3 * This source code is part of
7 * GROningen MAchine for Chemical Simulations
10 * Written by David van der Spoel, Erik Lindahl, Berk Hess, and others.
11 * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
12 * Copyright (c) 2001-2004, The GROMACS development team,
13 * check out http://www.gromacs.org for more information.
15 * This program is free software; you can redistribute it and/or
16 * modify it under the terms of the GNU General Public License
17 * as published by the Free Software Foundation; either version 2
18 * of the License, or (at your option) any later version.
20 * If you want to redistribute modifications, please consider that
21 * scientific software is very special. Version control is crucial -
22 * bugs must be traceable. We will be happy to consider code for
23 * inclusion in the official distribution, but derived work must not
24 * be called official GROMACS. Details are found in the README & COPYING
25 * files - if they are missing, get the official version at www.gromacs.org.
27 * To help us fund GROMACS development, we humbly ask that you cite
28 * the papers on the package - you can find them in the top README file.
30 * For more info, check our website at http://www.gromacs.org
33 * Green Red Orange Magenta Azure Cyan Skyblue
40 #include <gsl/gsl_rng.h>
41 #include <gsl/gsl_randist.h>
42 #include <gsl/gsl_vector.h>
43 #include <gsl/gsl_blas.h>
44 #include <gsl/gsl_multimin.h>
45 #include <gsl/gsl_multifit_nlin.h>
46 #include <gsl/gsl_sf.h>
47 #include <gsl/gsl_version.h>
63 /* The first few sections of this file contain functions that were adopted,
64 * and to some extent modified, by Erik Marklund (erikm[aT]xray.bmc.uu.se,
65 * http://folding.bmc.uu.se) from code written by Omer Markovitch (email, url).
66 * This is also the case with the function eq10v2().
68 * The parts menetioned in the previous paragraph were contributed under the BSD license.
72 /* This first part is from complex.c which I recieved from Omer Markowitch.
75 * ------------- from complex.c ------------- */
77 /* Complexation of a paired number (r,i) */
78 static gem_complex gem_cmplx(double r, double i)
86 /* Complexation of a real number, x */
87 static gem_complex gem_c(double x)
95 /* Magnitude of a complex number z */
96 static double gem_cx_abs(gem_complex z) { return (sqrt(z.r*z.r+z.i*z.i)); }
98 /* Addition of two complex numbers z1 and z2 */
99 static gem_complex gem_cxadd(gem_complex z1, gem_complex z2)
107 /* Addition of a complex number z1 and a real number r */
108 static gem_complex gem_cxradd(gem_complex z, double r)
116 /* Subtraction of two complex numbers z1 and z2 */
117 static gem_complex gem_cxsub(gem_complex z1, gem_complex z2)
125 /* Multiplication of two complex numbers z1 and z2 */
126 static gem_complex gem_cxmul(gem_complex z1, gem_complex z2)
129 value.r = z1.r*z2.r-z1.i*z2.i;
130 value.i = z1.r*z2.i+z1.i*z2.r;
134 /* Square of a complex number z */
135 static gem_complex gem_cxsq(gem_complex z)
138 value.r = z.r*z.r-z.i*z.i;
139 value.i = z.r*z.i*2.;
143 /* multiplication of a complex number z and a real number r */
144 static gem_complex gem_cxrmul(gem_complex z, double r)
152 /* Division of two complex numbers z1 and z2 */
153 static gem_complex gem_cxdiv(gem_complex z1, gem_complex z2)
157 num = z2.r*z2.r+z2.i*z2.i;
160 fprintf(stderr, "ERROR in gem_cxdiv function\n");
162 value.r = (z1.r*z2.r+z1.i*z2.i)/num; value.i = (z1.i*z2.r-z1.r*z2.i)/num;
166 /* division of a complex z number by a real number x */
167 static gem_complex gem_cxrdiv(gem_complex z, double r)
175 /* division of a real number r by a complex number x */
176 static gem_complex gem_rxcdiv(double r, gem_complex z)
180 f = r/(z.r*z.r+z.i*z.i);
186 /* Exponential of a complex number-- exp (z)=|exp(z.r)|*{cos(z.i)+I*sin(z.i)}*/
187 static gem_complex gem_cxdexp(gem_complex z)
192 value.r = exp_z_r*cos(z.i);
193 value.i = exp_z_r*sin(z.i);
197 /* Logarithm of a complex number -- log(z)=log|z|+I*Arg(z), */
198 /* where -PI < Arg(z) < PI */
199 static gem_complex gem_cxlog(gem_complex z)
203 mag2 = z.r*z.r+z.i*z.i;
205 fprintf(stderr, "ERROR in gem_cxlog func\n");
207 value.r = log(sqrt(mag2));
214 value.i = atan2(z.i, z.r);
219 /* Square root of a complex number z = |z| exp(I*the) -- z^(1/2) */
220 /* z^(1/2)=|z|^(1/2)*[cos(the/2)+I*sin(the/2)] */
221 /* where 0 < the < 2*PI */
222 static gem_complex gem_cxdsqrt(gem_complex z)
227 value.r = sqrt(fabs((sq+z.r)*0.5)); /* z'.r={|z|*[1+cos(the)]/2}^(1/2) */
228 value.i = sqrt(fabs((sq-z.r)*0.5)); /* z'.i={|z|*[1-cos(the)]/2}^(1/2) */
235 /* Complex power of a complex number z1^z2 */
236 static gem_complex gem_cxdpow(gem_complex z1, gem_complex z2)
239 value=gem_cxdexp(gem_cxmul(gem_cxlog(z1),z2));
243 /* ------------ end of complex.c ------------ */
245 /* This next part was derived from cubic.c, also received from Omer Markovitch.
246 * ------------- from cubic.c ------------- */
248 /* Solver for a cubic equation: x^3-a*x^2+b*x-c=0 */
249 static void gem_solve(gem_complex *al, gem_complex *be, gem_complex *gam,
250 double a, double b, double c)
252 double t1, t2, two_3, temp;
253 gem_complex ctemp, ct3;
255 two_3=pow(2., 1./3.); t1 = -a*a+3.*b; t2 = 2.*a*a*a-9.*a*b+27.*c;
256 temp = 4.*t1*t1*t1+t2*t2;
258 ctemp = gem_cmplx(temp,0.); ctemp = gem_cxadd(gem_cmplx(t2,0.),gem_cxdsqrt(ctemp));
259 ct3 = gem_cxdpow(ctemp, gem_cmplx(1./3.,0.));
261 ctemp = gem_rxcdiv(-two_3*t1/3., ct3);
262 ctemp = gem_cxadd(ctemp, gem_cxrdiv(ct3, 3.*two_3));
264 *gam = gem_cxadd(gem_cmplx(a/3.,0.), ctemp);
266 ctemp=gem_cxmul(gem_cxsq(*gam), gem_cxsq(gem_cxsub(*gam, gem_cmplx(a,0.))));
267 ctemp=gem_cxadd(ctemp, gem_cxmul(gem_cmplx(-4.*c,0.), *gam));
268 ctemp = gem_cxdiv(gem_cxdsqrt(ctemp), *gam);
269 *al = gem_cxrmul(gem_cxsub(gem_cxsub(gem_cmplx(a,0.), *gam),ctemp),0.5);
270 *be = gem_cxrmul(gem_cxadd(gem_cxsub(gem_cmplx(a,0.), *gam),ctemp),0.5);
273 /* ------------ end of cubic.c ------------ */
275 /* This next part was derived from cerror.c and rerror.c, also received from Omer Markovitch.
276 * ------------- from [cr]error.c ------------- */
278 /************************************************************/
279 /* Real valued error function and related functions */
280 /* x, y : real variables */
281 /* erf(x) : error function */
282 /* erfc(x) : complementary error function */
283 /* omega(x) : exp(x*x)*erfc(x) */
284 /* W(x,y) : exp(-x*x)*omega(x+y)=exp(2*x*y+y^2)*erfc(x+y) */
285 /************************************************************/
287 /*---------------------------------------------------------------------------*/
288 /* Utilzed the series approximation of erf(x) */
289 /* Relative error=|err(x)|/erf(x)<EPS */
290 /* Handbook of Mathematical functions, Abramowitz, p 297 */
291 /* Note: When x>=6 series sum deteriorates -> Asymptotic series used instead */
292 /*---------------------------------------------------------------------------*/
293 /* This gives erfc(z) correctly only upto >10-15 */
295 static double gem_erf(double x)
297 double n,sum,temp,exp2,xm,x2,x4,x6,x8,x10,x12;
310 for(n=1.; n<=2000.; n+=1.){
311 temp *= 2.*x2/(2.*n+1.);
313 if(fabs(temp/sum)<1.E-16)
318 fprintf(stderr, "In Erf calc - iteration exceeds %lg\n",n);
323 /* from the asymptotic expansion of experfc(x) */
324 sum = (1. - 0.5/x2 + 0.75/x4
325 - 1.875/x6 + 6.5625/x8
326 - 29.53125/x10 + 162.421875/x12)
328 sum*=exp2; /* now sum is erfc(x) */
331 return x>=0.0 ? sum : -sum;
334 /* Result --> Alex's code for erfc and experfc behaves better than this */
335 /* complementray error function. Returns 1.-erf(x) */
336 static double gem_erfc(double x)
342 ans = t * exp(-z*z - 1.26551223 +
351 t*0.17087277)))))))));
353 return x>=0.0 ? ans : 2.0-ans;
356 /* omega(x)=exp(x^2)erfc(x) */
357 static double gem_omega(double x)
359 double xm, ans, xx, x4, x6, x8, x10, x12;
369 ans = exp(xx)*gem_erfc(x);
371 /* Asymptotic expansion */
372 ans = (1. - 0.5/xx + 0.75/x4 - 1.875/x6 + 6.5625/x8 - 29.53125/x10 + 162.421875/x12) / sPI/x;
377 /*---------------------------------------------------------------------------*/
378 /* Utilzed the series approximation of erf(z=x+iy) */
379 /* Relative error=|err(z)|/|erf(z)|<EPS */
380 /* Handbook of Mathematical functions, Abramowitz, p 299 */
381 /* comega(z=x+iy)=cexp(z^2)*cerfc(z) */
382 /*---------------------------------------------------------------------------*/
383 static gem_complex gem_comega(gem_complex z)
387 double sumr,sumi,n,n2,f,temp,temp1;
388 double x2, y2,cos_2xy,sin_2xy,cosh_2xy,sinh_2xy,cosh_ny,sinh_ny,exp_y2;
396 cos_2xy = cos(2.*x*y);
397 sin_2xy = sin(2.*x*y);
398 cosh_2xy = cosh(2.*x*y);
399 sinh_2xy = sinh(2.*x*y);
402 for(n=1.0, temp=0.; n<=2000.; n+=1.0){
406 f = exp(-n2/4.)/(n2+4.*x2);
407 /* if(f<1.E-200) break; */
408 sumr += (2.*x - 2.*x*cosh_ny*cos_2xy + n*sinh_ny*sin_2xy)*f;
409 sumi += (2.*x*cosh_ny*sin_2xy + n*sinh_ny*cos_2xy)*f;
410 temp1 = sqrt(sumr*sumr+sumi*sumi);
411 if(fabs((temp1-temp)/temp1)<1.E-16) {
417 fprintf(stderr, "iteration exceeds %lg\n",n);
427 value.r = gem_omega(x)-(f*(1.-cos_2xy)+sumr);
428 value.i = -(f*sin_2xy+sumi);
429 value = gem_cxmul(value,gem_cmplx(exp_y2*cos_2xy,exp_y2*sin_2xy));
433 /* ------------ end of [cr]error.c ------------ */
435 /*_ REVERSIBLE GEMINATE RECOMBINATION
437 * Here are the functions for reversible geminate recombination. */
439 /* Changes the unit from square cm per s to square Ångström per ps,
440 * since Omers code uses the latter units while g_mds outputs the former.
441 * g_hbond expects a diffusion coefficent given in square cm per s. */
442 static double sqcm_per_s_to_sqA_per_ps (real D) {
443 fprintf(stdout, "Diffusion coefficient is %f A^2/ps\n", D*1e4);
444 return (double)(D*1e4);
448 static double eq10v2(double theoryCt[], double time[], int manytimes,
449 double ka, double kd, t_gemParams *params)
451 /* Finding the 3 roots */
453 double kD, D, r, a, b, c, tsqrt, sumimaginary;
458 part1, part2, part3, part4;
463 a = (1.0 + ka/kD) * sqrt(D)/r;
467 gem_solve(&alpha, &beta, &gamma, a, b, c);
468 /* Finding the 3 roots */
471 part1 = gem_cxmul(alpha, gem_cxmul(gem_cxadd(beta, gamma), gem_cxsub(beta, gamma))); /* 1(2+3)(2-3) */
472 part2 = gem_cxmul(beta, gem_cxmul(gem_cxadd(gamma, alpha), gem_cxsub(gamma, alpha))); /* 2(3+1)(3-1) */
473 part3 = gem_cxmul(gamma, gem_cxmul(gem_cxadd(alpha, beta) , gem_cxsub(alpha, beta))); /* 3(1+2)(1-2) */
474 part4 = gem_cxmul(gem_cxsub(gamma, alpha), gem_cxmul(gem_cxsub(alpha, beta), gem_cxsub(beta, gamma))); /* (3-1)(1-2)(2-3) */
477 #pragma omp parallel for \
478 private(i, tsqrt, oma, omb, omc, c1, c2, c3, c4), \
479 reduction(+:sumimaginary), \
483 for (i=0; i<manytimes; i++){
484 tsqrt = sqrt(time[i]);
485 oma = gem_comega(gem_cxrmul(alpha, tsqrt));
486 c1 = gem_cxmul(oma, gem_cxdiv(part1, part4));
487 omb = gem_comega(gem_cxrmul(beta, tsqrt));
488 c2 = gem_cxmul(omb, gem_cxdiv(part2, part4));
489 omc = gem_comega(gem_cxrmul(gamma, tsqrt));
490 c3 = gem_cxmul(omc, gem_cxdiv(part3, part4));
491 c4.r = c1.r+c2.r+c3.r;
492 c4.i = c1.i+c2.i+c3.i;
494 sumimaginary += c4.i * c4.i;
501 /* This returns the real-valued index(!) to an ACF, equidistant on a log scale. */
502 static double getLogIndex(const int i, const t_gemParams *params)
504 return (exp(((double)(i)) * params->logQuota) -1);
507 extern t_gemParams *init_gemParams(const double sigma, const double D,
508 const real *t, const int len, const int nFitPoints,
509 const real begFit, const real endFit,
510 const real ballistic, const int nBalExp, const gmx_bool bDt)
517 /* A few hardcoded things here. For now anyway. */
519 /* p->ka_max = 100; */
527 /* p->lifetime = 0; */
528 p->sigma = sigma*10; /* Omer uses Ã…, not nm */
529 /* p->lsq_old = 99999; */
530 p->D = sqcm_per_s_to_sqA_per_ps(D);
531 p->kD = 4*acos(-1.0)*sigma*p->D;
534 /* Parameters used by calcsquare(). Better to calculate them
535 * here than in calcsquare every time it's called. */
537 /* p->logAfterTime = logAfterTime; */
538 tDelta = (t[len-1]-t[0]) / len;
540 gmx_fatal(FARGS, "Time between frames is non-positive!");
545 p->nExpFit = nBalExp;
546 /* p->nLin = logAfterTime / tDelta; */
547 p->nFitPoints = nFitPoints;
550 p->logQuota = (double)(log(p->len))/(p->nFitPoints-1);
551 /* if (p->nLin <= 0) { */
552 /* fprintf(stderr, "Number of data points in the linear regime is non-positive!\n"); */
556 /* We want the same number of data points in the log regime. Not crucial, but seems like a good idea. */
557 /* p->logDelta = log(((float)len)/p->nFitPoints) / p->nFitPoints;/\* log(((float)len)/p->nLin) / p->nLin; *\/ */
558 /* p->logPF = p->nFitPoints*p->nFitPoints/(float)len; /\* p->nLin*p->nLin/(float)len; *\/ */
559 /* logPF and logDelta are stitched together with the macro GETLOGINDEX defined in geminate.h */
561 /* p->logMult = pow((float)len, 1.0/nLin);/\* pow(t[len-1]-t[0], 1.0/p->nLin); *\/ */
562 p->ballistic = ballistic;
566 /* There was a misunderstanding regarding the fitting. From our
567 * recent correspondence it appears that Omer's code require
568 * the ACF data on a log-scale and does not operate on the raw data.
569 * This needs to be redone in gemFunc_residual() as well as in the
570 * t_gemParams structure. */
572 static double gemFunc_residual2(const gsl_vector *p, void *data)
575 int i, iLog, nLin, nFitPoints, nData;
576 double r, residual2, *ctTheory, *y;
578 GD = (gemFitData *)data;
579 nLin = GD->params->nLin;
580 nFitPoints = GD->params->nFitPoints;
583 ctTheory = GD->ctTheory;
586 /* Now, we'd save a lot of time by not calculating eq10v2 for all
587 * time points, but only those that we sample to calculate the mse.
590 eq10v2(GD->ctTheory, GD->doubleLogTime/* GD->time */, nFitPoints/* GD->nData */,
591 gsl_vector_get(p, 0), gsl_vector_get(p, 1),
594 fixGemACF(GD->ctTheory, nFitPoints);
596 /* Removing a bunch of points from the log-part. */
598 #pragma omp parallel for schedule(dynamic) \
599 firstprivate(nData, ctTheory, y, nFitPoints) \
600 private (i, iLog, r) \
601 reduction(+:residual2) \
604 for(i=0; i<nFitPoints; i++)
606 iLog = GD->logtime[i];
607 r = log(ctTheory[i /* iLog */]);
608 residual2 += sqr(r-log(y[iLog]));
610 residual2 /= nFitPoints; /* Not really necessary for the fitting, but gives more meaning to the returned data. */
611 /* printf("ka=%3.5f\tkd=%3.5f\trmse=%3.5f\n", gsl_vector_get(p,0), gsl_vector_get(p,1), residual2); */
614 /* for (i=0; i<nLin; i++) { */
615 /* /\* Linear part ----------*\/ */
616 /* r = ctTheory[i]; */
617 /* residual2 += sqr(r-y[i]); */
618 /* /\* Log part -------------*\/ */
619 /* iLog = GETLOGINDEX(i, GD->params); */
620 /* if (iLog >= nData) */
621 /* gmx_fatal(FARGS, "log index out of bounds: %i", iLog); */
622 /* r = ctTheory[iLog]; */
623 /* residual2 += sqr(r-y[iLog]); */
626 /* residual2 /= GD->n; */
627 /* return residual2; */
631 static real* d2r(const double *d, const int nn);
633 extern real fitGemRecomb(double *ct, double *time, double **ctFit,
634 const int nData, t_gemParams *params)
637 int nThreads, i, iter, status, maxiter;
638 real size, d2, tol, *dumpdata;
641 char *dumpstr, dumpname[128];
643 /* nmsimplex2 had convergence problems prior to gsl v1.14,
644 * but it's O(N) instead of O(N) operations, so let's use it if v >= 1.14 */
646 gsl_multimin_fminimizer *s;
647 gsl_vector *x,*dx; /* parameters and initial step size */
648 gsl_multimin_function fitFunc;
649 #ifdef GSL_MAJOR_VERSION
650 #ifdef GSL_MINOR_VERSION
651 #if ((GSL_MAJOR_VERSION == 1 && GSL_MINOR_VERSION >= 14) || \
652 (GSL_MAJOR_VERSION > 1))
653 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex2;
655 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex;
657 #endif /* GSL_MINOR_VERSION */
659 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex;
660 #endif /* GSL_MAJOR_VERSION */
661 fprintf(stdout, "Will fit ka and kd to the ACF according to the reversible geminate recombination model.\n");
662 #else /* HAVE_LIBGSL */
663 fprintf(stderr, "Sorry, can't do reversible geminate recombination without gsl. "
664 "Recompile using --with-gsl.\n");
666 #endif /* HAVE_LIBGSL */
670 nThreads = omp_get_num_procs();
671 omp_set_num_threads(nThreads);
672 fprintf(stdout, "We will be using %i threads.\n", nThreads);
680 p = 2; /* Number of parameters to fit. ka and kd. */
681 n = params->nFitPoints; /* params->nLin*2 */; /* Number of points in the reduced dataset */
685 fprintf(stderr, "Fitting of D is not implemented yet. It must be provided on the command line.\n");
690 /* fprintf(stderr, "Reduced data set larger than the complete data set!\n"); */
693 snew(dumpdata, nData);
699 snew(GD->ctTheory, nData);
705 GD->tDelta = time[1]-time[0];
708 snew(GD->logtime,params->nFitPoints);
709 snew(GD->doubleLogTime,params->nFitPoints);
711 for (i=0; i<params->nFitPoints; i++)
713 GD->doubleLogTime[i] = (double)(getLogIndex(i, params));
714 GD->logtime[i] = (int)(GD->doubleLogTime[i]);
715 GD->doubleLogTime[i]*=GD->tDelta;
717 if (GD->logtime[i] >= nData)
719 fprintf(stderr, "Ayay. It seems we're indexing out of bounds.\n");
720 params->nFitPoints = i;
724 fitFunc.f = &gemFunc_residual2;
726 fitFunc.params = (void*)GD;
728 x = gsl_vector_alloc (fitFunc.n);
729 dx = gsl_vector_alloc (fitFunc.n);
730 gsl_vector_set (x, 0, 25);
731 gsl_vector_set (x, 1, 0.5);
732 gsl_vector_set (dx, 0, 0.1);
733 gsl_vector_set (dx, 1, 0.01);
736 s = gsl_multimin_fminimizer_alloc (T, fitFunc.n);
737 gsl_multimin_fminimizer_set (s, &fitFunc, x, dx);
739 gsl_vector_free (dx);
743 status = gsl_multimin_fminimizer_iterate (s);
746 gmx_fatal(FARGS,"Something went wrong in the iteration in minimizer %s:\n \"%s\"\n",
747 gsl_multimin_fminimizer_name(s), gsl_strerror(status));
749 d2 = gsl_multimin_fminimizer_minimum(s);
750 size = gsl_multimin_fminimizer_size(s);
751 params->ka = gsl_vector_get (s->x, 0);
752 params->kd = gsl_vector_get (s->x, 1);
756 fprintf(stderr, "%s\n", gsl_strerror(status));
760 status = gsl_multimin_test_size(size,tol);
762 if (status == GSL_SUCCESS) {
763 fprintf(stdout, "Converged to minimum at\n");
766 printf ("iter %5d: ka = %2.5f kd = %2.5f f() = %7.3f size = %.3f chi2 = %2.5f\n",
774 eq10v2(GD->ctTheory, time, nData, params->ka, params->kd, params);
775 /* fixGemACF(GD->ctTheory, nFitPoints); */
776 sprintf(dumpname, "Iter_%i.xvg", iter);
777 for(i=0; i<GD->nData; i++)
779 dumpdata[i] = (real)(GD->ctTheory[i]);
780 if (!gmx_isfinite(dumpdata[i]))
782 gmx_fatal(FARGS, "Non-finite value in acf.");
785 dumpN(dumpdata, GD->nData, dumpname);
788 while ((status == GSL_CONTINUE) && (iter < maxiter));
790 /* /\* Calculate the theoretical ACF from the parameters one last time. *\/ */
791 eq10v2(GD->ctTheory, time, nData, params->ka, params->kd, params);
792 *ctFit = GD->ctTheory;
795 gsl_multimin_fminimizer_free (s);
800 #endif /* HAVE_LIBGSL */
804 static int balFunc_f(const gsl_vector *x, void *data, gsl_vector *f)
806 /* C + sum{ A_i * exp(-B_i * t) }*/
810 double *y, *A, *B, C, /* There are the parameters to be optimized. */
813 BD = (balData *)data;
820 for (i = 0; i<nexp; i++)
822 A[i] = gsl_vector_get(x, i*2);
823 B[i] = gsl_vector_get(x, i*2+1);
825 C = gsl_vector_get(x, nexp*2);
831 for (j=0; j<nexp; j++) {
832 ct += A[j] * exp(B[j] * t);
835 gsl_vector_set (f, i, ct - y[i]);
840 /* The derivative stored in jacobian form (J)*/
841 static int balFunc_df(const gsl_vector *params, void *data, gsl_matrix *J)
845 double *y, *A, *B, C, /* There are the parameters. */
857 for (i=0; i<nexp; i++)
859 A[i] = gsl_vector_get(params, i*2);
860 B[i] = gsl_vector_get(params, i*2+1);
862 C = gsl_vector_get(params, nexp*2);
866 for (j=0; j<nexp; j++)
868 gsl_matrix_set (J, i, j*2, exp(B[j]*t)); /* df(t)/dA_j */
869 gsl_matrix_set (J, i, j*2+1, A[j]*t*exp(B[j]*t)); /* df(t)/dB_j */
871 gsl_matrix_set (J, i, nexp*2, 1); /* df(t)/dC */
876 /* Calculation of the function and its derivative */
877 static int balFunc_fdf(const gsl_vector *params, void *data,
878 gsl_vector *f, gsl_matrix *J)
880 balFunc_f(params, data, f);
881 balFunc_df(params, data, J);
884 #endif /* HAVE_LIBGSL */
886 /* Removes the ballistic term from the beginning of the ACF,
887 * just like in Omer's paper.
889 extern void takeAwayBallistic(double *ct, double *t, int len, real tMax, int nexp, gmx_bool bDerivative)
892 /* Use nonlinear regression with GSL instead.
893 * Fit with 4 exponentials and one constant term,
894 * subtract the fatest exponential. */
896 int nData,i,status, iter;
898 double *guess, /* Initial guess. */
899 *A, /* The fitted parameters. (A1, B1, A2, B2,... C) */
909 } while (t[nData]<tMax+t[0] && nData<len);
911 p = nexp*2+1; /* Number of parameters. */
914 const gsl_multifit_fdfsolver_type *T
915 = gsl_multifit_fdfsolver_lmsder;
917 gsl_multifit_fdfsolver *s; /* The solver itself. */
918 gsl_multifit_function_fdf fitFunction; /* The function to be fitted. */
919 gsl_matrix *covar; /* Covariance matrix for the parameters.
920 * We'll not use the result, though. */
921 gsl_vector_view theParams;
926 } while (t[nData]<tMax+t[0] && nData<len);
933 covar = gsl_matrix_alloc (p, p);
935 /* Set up an initial gess for the parameters.
936 * The solver is somewhat sensitive to the initial guess,
937 * but this worked fine for a TIP3P box with -geminate dd
938 * EDIT: In fact, this seems like a good starting pont for other watermodels too. */
939 for (i=0; i<nexp; i++)
942 guess[i*2+1] = -0.5 + (((double)i)/nexp - 0.5)*0.3;
944 guess[nexp * 2] = 0.01;
946 theParams = gsl_vector_view_array(guess, p);
951 BD->tDelta = t[1]-t[0];
954 fitFunction.f = &balFunc_f;
955 fitFunction.df = &balFunc_df;
956 fitFunction.fdf = &balFunc_fdf;
957 fitFunction.n = nData;
959 fitFunction.params = BD;
961 s = gsl_multifit_fdfsolver_alloc (T, nData, p);
963 gmx_fatal(FARGS, "Could not set up the nonlinear solver.");
965 gsl_multifit_fdfsolver_set(s, &fitFunction, &theParams.vector);
967 /* \=============================================/ */
973 status = gsl_multifit_fdfsolver_iterate (s);
977 status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4);
979 while (iter < 5000 && status == GSL_CONTINUE);
983 fprintf(stderr, "The non-linear fitting did not converge in 5000 steps.\n"
984 "Check the quality of the fit!\n");
988 fprintf(stderr, "Non-linear fitting of ballistic term converged in %d steps.\n\n", (int)iter);
990 for (i=0; i<nexp; i++) {
991 fprintf(stdout, "%c * exp(%c * t) + ", 'A'+(char)i*2, 'B'+(char)i*2);
994 fprintf(stdout, "%c\n", 'A'+(char)nexp*2);
995 fprintf(stdout, "Here are the actual numbers for A-%c:\n", 'A'+nexp*2);
997 for (i=0; i<nexp; i++)
999 A[i*2] = gsl_vector_get(s->x, i*2);
1000 A[i*2+1] = gsl_vector_get(s->x, i*2+1);
1001 fprintf(stdout, " %g*exp(%g * x) +", A[i*2], A[i*2+1]);
1003 A[i*2] = gsl_vector_get(s->x, i*2); /* The last and constant term */
1004 fprintf(stdout, " %g\n", A[i*2]);
1008 /* Implement some check for parameter quality */
1009 for (i=0; i<nexp; i++)
1011 if (A[i*2]<0 || A[i*2]>1) {
1012 fprintf(stderr, "WARNING: ----------------------------------\n"
1013 " | A coefficient does not lie within [0,1].\n"
1014 " | This may or may not be a problem.\n"
1015 " | Double check the quality of the fit!\n");
1018 fprintf(stderr, "WARNING: ----------------------------------\n"
1019 " | One factor in the exponent is positive.\n"
1020 " | This could be a problem if the coefficient\n"
1021 " | is large. Double check the quality of the fit!\n");
1024 if (A[i*2]<0 || A[i*2]>1) {
1025 fprintf(stderr, "WARNING: ----------------------------------\n"
1026 " | The constant term does not lie within [0,1].\n"
1027 " | This may or may not be a problem.\n"
1028 " | Double check the quality of the fit!\n");
1031 /* Sort the terms */
1032 sorted = (nexp > 1) ? FALSE : TRUE;
1036 for (i=0;i<nexp-1;i++)
1038 ddt[0] = A[i*2] * A[i*2+1];
1039 ddt[1] =A[i*2+2] * A[i*2+3];
1041 if ((bDerivative && (ddt[0]<0 && ddt[1]<0 && ddt[0]>ddt[1])) || /* Compare derivative at t=0... */
1042 (!bDerivative && (A[i*2+1] > A[i*2+3]))) /* Or just the coefficient in the exponent */
1045 a[0] = A[i*2]; /* coefficient */
1046 a[1] = A[i*2+1]; /* parameter in the exponent */
1049 A[i*2+1] = A[i*2+3];
1057 /* Subtract the fastest component */
1058 fprintf(stdout, "Fastest component is %g * exp(%g * t)\n"
1059 "Subtracting fastest component from ACF.\n", A[0], A[1]);
1061 for (i=0; i<len; i++) {
1062 ct[i] = (ct[i] - A[0] * exp(A[1] * i*BD->tDelta)) / (1-A[0]);
1068 gsl_multifit_fdfsolver_free(s);
1069 gsl_matrix_free(covar);
1073 /* We have no gsl. */
1074 fprintf(stderr, "Sorry, can't take away ballistic component without gsl. "
1075 "Recompile using --with-gsl.\n");
1077 #endif /* HAVE_LIBGSL */
1081 extern void dumpN(const real *e, const int nn, char *fn)
1083 /* For debugging only */
1086 char standardName[] = "Nt.xvg";
1094 "@ xaxis label \"Frame\"\n"
1095 "@ yaxis label \"N\"\n"
1096 "@ s0 line type 3\n");
1098 for (i=0; i<nn; i++) {
1099 fprintf(f, "%-10i %-g\n", i, e[i]);
1105 static real* d2r(const double *d, const int nn)
1111 for (i=0; i<nn; i++)
1117 static void _patchBad(double *ct, int n, double dy)
1119 /* Just do lin. interpolation for now. */
1128 static void patchBadPart(double *ct, int n)
1130 _patchBad(ct,n,(ct[n] - ct[0])/n);
1133 static void patchBadTail(double *ct, int n)
1135 _patchBad(ct+1,n-1,ct[1]-ct[0]);
1139 extern void fixGemACF(double *ct, int len)
1144 /* Let's separate two things:
1145 * - identification of bad parts
1146 * - patching of bad parts.
1149 b = 0; /* Start of a bad stretch */
1150 e = 0; /* End of a bad stretch */
1153 /* An acf of binary data must be one at t=0. */
1154 if (abs(ct[0]-1.0) > 1e-6)
1157 fprintf(stderr, "|ct[0]-1.0| = %1.6d. Setting ct[0] to 1.0.\n", abs(ct[0]-1.0));
1160 for (i=0; i<len; i++)
1164 if (isfinite(ct[i]))
1165 #elif defined(HAS__ISFINITE)
1166 if (_isfinite(ct[i]))
1173 /* Still on a good stretch. Proceed.*/
1177 /* Patch up preceding bad stretch. */
1183 gmx_fatal(FARGS, "The ACF is mostly NaN or Inf. Aborting.");
1185 patchBadTail(&(ct[b-2]), (len-b)+1);
1189 patchBadPart(&(ct[b-1]), (e-b)+1);