   fprintf(ficgp,"set ylabel \"Years\" \nset ter gif small size 400,300\nplot [%.f:%.f] ",agemin,fage);
                   1967:   for (i=1; i<= nlstate+1 ; i ++) {
                   1968: k=2*i;
                   1969:     fprintf(ficgp,"\"t%s\" u 1:%d \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k);
                   1970:     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");
                   1971:     if (i== 1) fprintf(ficgp,"\" t\"TLE\" w l ,");
                   1972:     else fprintf(ficgp,"\" t\"LE in state (%d)\" w l ,",i-1);
                   1973:     fprintf(ficgp,"\"t%s\" u 1:($%d-2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);
                   1974:     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");
                   1975:     fprintf(ficgp,"\" t\"\" w l 0,");
                   1976: fprintf(ficgp,"\"t%s\" u 1:($%d+2*$%d) \"\%%lf \%%lf (\%%lf) \%%lf (\%%lf)",fileres,k,k+1);
                   1977:     for (j=1; j< nlstate ; j ++) fprintf(ficgp," \%%lf (\%%lf)");
                   1978:     if (i== (nlstate+1)) fprintf(ficgp,"\" t\"\" w l 0");
                   1979: else fprintf(ficgp,"\" t\"\" w l 0,");
                   1980:   } 
                   1981:   fprintf(ficgp,"\nset out \"e%s.gif\" \nreplot\n\n",strtok(optionfile, "."));
                   1982: 
                   1983:   /*3eme*/
                   1984: for (cpt=1; cpt<= nlstate ; cpt ++) {
                   1985:   k=2+nlstate*(cpt-1);
                   1986:     fprintf(ficgp,"set ter gif small size 400,300\nplot [%.f:%.f] \"e%s\" u 1:%d t \"e%d1\" w l",agemin,fage,fileres,k,cpt);
                   1987: for (i=1; i< nlstate ; i ++) {
                   1988: fprintf(ficgp,",\"e%s\" u 1:%d t \"e%d%d\" w l",fileres,k+1,cpt,i+1);
                   1989: } 
                   1990: fprintf(ficgp,"\nset out \"ex%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);
                   1991: }
                   1992:  
                   1993: /* CV preval stat */
                   1994: for (cpt=1; cpt<nlstate ; cpt ++) {
                   1995:     k=3;
                   1996:     fprintf(ficgp,"set xlabel \"Age\" \nset ylabel \"Probability\" \nset ter gif small size 400,300\nplot [%.f:%.f] \"pij%s\" u 2:($%d/($%d",agemin,agemax,fileres,k+cpt,k);
                   1997:     for (i=1; i< nlstate ; i ++)
                   1998:       fprintf(ficgp,"+$%d",k+i);
                   1999:     fprintf(ficgp,")) t\"prev(%d,%d)\" w l",cpt,cpt+1);
                   2000:     
                   2001:  l=3+(nlstate+ndeath)*cpt;
                   2002:    fprintf(ficgp,",\"pij%s\" u 2:($%d/($%d",fileres,l+cpt,l);
                   2003:  
                   2004:    for (i=1; i< nlstate ; i ++) {
                   2005:    l=3+(nlstate+ndeath)*cpt;
                   2006:     fprintf(ficgp,"+$%d",l+i);
                   2007:    }
                   2008:   fprintf(ficgp,")) t\"prev(%d,%d)\" w l\n",cpt+1,cpt+1);
                   2009:   
                   2010:   
                   2011:   fprintf(ficgp,"set out \"p%s%d.gif\" \nreplot\n\n",strtok(optionfile, "."),cpt);
                   2012:   } 
                   2013: 
                   2014: 
                   2015:   fclose(ficgp);
                   2016:    
                   2017: chdir(path);
                   2018:     free_matrix(agev,1,maxwav,1,imx);
                   2019:     free_ivector(wav,1,imx);
                   2020:     free_imatrix(dh,1,lastpass-firstpass+1,1,imx);
                   2021:     free_imatrix(mw,1,lastpass-firstpass+1,1,imx);
                   2022:     
                   2023:     free_imatrix(s,1,maxwav+1,1,n);
                   2024:     
                   2025:     
                   2026:     free_ivector(num,1,n);
                   2027:     free_vector(agedc,1,n);
                   2028:     free_vector(weight,1,n);
                   2029:     free_matrix(covar,1,NCOVMAX,1,n);
                   2030:     fclose(ficparo);
                   2031:     fclose(ficres);
                   2032:   }
                   2033: 
                   2034:   /*________fin mle=1_________*/
                   2035:   
                   2036:   
                   2037: 
                   2038:   /* No more information from the sample is required now */
                   2039:   /* Reads comments: lines beginning with '#' */
                   2040:   while((c=getc(ficpar))=='#' && c!= EOF){
                   2041:     ungetc(c,ficpar);
                   2042:     fgets(line, MAXLINE, ficpar);
                   2043:     puts(line);
                   2044:     fputs(line,ficparo);
                   2045:   }
                   2046:   ungetc(c,ficpar);
                   2047:   
                   2048:   fscanf(ficpar,"agemin=%lf agemax=%lf bage=%lf fage=%lf\n",&agemin,&agemax, &bage, &fage);
                   2049:   printf("agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax, bage, fage);
                   2050:   fprintf(ficparo,"agemin=%.0f agemax=%.0f bage=%.0f fage=%.0f\n",agemin,agemax,bage,fage);
                   2051: 
                   2052:   /*--------------- Prevalence limit --------------*/
                   2053:   
                   2054:   strcpy(filerespl,"pl");
                   2055:   strcat(filerespl,fileres);
                   2056:   if((ficrespl=fopen(filerespl,"w"))==NULL) {
                   2057:     printf("Problem with Prev limit resultfile: %s\n", filerespl);goto end;
                   2058:   }
                   2059:   printf("Computing prevalence limit: result on file '%s' \n", filerespl);
                   2060:   fprintf(ficrespl,"#Prevalence limit\n");
                   2061:   fprintf(ficrespl,"#Age ");
                   2062:   for(i=1; i<=nlstate;i++) fprintf(ficrespl,"%d-%d ",i,i);
                   2063:   fprintf(ficrespl,"\n");
                   2064:   
                   2065:   prlim=matrix(1,nlstate,1,nlstate);
                   2066:   pmmij= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   2067:   oldms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   2068:   newms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   2069:   savms= matrix(1,nlstate+ndeath,1,nlstate+ndeath); /* creation */
                   2070:   oldm=oldms; newm=newms; savm=savms; /* Keeps fixed addresses to free */
                   2071:   
                   2072:   agebase=agemin;
                   2073:   agelim=agemax;
                   2074:   ftolpl=1.e-10;
                   2075:   for (age=agebase; age<=agelim; age++){
                   2076:     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);
                   2077:     fprintf(ficrespl,"%.0f",age );
                   2078:     for(i=1; i<=nlstate;i++)
                   2079:       fprintf(ficrespl," %.5f", prlim[i][i]);
                   2080:     fprintf(ficrespl,"\n");
                   2081:   }
                   2082:   fclose(ficrespl);
                   2083:   
                   2084:   /*------------- h Pij x at various ages ------------*/
                   2085:   
                   2086:   strcpy(filerespij,"pij");  strcat(filerespij,fileres);
                   2087:   if((ficrespij=fopen(filerespij,"w"))==NULL) {
                   2088:     printf("Problem with Pij resultfile: %s\n", filerespij);goto end;
                   2089:   }
                   2090:   printf("Computing pij: result on file '%s' \n", filerespij);
                   2091:   stepsize=(int) (stepm+YEARM-1)/YEARM;
                   2092:   if (stepm<=24) stepsize=2;
                   2093: 
                   2094:   agelim=AGESUP;
                   2095:   hstepm=stepsize*YEARM; /* Every year of age */
                   2096:   hstepm=hstepm/stepm; /* Typically 2 years, = 2/6 months = 4 */ 
                   2097:   for (agedeb=fage; agedeb>=bage; agedeb--){ /* If stepm=6 months */
                   2098:     nhstepm=(int) rint((agelim-agedeb)*YEARM/stepm); /* Typically 20 years = 20*12/6=40 */ 
                   2099:     nhstepm = nhstepm/hstepm; /* Typically 40/4=10 */
                   2100:     p3mat=ma3x(1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   2101:     oldm=oldms;savm=savms;
                   2102:     hpxij(p3mat,nhstepm,agedeb,hstepm,p,nlstate,stepm,oldm,savm);  
                   2103:     fprintf(ficrespij,"# Age");
                   2104:     for(i=1; i<=nlstate;i++)
                   2105:       for(j=1; j<=nlstate+ndeath;j++)
                   2106:        fprintf(ficrespij," %1d-%1d",i,j);
                   2107:     fprintf(ficrespij,"\n");
                   2108:     for (h=0; h<=nhstepm; h++){
                   2109:       fprintf(ficrespij,"%.0f %.0f",agedeb, agedeb+ h*hstepm/YEARM*stepm );
                   2110:       for(i=1; i<=nlstate;i++)
                   2111:        for(j=1; j<=nlstate+ndeath;j++)
                   2112:          fprintf(ficrespij," %.5f", p3mat[i][j][h]);
                   2113:       fprintf(ficrespij,"\n");
                   2114:     }
                   2115:     free_ma3x(p3mat,1,nlstate+ndeath,1, nlstate+ndeath, 0,nhstepm);
                   2116:     fprintf(ficrespij,"\n");
                   2117:   }
                   2118:   fclose(ficrespij);
                   2119: 
                   2120:   /*---------- Health expectancies and variances ------------*/
                   2121:   
                   2122:   eij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
                   2123:   oldm=oldms;savm=savms;
                   2124:   evsij(fileres, eij, p, nlstate, stepm, (int) bage, (int)fage, oldm, savm);
                   2125:   
                   2126:   vareij=ma3x(1,nlstate,1,nlstate,(int) bage, (int) fage);
                   2127:   oldm=oldms;savm=savms;
                   2128:   varevsij(fileres, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);
                   2129: 
                   2130:   strcpy(filerest,"t");
                   2131:   strcat(filerest,fileres);
                   2132:   if((ficrest=fopen(filerest,"w"))==NULL) {
                   2133:     printf("Problem with total LE resultfile: %s\n", filerest);goto end;
                   2134:   }
                   2135:   printf("Computing Total LEs with variances: file '%s' \n", filerest);
                   2136:   fprintf(ficrest,"#Total LEs with variances: e.. (std) ");
                   2137:   for (i=1;i<=nlstate;i++) fprintf(ficrest,"e.%d (std) ",i);
                   2138:   fprintf(ficrest,"\n");
                   2139: 
                   2140:   hf=1;
                   2141:   if (stepm >= YEARM) hf=stepm/YEARM;
                   2142:   epj=vector(1,nlstate+1);
                   2143:   for(age=bage; age <=fage ;age++){
                   2144:     prevalim(prlim, nlstate, p, age, oldm, savm,ftolpl);
                   2145:     fprintf(ficrest," %.0f",age);
                   2146:     for(j=1, epj[nlstate+1]=0.;j <=nlstate;j++){
                   2147:       for(i=1, epj[j]=0.;i <=nlstate;i++) {
                   2148:        epj[j] += prlim[i][i]*hf*eij[i][j][(int)age];
                   2149:       }
                   2150:       epj[nlstate+1] +=epj[j];
                   2151:     }
                   2152:     for(i=1, vepp=0.;i <=nlstate;i++)
                   2153:       for(j=1;j <=nlstate;j++)
                   2154:        vepp += vareij[i][j][(int)age];
                   2155:     fprintf(ficrest," %.2f (%.2f)", epj[nlstate+1],hf*sqrt(vepp));
                   2156:     for(j=1;j <=nlstate;j++){
                   2157:       fprintf(ficrest," %.2f (%.2f)", epj[j],hf*sqrt(vareij[j][j][(int)age]));
                   2158:     }
                   2159:     fprintf(ficrest,"\n");
                   2160:   }
                   2161:   fclose(ficrest);
                   2162:   fclose(ficpar);
                   2163:   free_vector(epj,1,nlstate+1);
                   2164: 
                   2165:   /*------- Variance limit prevalence------*/   
                   2166: 
                   2167:   varpl=matrix(1,nlstate,(int) bage, (int) fage);
                   2168:   oldm=oldms;savm=savms;
                   2169:   varprevlim(fileres, varpl, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl);
                   2170:   
                   2171:   
                   2172:   free_matrix(varpl,1,nlstate,(int) bage, (int)fage);
                   2173:   
                   2174:   free_ma3x(vareij,1,nlstate,1,nlstate,(int) bage, (int)fage);
                   2175:   free_ma3x(eij,1,nlstate,1,nlstate,(int) bage, (int)fage);
                   2176:   
                   2177:   
                   2178:   free_matrix(pmmij,1,nlstate+ndeath,1,nlstate+ndeath);
                   2179:   free_matrix(oldms, 1,nlstate+ndeath,1,nlstate+ndeath);
                   2180:   free_matrix(newms, 1,nlstate+ndeath,1,nlstate+ndeath);
                   2181:   free_matrix(savms, 1,nlstate+ndeath,1,nlstate+ndeath);
                   2182:   
                   2183:   free_matrix(matcov,1,npar,1,npar);
                   2184:   free_vector(delti,1,npar);
                   2185:   
                   2186:   free_ma3x(param,1,nlstate,1, nlstate+ndeath-1,1,ncov);
                   2187: 
                   2188:   printf("End of Imach\n");
                   2189:   /*  gettimeofday(&end_time, (struct timezone*)0);*/  /* after time */
                   2190:   
                   2191:   /* 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);*/
                   2192:   /*printf("Total time was %d uSec.\n", total_usecs);*/
                   2193:   /*------ End -----------*/
                   2194: 
                   2195:  end:
                   2196: #ifdef windows
                   2197:  chdir(pathcd);
                   2198: #endif 
                   2199:  system("gnuplot graph.gp");
                   2200: 
                   2201: #ifdef windows
                   2202:   while (z[0] != 'q') {
                   2203:     chdir(pathcd); 
                   2204:     printf("\nType e to edit output files, c to start again, and q for exiting: ");
                   2205:     scanf("%s",z);
                   2206:     if (z[0] == 'c') system("./imach");
                   2207:     else if (z[0] == 'e') {
                   2208:       chdir(path);
                   2209:       system("index.htm");
                   2210:     }
                   2211:     else if (z[0] == 'q') exit(0);
                   2212:   }
                   2213: #endif 
                   2214: }
                   2215: 

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