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52 int nfp_ffn[effnNR] = { 0, 1, 2, 3, 2, 5, 7, 9, 3 };
54 const char *s_ffn[effnNR+2] = { NULL, "none", "exp", "aexp", "exp_exp", "vac",
55 "exp5", "exp7", "exp9", NULL, NULL };
56 /* We don't allow errest as a choice on the command line */
58 const char *longs_ffn[effnNR] = {
62 "y = a2 exp(-x/a1) + (1-a2) exp(-x/a3)",
63 "y = exp(-v) (cosh(wv) + 1/w sinh(wv)), v = x/(2 a1), w = sqrt(1 - a2)",
64 "y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5",
65 "y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5 exp(-x/a6) + a7",
66 "y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5 exp(-x/a6) + a7 exp(-x/a8) + a9",
67 "y = a2*ee(a1,x) + (1-a2)*ee(a2,x)"
70 extern gmx_bool mrqmin(real x[],real y[],real sig[],int ndata,real a[],
71 int ma,int lista[],int mfit,real **covar,real **alpha,
73 void (*funcs)(real x,real a[],real *y,real dyda[]),
76 extern gmx_bool mrqmin_new(real x[],real y[],real sig[],int ndata,real a[],
77 int ia[],int ma,real **covar,real **alpha,real *chisq,
78 void (*funcs)(real, real [], real *, real []),
81 static real myexp(real x,real A,real tau)
83 if ((A == 0) || (tau == 0))
88 static void exp_one_parm(real x,real a[],real *y,real dyda[])
100 dyda[1] = x*e1/sqr(a[1]);
103 static void exp_two_parm(real x,real a[],real *y,real dyda[])
115 dyda[1] = x*a[2]*e1/sqr(a[1]);
119 static void exp_3_parm(real x,real a[],real *y,real dyda[])
123 * y = a2 exp(-x/a1) + (1-a2) exp(-x/a3)
131 *y = a[2]*e1 + (1-a[2])*e2;
132 dyda[1] = x*a[2]*e1/sqr(a[1]);
134 dyda[3] = x*(1-a[2])*e2/sqr(a[3]);
137 static void exp_5_parm(real x,real a[],real *y,real dyda[])
141 * y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5
149 *y = a[1]*e1 + a[3]*e2 + a[5];
152 fprintf(debug,"exp_5_parm called: x = %10.3f y = %10.3f\n"
153 "a = ( %8.3f %8.3f %8.3f %8.3f %8.3f)\n",
154 x,*y,a[1],a[2],a[3],a[4],a[5]);
156 dyda[2] = x*e1/sqr(a[2]);
158 dyda[4] = x*e2/sqr(a[4]);
162 static void exp_7_parm(real x,real a[],real *y,real dyda[])
166 * y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5 exp(-x/a6) + a7
175 *y = a[1]*e1 + a[3]*e2 + a[5]*e3 + a[7];
178 dyda[2] = x*e1/sqr(a[2]);
180 dyda[4] = x*e2/sqr(a[4]);
182 dyda[6] = x*e3/sqr(a[6]);
186 static void exp_9_parm(real x,real a[],real *y,real dyda[])
190 * y = a1 exp(-x/a2) + a3 exp(-x/a4) + a5 exp(-x/a6) + a7
200 *y = a[1]*e1 + a[3]*e2 + a[5]*e3 + a[7]*e4 + a[9];
203 dyda[2] = x*e1/sqr(a[2]);
205 dyda[4] = x*e2/sqr(a[4]);
207 dyda[6] = x*e3/sqr(a[6]);
209 dyda[8] = x*e4/sqr(a[8]);
213 static void vac_2_parm(real x,real a[],real *y,real dyda[])
217 * y = 1/2 (1 - 1/w) exp(-(1+w)v) + 1/2 (1 + 1/w) exp(-(1-w)v)
219 * = exp(-v) (cosh(wv) + 1/w sinh(wv))
224 * For tranverse current autocorrelation functions:
226 * a2 = 4 tau (eta/rho) k^2
230 double v,det,omega,omega2,em,ec,es;
237 omega = sqrt(omega2);
239 ec = em*0.5*(exp(omega*v)+exp(-omega*v));
240 es = em*0.5*(exp(omega*v)-exp(-omega*v))/omega;
242 ec = em*cos(omega*v);
243 es = em*sin(omega*v)/omega;
246 dyda[2] = (v/det*ec+(v-1/det)*es)/(-2.0);
247 dyda[1] = (1-det)*v/a[1]*es;
250 dyda[2] = -v*v*em*(0.5+v/6);
251 dyda[1] = v*v/a[1]*em;
255 static void errest_3_parm(real x,real a[],real *y,real dyda[])
260 e1 = exp(-x/a[1]) - 1;
264 e2 = exp(-x/a[3]) - 1;
269 v1 = 2*a[1]*(e1*a[1]/x + 1);
270 v2 = 2*a[3]*(e2*a[3]/x + 1);
271 *y = a[2]*v1 + (1-a[2])*v2;
272 dyda[1] = 2* a[2] *(v1/a[1] + e1);
273 dyda[3] = 2*(1 - a[2])*(v2/a[3] + e2);
283 typedef void (*myfitfn)(real x,real a[],real *y,real dyda[]);
284 myfitfn mfitfn[effnNR] = {
285 exp_one_parm, exp_one_parm, exp_two_parm, exp_3_parm, vac_2_parm,
286 exp_5_parm, exp_7_parm, exp_9_parm, errest_3_parm
289 real fit_function(int eFitFn,real *parm,real x)
291 static real y,dum[8];
293 mfitfn[eFitFn](x,parm-1,&y,dum);
298 /* lmfit_exp supports up to 3 parameter fitting of exponential functions */
299 static gmx_bool lmfit_exp(int nfit,real x[],real y[],real dy[],real ftol,
300 real parm[],real dparm[],gmx_bool bVerbose,
303 real chisq,ochisq,alamda;
304 real *a,**covar,**alpha,*dum;
306 int i,j,ma,mfit,*lista,*ia;
308 if ((eFitFn < 0) || (eFitFn >= effnNR))
309 gmx_fatal(FARGS,"fitfn = %d, should be in 0..%d (%s,%d)",
310 effnNR-1,eFitFn,__FILE__,__LINE__);
312 ma=mfit=nfp_ffn[eFitFn]; /* number of parameters to fit */
319 for(i=1; (i<ma+1); i++) {
327 fprintf(stderr,"Will keep parameters fixed during fit procedure: %d\n",
334 fprintf(debug,"%d parameter fit\n",mfit);
337 alamda = -1; /* Starting value */
339 for(i=0; (i<mfit); i++)
344 fprintf(stderr,"%4s %10s %10s %10s %10s %10s\n",
345 "Step","chi^2","Lambda","A1","A2","A3");
348 /* mrqmin(x-1,y-1,dy-1,nfit,a,ma,lista,mfit,covar,alpha,
349 * &chisq,expfn[mfit-1],&alamda)
351 if (!mrqmin_new(x-1,y-1,dy-1,nfit,a,ia,ma,covar,alpha,&chisq,
352 mfitfn[eFitFn],&alamda))
356 fprintf(stderr,"%4d %10.5e %10.5e %10.5e",
357 j,chisq,alamda,a[1]);
359 fprintf(stderr," %10.5e",a[2]);
361 fprintf(stderr," %10.5e",a[3]);
362 fprintf(stderr,"\n");
365 bCont = ((fabs(ochisq - chisq) > fabs(ftol*chisq)) ||
366 ((ochisq == chisq)));
367 } while (bCont && (alamda != 0.0) && (j < 50));
369 fprintf(stderr,"\n");
371 /* Now get the covariance matrix out */
374 /* mrqmin(x-1,y-1,dy-1,nfit,a,ma,lista,mfit,covar,alpha,
375 * &chisq,expfn[mfit-1],&alamda)
377 if ( !mrqmin_new(x-1,y-1,dy-1,nfit,a,ia,ma,covar,alpha,&chisq,
378 mfitfn[eFitFn],&alamda))
381 for(j=0; (j<mfit); j++) {
383 dparm[j] = covar[j+1][j+1];
386 for(i=0; (i<ma+1); i++) {
399 real do_lmfit(int ndata,real c1[],real sig[],real dt,real x0[],
400 real begintimefit,real endtimefit,const output_env_t oenv,
401 gmx_bool bVerbose, int eFitFn,real fitparms[],int fix)
406 int i,j,nparm,nfitpnts;
412 nparm = nfp_ffn[eFitFn];
414 fprintf(debug,"There are %d points to fit %d vars!\n",ndata,nparm);
415 fprintf(debug,"Fit to function %d from %g through %g, dt=%g\n",
416 eFitFn,begintimefit,endtimefit,dt);
424 for(i=0; i<ndata; i++) {
425 ttt = x0 ? x0[i] : dt*i;
426 if (ttt>=begintimefit && ttt<=endtimefit) {
430 /* mrqmin does not like sig to be zero */
436 fprintf(debug,"j= %d, i= %d, x= %g, y= %g, dy= %g\n",
437 j,i,x[j],y[j],dy[j]);
443 if (nfitpnts < nparm)
444 fprintf(stderr,"Not enough data points for fitting!\n");
449 for(i=0; (i < nparm); i++)
452 if (!lmfit_exp(nfitpnts,x,y,dy,ftol,parm,dparm,bVerbose,eFitFn,fix))
453 fprintf(stderr,"Fit failed!\n");
454 else if (nparm <= 3) {
455 /* Compute the integral from begintimefit */
457 integral=(parm[0]*myexp(begintimefit,parm[1], parm[0]) +
458 parm[2]*myexp(begintimefit,1-parm[1],parm[2]));
460 integral=parm[0]*myexp(begintimefit,parm[1], parm[0]);
462 integral=parm[0]*myexp(begintimefit,1, parm[0]);
464 gmx_fatal(FARGS,"nparm = %d in file %s, line %d",
465 nparm,__FILE__,__LINE__);
467 /* Generate THE output */
469 fprintf(stderr,"FIT: # points used in fit is: %d\n",nfitpnts);
470 fprintf(stderr,"FIT: %21s%21s%21s\n",
471 "parm0 ","parm1 (ps) ","parm2 (ps) ");
472 fprintf(stderr,"FIT: ------------------------------------------------------------\n");
473 fprintf(stderr,"FIT: %8.3g +/- %8.3g%9.4g +/- %8.3g%8.3g +/- %8.3g\n",
474 parm[0],dparm[0],parm[1],dparm[1],parm[2],dparm[2]);
475 fprintf(stderr,"FIT: Integral (calc with fitted function) from %g ps to inf. is: %g\n",
476 begintimefit,integral);
478 sprintf(buf,"test%d.xvg",nfitpnts);
479 fp = xvgropen(buf,"C(t) + Fit to C(t)","Time (ps)","C(t)",oenv);
480 fprintf(fp,"# parm0 = %g, parm1 = %g, parm2 = %g\n",
481 parm[0],parm[1],parm[2]);
482 for(j=0; (j<nfitpnts); j++) {
483 ttt = x0 ? x0[j] : dt*j;
484 fprintf(fp,"%10.5e %10.5e %10.5e\n",
485 ttt,c1[j],fit_function(eFitFn,parm,ttt));
490 for(i=0;(i<nparm);i++)
491 fitparms[i] = parm[i];
503 void do_expfit(int ndata,real c1[],real dt,real begintimefit,real endtimefit)
507 real aa,bb,saa,sbb,A,tau,dA,dtau;
509 fprintf(stderr,"Will fit data from %g (ps) to %g (ps).\n",
510 begintimefit,endtimefit);
512 snew(x,ndata); /* allocate the maximum necessary space */
517 for(i=0; (i<ndata); i++) {
518 if ( (dt*i >= begintimefit) && (dt*i <= endtimefit) ) {
522 fprintf(stderr,"n= %d, i= %d, x= %g, y= %g\n",n,i,x[n],y[n]);
526 fprintf(stderr,"# of data points used in the fit is : %d\n\n",n);
527 expfit(n,x,y,Dy,&aa,&saa,&bb,&sbb);
533 fprintf(stderr,"Fitted to y=exp(a+bx):\n");
534 fprintf(stderr,"a = %10.5f\t b = %10.5f",aa,bb);
535 fprintf(stderr,"\n");
536 fprintf(stderr,"Fitted to y=Aexp(-x/tau):\n");
537 fprintf(stderr,"A = %10.5f\t tau = %10.5f\n",A,tau);
538 fprintf(stderr,"dA = %10.5f\t dtau = %10.5f\n",dA,dtau);
542 void expfit(int n, real *x, real *y, real *Dy, real *a, real *sa,
545 real *w,*ly,A,SA,B,SB;
547 real sum,xbar,ybar,Sxx,Sxy,wr2,chi2,gamma,Db;
554 #define sqr(x) ((x)*(x))
560 /* Calculate weights and values of ln(y). */
562 w[i]=sqr(y[i]/Dy[i]);
566 /* The weighted averages of x and y: xbar and ybar. */
578 /* The centered product sums Sxx and Sxy, and hence A and B. */
582 Sxx+=w[i]*sqr(x[i]-xbar);
583 Sxy+=w[i]*(x[i]-xbar)*(ly[i]-ybar);
588 /* Chi-squared (chi2) and gamma. */
592 wr2=w[i]*sqr(ly[i]-A-B*x[i]);
594 gamma+=wr2*(x[i]-xbar);
597 /* Refined values of A and B. Also SA and SB. */
600 A-=ONEP5*chi2/sum-xbar*Db;
601 SB=sqrt((chi2/(n-2))/Sxx);
602 SA=SB*sqrt(Sxx/sum+sqr(xbar));