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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>
62 /* The first few sections of this file contain functions that were adopted,
63 * and to some extent modified, by Erik Marklund (erikm[aT]xray.bmc.uu.se,
64 * http://folding.bmc.uu.se) from code written by Omer Markovitch (email, url).
65 * This is also the case with the function eq10v2().
67 * The parts menetioned in the previous paragraph were contributed under the BSD license.
71 /* This first part is from complex.c which I recieved from Omer Markowitch.
74 * ------------- from complex.c ------------- */
76 /* Complexation of a paired number (r,i) */
77 static gem_complex gem_cmplx(double r, double i)
85 /* Complexation of a real number, x */
86 static gem_complex gem_c(double x)
94 /* Real and Imaginary part of a complex number z -- Re (z) and Im (z) */
95 static double gem_Re(gem_complex z) {return z.r;}
96 static double gem_Im(gem_complex z) {return z.i;}
98 /* Magnitude of a complex number z */
99 static double gem_cx_abs(gem_complex z) { return (sqrt(z.r*z.r+z.i*z.i)); }
101 /* Addition of two complex numbers z1 and z2 */
102 static gem_complex gem_cxadd(gem_complex z1, gem_complex z2)
110 /* Addition of a complex number z1 and a real number r */
111 static gem_complex gem_cxradd(gem_complex z, double r)
119 /* Subtraction of two complex numbers z1 and z2 */
120 static gem_complex gem_cxsub(gem_complex z1, gem_complex z2)
128 /* Multiplication of two complex numbers z1 and z2 */
129 static gem_complex gem_cxmul(gem_complex z1, gem_complex z2)
132 value.r = z1.r*z2.r-z1.i*z2.i;
133 value.i = z1.r*z2.i+z1.i*z2.r;
137 /* Square of a complex number z */
138 static gem_complex gem_cxsq(gem_complex z)
141 value.r = z.r*z.r-z.i*z.i;
142 value.i = z.r*z.i*2.;
146 /* multiplication of a complex number z and a real number r */
147 static gem_complex gem_cxrmul(gem_complex z, double r)
155 /* Division of two complex numbers z1 and z2 */
156 static gem_complex gem_cxdiv(gem_complex z1, gem_complex z2)
160 num = z2.r*z2.r+z2.i*z2.i;
163 fprintf(stderr, "ERROR in gem_cxdiv function\n");
165 value.r = (z1.r*z2.r+z1.i*z2.i)/num; value.i = (z1.i*z2.r-z1.r*z2.i)/num;
169 /* division of a complex z number by a real number x */
170 static gem_complex gem_cxrdiv(gem_complex z, double r)
178 /* division of a real number r by a complex number x */
179 static gem_complex gem_rxcdiv(double r, gem_complex z)
183 f = r/(z.r*z.r+z.i*z.i);
189 /* Integer power of a complex number z -- z^x */
190 static gem_complex gem_cxintpow(gem_complex z, int x)
201 value = gem_cxmul(value, z);
208 value = gem_cxdiv(value, z);
217 /* Exponential of a complex number-- exp (z)=|exp(z.r)|*{cos(z.i)+I*sin(z.i)}*/
218 static gem_complex gem_cxdexp(gem_complex z)
223 value.r = exp_z_r*cos(z.i);
224 value.i = exp_z_r*sin(z.i);
228 /* Logarithm of a complex number -- log(z)=log|z|+I*Arg(z), */
229 /* where -PI < Arg(z) < PI */
230 static gem_complex gem_cxlog(gem_complex z)
234 mag2 = z.r*z.r+z.i*z.i;
236 fprintf(stderr, "ERROR in gem_cxlog func\n");
238 value.r = log(sqrt(mag2));
245 value.i = atan2(z.i, z.r);
250 /* Square root of a complex number z = |z| exp(I*the) -- z^(1/2) */
251 /* z^(1/2)=|z|^(1/2)*[cos(the/2)+I*sin(the/2)] */
252 /* where 0 < the < 2*PI */
253 static gem_complex gem_cxdsqrt(gem_complex z)
258 value.r = sqrt(fabs((sq+z.r)*0.5)); /* z'.r={|z|*[1+cos(the)]/2}^(1/2) */
259 value.i = sqrt(fabs((sq-z.r)*0.5)); /* z'.i={|z|*[1-cos(the)]/2}^(1/2) */
266 /* square root of a real number r */
267 static gem_complex gem_cxrsqrt(double r) {
270 return(gem_cmplx(0, sqrt(-r)));
274 return(gem_c(sqrt(r)));
278 /* Complex power of a complex number z1^z2 */
279 static gem_complex gem_cxdpow(gem_complex z1, gem_complex z2)
282 value=gem_cxdexp(gem_cxmul(gem_cxlog(z1),z2));
286 /* Print out a complex number z as z: z.r, z.i */
287 static void gem_cxprintf(gem_complex z) { fprintf(stdout, "z: %lg + %lg_i\n", z.r, z.i); }
288 /* ------------ end of complex.c ------------ */
290 /* This next part was derived from cubic.c, also received from Omer Markovitch.
291 * ------------- from cubic.c ------------- */
293 /* Solver for a cubic equation: x^3-a*x^2+b*x-c=0 */
294 static void gem_solve(gem_complex *al, gem_complex *be, gem_complex *gam,
295 double a, double b, double c)
297 double t1, t2, two_3, temp;
298 gem_complex ctemp, ct3;
300 two_3=pow(2., 1./3.); t1 = -a*a+3.*b; t2 = 2.*a*a*a-9.*a*b+27.*c;
301 temp = 4.*t1*t1*t1+t2*t2;
303 ctemp = gem_cmplx(temp,0.); ctemp = gem_cxadd(gem_cmplx(t2,0.),gem_cxdsqrt(ctemp));
304 ct3 = gem_cxdpow(ctemp, gem_cmplx(1./3.,0.));
306 ctemp = gem_rxcdiv(-two_3*t1/3., ct3);
307 ctemp = gem_cxadd(ctemp, gem_cxrdiv(ct3, 3.*two_3));
309 *gam = gem_cxadd(gem_cmplx(a/3.,0.), ctemp);
311 ctemp=gem_cxmul(gem_cxsq(*gam), gem_cxsq(gem_cxsub(*gam, gem_cmplx(a,0.))));
312 ctemp=gem_cxadd(ctemp, gem_cxmul(gem_cmplx(-4.*c,0.), *gam));
313 ctemp = gem_cxdiv(gem_cxdsqrt(ctemp), *gam);
314 *al = gem_cxrmul(gem_cxsub(gem_cxsub(gem_cmplx(a,0.), *gam),ctemp),0.5);
315 *be = gem_cxrmul(gem_cxadd(gem_cxsub(gem_cmplx(a,0.), *gam),ctemp),0.5);
318 /* ------------ end of cubic.c ------------ */
320 /* This next part was derived from cerror.c and rerror.c, also received from Omer Markovitch.
321 * ------------- from [cr]error.c ------------- */
323 /************************************************************/
324 /* Real valued error function and related functions */
325 /* x, y : real variables */
326 /* erf(x) : error function */
327 /* erfc(x) : complementary error function */
328 /* omega(x) : exp(x*x)*erfc(x) */
329 /* W(x,y) : exp(-x*x)*omega(x+y)=exp(2*x*y+y^2)*erfc(x+y) */
330 /************************************************************/
332 /*---------------------------------------------------------------------------*/
333 /* Utilzed the series approximation of erf(x) */
334 /* Relative error=|err(x)|/erf(x)<EPS */
335 /* Handbook of Mathematical functions, Abramowitz, p 297 */
336 /* Note: When x>=6 series sum deteriorates -> Asymptotic series used instead */
337 /*---------------------------------------------------------------------------*/
338 /* This gives erfc(z) correctly only upto >10-15 */
340 static double gem_erf(double x)
342 double n,sum,temp,exp2,xm,x2,x4,x6,x8,x10,x12;
355 for(n=1.; n<=2000.; n+=1.){
356 temp *= 2.*x2/(2.*n+1.);
358 if(fabs(temp/sum)<1.E-16)
363 fprintf(stderr, "In Erf calc - iteration exceeds %lg\n",n);
368 /* from the asymptotic expansion of experfc(x) */
369 sum = (1. - 0.5/x2 + 0.75/x4
370 - 1.875/x6 + 6.5625/x8
371 - 29.53125/x10 + 162.421875/x12)
373 sum*=exp2; /* now sum is erfc(x) */
376 return x>=0.0 ? sum : -sum;
379 /* Result --> Alex's code for erfc and experfc behaves better than this */
380 /* complementray error function. Returns 1.-erf(x) */
381 static double gem_erfc(double x)
387 ans = t * exp(-z*z - 1.26551223 +
396 t*0.17087277)))))))));
398 return x>=0.0 ? ans : 2.0-ans;
401 /* omega(x)=exp(x^2)erfc(x) */
402 static double gem_omega(double x)
404 double xm, ans, xx, x4, x6, x8, x10, x12;
414 ans = exp(xx)*gem_erfc(x);
416 /* Asymptotic expansion */
417 ans = (1. - 0.5/xx + 0.75/x4 - 1.875/x6 + 6.5625/x8 - 29.53125/x10 + 162.421875/x12) / sPI/x;
422 /* W(x,y)=exp(-x^2)*omega(x+y)=exp(2xy+y^2)*erfc(x+y) */
423 static double gem_W(double x, double y){ return(exp(-x*x)*gem_omega(x+y)); }
425 /**************************************************************/
426 /* Complex error function and related functions */
427 /* x, y : real variables */
428 /* z : complex variable */
429 /* cerf(z) : error function */
430 /* comega(z): exp(z*z)*cerfc(z) */
431 /* W(x,z) : exp(-x*x)*comega(x+z)=exp(2*x*z+z^2)*cerfc(x+z) */
432 /**************************************************************/
433 static gem_complex gem_cerf(gem_complex z)
437 double sumr,sumi,n,n2,f,temp,temp1;
438 double x2,cos_2xy,sin_2xy,cosh_2xy,sinh_2xy,cosh_ny,sinh_ny;
445 cos_2xy = cos(2.*x*y);
446 sin_2xy = sin(2.*x*y);
447 cosh_2xy = cosh(2.*x*y);
448 sinh_2xy = sinh(2.*x*y);
450 for(n=1.0,temp=0.; n<=2000.; n+=1.0)
455 f = exp(-n2/4.)/(n2+4.*x2);
456 sumr += (2.*x - 2.*x*cosh_ny*cos_2xy+n*sinh_ny*sin_2xy)*f;
457 sumi += (2.*x*cosh_ny*sin_2xy + n*sinh_ny*cos_2xy)*f;
458 temp1 = sqrt(sumr*sumr+sumi*sumi);
459 if(fabs((temp1-temp)/temp1)<1.E-16) {
466 fprintf(stderr, "iteration exceeds %lg\n",n);
477 value.r = gem_erf(x) + (f*(1.-cos_2xy) + sumr)*exp(-x2);
478 value.i = (f*sin_2xy+sumi)*exp(-x2);
482 /*---------------------------------------------------------------------------*/
483 /* Utilzed the series approximation of erf(z=x+iy) */
484 /* Relative error=|err(z)|/|erf(z)|<EPS */
485 /* Handbook of Mathematical functions, Abramowitz, p 299 */
486 /* comega(z=x+iy)=cexp(z^2)*cerfc(z) */
487 /*---------------------------------------------------------------------------*/
488 static gem_complex gem_comega(gem_complex z)
492 double sumr,sumi,n,n2,f,temp,temp1;
493 double x2, y2,cos_2xy,sin_2xy,cosh_2xy,sinh_2xy,cosh_ny,sinh_ny,exp_y2;
501 cos_2xy = cos(2.*x*y);
502 sin_2xy = sin(2.*x*y);
503 cosh_2xy = cosh(2.*x*y);
504 sinh_2xy = sinh(2.*x*y);
507 for(n=1.0, temp=0.; n<=2000.; n+=1.0){
511 f = exp(-n2/4.)/(n2+4.*x2);
512 /* if(f<1.E-200) break; */
513 sumr += (2.*x - 2.*x*cosh_ny*cos_2xy + n*sinh_ny*sin_2xy)*f;
514 sumi += (2.*x*cosh_ny*sin_2xy + n*sinh_ny*cos_2xy)*f;
515 temp1 = sqrt(sumr*sumr+sumi*sumi);
516 if(fabs((temp1-temp)/temp1)<1.E-16) {
522 fprintf(stderr, "iteration exceeds %lg\n",n);
532 value.r = gem_omega(x)-(f*(1.-cos_2xy)+sumr);
533 value.i = -(f*sin_2xy+sumi);
534 value = gem_cxmul(value,gem_cmplx(exp_y2*cos_2xy,exp_y2*sin_2xy));
538 /* W(x,z) exp(-x^2)*omega(x+z) */
539 static gem_complex gem_cW(double x, gem_complex z){ return(gem_cxrmul(gem_comega(gem_cxradd(z,x)),exp(-x*x))); }
541 /* ------------ end of [cr]error.c ------------ */
543 /*_ REVERSIBLE GEMINATE RECOMBINATION
545 * Here are the functions for reversible geminate recombination. */
547 /* Changes the unit from square cm per s to square Ångström per ps,
548 * since Omers code uses the latter units while g_mds outputs the former.
549 * g_hbond expects a diffusion coefficent given in square cm per s. */
550 static double sqcm_per_s_to_sqA_per_ps (real D) {
551 fprintf(stdout, "Diffusion coefficient is %f A^2/ps\n", D*1e4);
552 return (double)(D*1e4);
556 static double eq10v2(double theoryCt[], double time[], int manytimes,
557 double ka, double kd, t_gemParams *params)
559 /* Finding the 3 roots */
561 double kD, D, r, a, b, c, tsqrt, sumimaginary;
566 part1, part2, part3, part4;
571 a = (1.0 + ka/kD) * sqrt(D)/r;
575 gem_solve(&alpha, &beta, &gamma, a, b, c);
576 /* Finding the 3 roots */
579 part1 = gem_cxmul(alpha, gem_cxmul(gem_cxadd(beta, gamma), gem_cxsub(beta, gamma))); /* 1(2+3)(2-3) */
580 part2 = gem_cxmul(beta, gem_cxmul(gem_cxadd(gamma, alpha), gem_cxsub(gamma, alpha))); /* 2(3+1)(3-1) */
581 part3 = gem_cxmul(gamma, gem_cxmul(gem_cxadd(alpha, beta) , gem_cxsub(alpha, beta))); /* 3(1+2)(1-2) */
582 part4 = gem_cxmul(gem_cxsub(gamma, alpha), gem_cxmul(gem_cxsub(alpha, beta), gem_cxsub(beta, gamma))); /* (3-1)(1-2)(2-3) */
585 #pragma omp parallel for \
586 private(i, tsqrt, oma, omb, omc, c1, c2, c3, c4), \
587 reduction(+:sumimaginary), \
591 for (i=0; i<manytimes; i++){
592 tsqrt = sqrt(time[i]);
593 oma = gem_comega(gem_cxrmul(alpha, tsqrt));
594 c1 = gem_cxmul(oma, gem_cxdiv(part1, part4));
595 omb = gem_comega(gem_cxrmul(beta, tsqrt));
596 c2 = gem_cxmul(omb, gem_cxdiv(part2, part4));
597 omc = gem_comega(gem_cxrmul(gamma, tsqrt));
598 c3 = gem_cxmul(omc, gem_cxdiv(part3, part4));
599 c4.r = c1.r+c2.r+c3.r;
600 c4.i = c1.i+c2.i+c3.i;
602 sumimaginary += c4.i * c4.i;
609 /* This returns the real-valued index(!) to an ACF, equidistant on a log scale. */
610 static double getLogIndex(const int i, const t_gemParams *params)
612 return (exp(((double)(i)) * params->logQuota) -1);
615 extern t_gemParams *init_gemParams(const double sigma, const double D,
616 const real *t, const int len, const int nFitPoints,
617 const real begFit, const real endFit,
618 const real ballistic, const int nBalExp, const gmx_bool bDt)
625 /* A few hardcoded things here. For now anyway. */
627 /* p->ka_max = 100; */
635 /* p->lifetime = 0; */
636 p->sigma = sigma*10; /* Omer uses Ã…, not nm */
637 /* p->lsq_old = 99999; */
638 p->D = sqcm_per_s_to_sqA_per_ps(D);
639 p->kD = 4*acos(-1.0)*sigma*p->D;
642 /* Parameters used by calcsquare(). Better to calculate them
643 * here than in calcsquare every time it's called. */
645 /* p->logAfterTime = logAfterTime; */
646 tDelta = (t[len-1]-t[0]) / len;
648 gmx_fatal(FARGS, "Time between frames is non-positive!");
653 p->nExpFit = nBalExp;
654 /* p->nLin = logAfterTime / tDelta; */
655 p->nFitPoints = nFitPoints;
658 p->logQuota = (double)(log(p->len))/(p->nFitPoints-1);
659 /* if (p->nLin <= 0) { */
660 /* fprintf(stderr, "Number of data points in the linear regime is non-positive!\n"); */
664 /* We want the same number of data points in the log regime. Not crucial, but seems like a good idea. */
665 /* p->logDelta = log(((float)len)/p->nFitPoints) / p->nFitPoints;/\* log(((float)len)/p->nLin) / p->nLin; *\/ */
666 /* p->logPF = p->nFitPoints*p->nFitPoints/(float)len; /\* p->nLin*p->nLin/(float)len; *\/ */
667 /* logPF and logDelta are stitched together with the macro GETLOGINDEX defined in geminate.h */
669 /* p->logMult = pow((float)len, 1.0/nLin);/\* pow(t[len-1]-t[0], 1.0/p->nLin); *\/ */
670 p->ballistic = ballistic;
675 /* There was a misunderstanding regarding the fitting. From our
676 * recent correspondence it appears that Omer's code require
677 * the ACF data on a log-scale and does not operate on the raw data.
678 * This needs to be redone in gemFunc_residual() as well as in the
679 * t_gemParams structure. */
681 static double gemFunc_residual2(const gsl_vector *p, void *data)
684 int i, iLog, nLin, nFitPoints, nData;
685 double r, residual2, *ctTheory, *y;
687 GD = (gemFitData *)data;
688 nLin = GD->params->nLin;
689 nFitPoints = GD->params->nFitPoints;
692 ctTheory = GD->ctTheory;
695 /* Now, we'd save a lot of time by not calculating eq10v2 for all
696 * time points, but only those that we sample to calculate the mse.
699 eq10v2(GD->ctTheory, GD->doubleLogTime/* GD->time */, nFitPoints/* GD->nData */,
700 gsl_vector_get(p, 0), gsl_vector_get(p, 1),
703 /* Removing a bunch of points from the log-part. */
705 #pragma omp parallel for schedule(dynamic) \
706 firstprivate(nData, ctTheory, y, nFitPoints) \
707 private (i, iLog, r) \
708 reduction(+:residual2) \
711 for(i=0; i<nFitPoints; i++)
713 iLog = GD->logtime[i];
714 r = log(ctTheory[i /* iLog */]);
715 residual2 += sqr(r-log(y[iLog]));
717 residual2 /= nFitPoints; /* Not really necessary for the fitting, but gives more meaning to the returned data. */
718 /* printf("ka=%3.5f\tkd=%3.5f\trmse=%3.5f\n", gsl_vector_get(p,0), gsl_vector_get(p,1), residual2); */
721 /* for (i=0; i<nLin; i++) { */
722 /* /\* Linear part ----------*\/ */
723 /* r = ctTheory[i]; */
724 /* residual2 += sqr(r-y[i]); */
725 /* /\* Log part -------------*\/ */
726 /* iLog = GETLOGINDEX(i, GD->params); */
727 /* if (iLog >= nData) */
728 /* gmx_fatal(FARGS, "log index out of bounds: %i", iLog); */
729 /* r = ctTheory[iLog]; */
730 /* residual2 += sqr(r-y[iLog]); */
733 /* residual2 /= GD->n; */
734 /* return residual2; */
738 static real* d2r(const double *d, const int nn);
740 extern real fitGemRecomb(double *ct, double *time, double **ctFit,
741 const int nData, t_gemParams *params)
744 int nThreads, i, iter, status, maxiter;
745 real size, d2, tol, *dumpdata;
748 char *dumpstr, dumpname[128];
750 /* nmsimplex2 had convergence problems prior to gsl v1.14,
751 * but it's O(N) instead of O(N) operations, so let's use it if v >= 1.14 */
753 gsl_multimin_fminimizer *s;
754 gsl_vector *x,*dx; /* parameters and initial step size */
755 gsl_multimin_function fitFunc;
756 #ifdef GSL_MAJOR_VERSION
757 #ifdef GSL_MINOR_VERSION
758 #if ((GSL_MAJOR_VERSION == 1 && GSL_MINOR_VERSION >= 14) || \
759 (GSL_MAJOR_VERSION > 1))
760 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex2;
762 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex;
764 #endif /* GSL_MINOR_VERSION */
766 const gsl_multimin_fminimizer_type *T = gsl_multimin_fminimizer_nmsimplex;
767 #endif /* GSL_MAJOR_VERSION */
768 fprintf(stdout, "Will fit ka and kd to the ACF according to the reversible geminate recombination model.\n");
769 #else /* HAVE_LIBGSL */
770 fprintf(stderr, "Sorry, can't do reversible geminate recombination without gsl. "
771 "Recompile using --with-gsl.\n");
773 #endif /* HAVE_LIBGSL */
777 nThreads = omp_get_num_procs();
778 omp_set_num_threads(nThreads);
779 fprintf(stdout, "We will be using %i threads.\n", nThreads);
787 p = 2; /* Number of parameters to fit. ka and kd. */
788 n = params->nFitPoints; /* params->nLin*2 */; /* Number of points in the reduced dataset */
792 fprintf(stderr, "Fitting of D is not implemented yet. It must be provided on the command line.\n");
797 /* fprintf(stderr, "Reduced data set larger than the complete data set!\n"); */
800 snew(dumpdata, nData);
806 snew(GD->ctTheory, nData);
812 GD->tDelta = time[1]-time[0];
815 snew(GD->logtime,params->nFitPoints);
816 snew(GD->doubleLogTime,params->nFitPoints);
818 for (i=0; i<params->nFitPoints; i++)
820 GD->doubleLogTime[i] = (double)(getLogIndex(i, params));
821 GD->logtime[i] = (int)(GD->doubleLogTime[i]);
822 GD->doubleLogTime[i]*=GD->tDelta;
824 if (GD->logtime[i] >= nData)
826 fprintf(stderr, "Ayay. It seems we're indexing out of bounds.\n");
827 params->nFitPoints = i;
831 fitFunc.f = &gemFunc_residual2;
833 fitFunc.params = (void*)GD;
835 x = gsl_vector_alloc (fitFunc.n);
836 dx = gsl_vector_alloc (fitFunc.n);
837 gsl_vector_set (x, 0, 25);
838 gsl_vector_set (x, 1, 0.5);
839 gsl_vector_set (dx, 0, 0.1);
840 gsl_vector_set (dx, 1, 0.01);
843 s = gsl_multimin_fminimizer_alloc (T, fitFunc.n);
844 gsl_multimin_fminimizer_set (s, &fitFunc, x, dx);
846 gsl_vector_free (dx);
850 status = gsl_multimin_fminimizer_iterate (s);
853 gmx_fatal(FARGS,"Something went wrong in the iteration in minimizer %s:\n \"%s\"\n",
854 gsl_multimin_fminimizer_name(s), gsl_strerror(status));
856 d2 = gsl_multimin_fminimizer_minimum(s);
857 size = gsl_multimin_fminimizer_size(s);
858 params->ka = gsl_vector_get (s->x, 0);
859 params->kd = gsl_vector_get (s->x, 1);
863 fprintf(stderr, "%s\n", gsl_strerror(status));
867 status = gsl_multimin_test_size(size,tol);
869 if (status == GSL_SUCCESS) {
870 fprintf(stdout, "Converged to minimum at\n");
873 printf ("iter %5d: ka = %2.5f kd = %2.5f f() = %7.3f size = %.3f chi2 = %2.5f\n",
881 eq10v2(GD->ctTheory, time, nData, params->ka, params->kd, params);
882 sprintf(dumpname, "Iter_%i.xvg", iter);
883 for(i=0; i<GD->nData; i++)
884 dumpdata[i] = (real)(GD->ctTheory[i]);
885 dumpN(dumpdata, GD->nData, dumpname);
888 while ((status == GSL_CONTINUE) && (iter < maxiter));
890 /* /\* Calculate the theoretical ACF from the parameters one last time. *\/ */
891 eq10v2(GD->ctTheory, time, nData, params->ka, params->kd, params);
892 *ctFit = GD->ctTheory;
895 gsl_multimin_fminimizer_free (s);
900 #endif /* HAVE_LIBGSL */
904 static int balFunc_f(const gsl_vector *x, void *data, gsl_vector *f)
906 /* C + sum{ A_i * exp(-B_i * t) }*/
910 double *y, *A, *B, C, /* There are the parameters to be optimized. */
913 BD = (balData *)data;
920 for (i = 0; i<nexp; i++)
922 A[i] = gsl_vector_get(x, i*2);
923 B[i] = gsl_vector_get(x, i*2+1);
925 C = gsl_vector_get(x, nexp*2);
931 for (j=0; j<nexp; j++) {
932 ct += A[j] * exp(B[j] * t);
935 gsl_vector_set (f, i, ct - y[i]);
940 /* The derivative stored in jacobian form (J)*/
941 static int balFunc_df(const gsl_vector *params, void *data, gsl_matrix *J)
945 double *y, *A, *B, C, /* There are the parameters. */
957 for (i=0; i<nexp; i++)
959 A[i] = gsl_vector_get(params, i*2);
960 B[i] = gsl_vector_get(params, i*2+1);
962 C = gsl_vector_get(params, nexp*2);
966 for (j=0; j<nexp; j++)
968 gsl_matrix_set (J, i, j*2, exp(B[j]*t)); /* df(t)/dA_j */
969 gsl_matrix_set (J, i, j*2+1, A[j]*t*exp(B[j]*t)); /* df(t)/dB_j */
971 gsl_matrix_set (J, i, nexp*2, 1); /* df(t)/dC */
976 /* Calculation of the function and its derivative */
977 static int balFunc_fdf(const gsl_vector *params, void *data,
978 gsl_vector *f, gsl_matrix *J)
980 balFunc_f(params, data, f);
981 balFunc_df(params, data, J);
984 #endif /* HAVE_LIBGSL */
986 /* Removes the ballistic term from the beginning of the ACF,
987 * just like in Omer's paper.
989 extern void takeAwayBallistic(double *ct, double *t, int len, real tMax, int nexp, gmx_bool bDerivative)
992 /* Use nonlinear regression with GSL instead.
993 * Fit with 4 exponentials and one constant term,
994 * subtract the fatest exponential. */
996 int nData,i,status, iter;
998 double *guess, /* Initial guess. */
999 *A, /* The fitted parameters. (A1, B1, A2, B2,... C) */
1009 } while (t[nData]<tMax+t[0] && nData<len);
1011 p = nexp*2+1; /* Number of parameters. */
1014 const gsl_multifit_fdfsolver_type *T
1015 = gsl_multifit_fdfsolver_lmsder;
1017 gsl_multifit_fdfsolver *s; /* The solver itself. */
1018 gsl_multifit_function_fdf fitFunction; /* The function to be fitted. */
1019 gsl_matrix *covar; /* Covariance matrix for the parameters.
1020 * We'll not use the result, though. */
1021 gsl_vector_view theParams;
1026 } while (t[nData]<tMax+t[0] && nData<len);
1033 covar = gsl_matrix_alloc (p, p);
1035 /* Set up an initial gess for the parameters.
1036 * The solver is somewhat sensitive to the initial guess,
1037 * but this worked fine for a TIP3P box with -geminate dd
1038 * EDIT: In fact, this seems like a good starting pont for other watermodels too. */
1039 for (i=0; i<nexp; i++)
1042 guess[i*2+1] = -0.5 + (((double)i)/nexp - 0.5)*0.3;
1044 guess[nexp * 2] = 0.01;
1046 theParams = gsl_vector_view_array(guess, p);
1051 BD->tDelta = t[1]-t[0];
1054 fitFunction.f = &balFunc_f;
1055 fitFunction.df = &balFunc_df;
1056 fitFunction.fdf = &balFunc_fdf;
1057 fitFunction.n = nData;
1059 fitFunction.params = BD;
1061 s = gsl_multifit_fdfsolver_alloc (T, nData, p);
1063 gmx_fatal(FARGS, "Could not set up the nonlinear solver.");
1065 gsl_multifit_fdfsolver_set(s, &fitFunction, &theParams.vector);
1067 /* \=============================================/ */
1073 status = gsl_multifit_fdfsolver_iterate (s);
1077 status = gsl_multifit_test_delta (s->dx, s->x, 1e-4, 1e-4);
1079 while (iter < 5000 && status == GSL_CONTINUE);
1083 fprintf(stderr, "The non-linear fitting did not converge in 5000 steps.\n"
1084 "Check the quality of the fit!\n");
1088 fprintf(stderr, "Non-linear fitting of ballistic term converged in %d steps.\n\n", (int)iter);
1090 for (i=0; i<nexp; i++) {
1091 fprintf(stdout, "%c * exp(%c * t) + ", 'A'+(char)i*2, 'B'+(char)i*2);
1094 fprintf(stdout, "%c\n", 'A'+(char)nexp*2);
1095 fprintf(stdout, "Here are the actual numbers for A-%c:\n", 'A'+nexp*2);
1097 for (i=0; i<nexp; i++)
1099 A[i*2] = gsl_vector_get(s->x, i*2);
1100 A[i*2+1] = gsl_vector_get(s->x, i*2+1);
1101 fprintf(stdout, " %g*exp(%g * x) +", A[i*2], A[i*2+1]);
1103 A[i*2] = gsl_vector_get(s->x, i*2); /* The last and constant term */
1104 fprintf(stdout, " %g\n", A[i*2]);
1108 /* Implement some check for parameter quality */
1109 for (i=0; i<nexp; i++)
1111 if (A[i*2]<0 || A[i*2]>1) {
1112 fprintf(stderr, "WARNING: ----------------------------------\n"
1113 " | A coefficient does not lie within [0,1].\n"
1114 " | This may or may not be a problem.\n"
1115 " | Double check the quality of the fit!\n");
1118 fprintf(stderr, "WARNING: ----------------------------------\n"
1119 " | One factor in the exponent is positive.\n"
1120 " | This could be a problem if the coefficient\n"
1121 " | is large. Double check the quality of the fit!\n");
1124 if (A[i*2]<0 || A[i*2]>1) {
1125 fprintf(stderr, "WARNING: ----------------------------------\n"
1126 " | The constant term does not lie within [0,1].\n"
1127 " | This may or may not be a problem.\n"
1128 " | Double check the quality of the fit!\n");
1131 /* Sort the terms */
1132 sorted = (nexp > 1) ? FALSE : TRUE;
1136 for (i=0;i<nexp-1;i++)
1138 ddt[0] = A[i*2] * A[i*2+1];
1139 ddt[1] =A[i*2+2] * A[i*2+3];
1141 if ((bDerivative && (ddt[0]<0 && ddt[1]<0 && ddt[0]>ddt[1])) || /* Compare derivative at t=0... */
1142 (!bDerivative && (A[i*2+1] > A[i*2+3]))) /* Or just the coefficient in the exponent */
1145 a[0] = A[i*2]; /* coefficient */
1146 a[1] = A[i*2+1]; /* parameter in the exponent */
1149 A[i*2+1] = A[i*2+3];
1157 /* Subtract the fastest component */
1158 fprintf(stdout, "Fastest component is %g * exp(%g * t)\n"
1159 "Subtracting fastest component from ACF.\n", A[0], A[1]);
1161 for (i=0; i<len; i++) {
1162 ct[i] = (ct[i] - A[0] * exp(A[1] * i*BD->tDelta)) / (1-A[0]);
1168 gsl_multifit_fdfsolver_free(s);
1169 gsl_matrix_free(covar);
1173 /* We have no gsl. */
1174 fprintf(stderr, "Sorry, can't take away ballistic component without gsl. "
1175 "Recompile using --with-gsl.\n");
1177 #endif /* HAVE_LIBGSL */
1181 extern void dumpN(const real *e, const int nn, char *fn)
1183 /* For debugging only */
1186 char standardName[] = "Nt.xvg";
1194 "@ xaxis label \"Frame\"\n"
1195 "@ yaxis label \"N\"\n"
1196 "@ s0 line type 3\n");
1198 for (i=0; i<nn; i++) {
1199 fprintf(f, "%-10i %-g\n", i, e[i]);
1205 static real* d2r(const double *d, const int nn)
1211 for (i=0; i<nn; i++)